DEPARTMENT OF MATHEMATICS

ALIGARH MUSLIM UNIVERSITY, ALIGARH

Syllabus of B.A./B.Sc. I Semester approved in BOS: 17-05-2022
Course Title Calculus
Course Number MMBSMJ1001
Credits 4
Course Category Major/Core
Prerequisite Courses None
Contact Hours 4 Lectures/week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives The main objectives of this course are to deal with the following topics:
 Some topics of Calculus which are ignored in Class XII, namely, indeterminate forms,
improper integrals, integration by beta and gamma functions, expansion of functions by
Maclaurin’s theorem and Taylor’s theorem, and Curve sketching.
 Polar coordinate system and curvature
 Volume and surface of solids of revolution
 Introduction of functions of several variables and the concepts of limit, continuity, and
differentiability for such functions
 Cylindrical and spherical coordinate systems
Course Outcomes On successful completion of this course, student will be able to know:
 How to sketch the graph of functions.
 Different kinds of coordinate systems, namely, polar coordinates, cylindrical
coordinates, spherical coordinates.
 How to find the volume and surface of solids of revolution by using integral
 Functions of several variables and the concept of limit, continuity, and differentiability
of such functions.
Contents of Syllabus No. of Lectures
UNIT I: Indeterminate forms, Improper integrals, Expansion of Functions, Curve sketching
Indeterminate forms, L’Hopital rule; Improper integrals, Integration by beta and gamma functions;
Successive differentiation (𝑛𝑡ℎ derivative) of well-known functions, Leibnitz’s theorem; Expansion 12
of functions: Maclaurin’s theorem and Taylor’s theorem; Curve sketching: Asymptotes of the
algebraic curves, parallel asymptotes, Asymptotes parallel to axes, Concavity, Double points and
their types, Equation of the tangent(s) at the origin.
UNIT II: Polar coordinates and Curvature
Parametric equations of plane curves; Polar coordinates and their relations with rectangular
coordinates; Asymptotes in polar coordinates; Graph of polar equation; Conics in polar coordinates;
Slope of tangent line in parametric and polar form; Area in polar coordinates; Curvature: curvature, 12
radius of curvature, arc length in parametric, Cartesian, and polar forms, Intrinsic formula for radius
of curvature; Cartesian, parametric and Polar formulae for radius of curvature, Pedal formula for the
radius of curvature
UNIT III: Volume and Surface of Solids of Revolution
Volume using cross-section (Slicing by parallel planes); Solids of revolution (Disk method and
Washer method); Volume by disks for rotation about x-axis and about y-axis; Volume using 12
cylindrical shell (slicing with cylinders); The shell formula for revolution about a vertical line; Area
of surface of revolution about x-axis and about y-axis.
UNIT IV: Functions of Several Variables: Limit, Continuity and Differentiability
Functions of several variables, Contour curves, level curves and level surfaces, Cylindrical and
spherical coordinate systems and their relations with Cartesian coordinates, Limit, and continuity for 12
functions of several variables, Partial derivatives, Geometric meaning of partial derivative, Relation
between partial derivatives and continuity, homogeneous functions, Euler’s theorem and higher
derivatives, Differentiability, Total differentiation, Chain rule for functions of several variables.
Total No. of Lectures 48
Textbooks*/ 1. *G. B. Thomas Jr., M.D. Weir, J. Hass, Calculus, 12th Ed., Pearson Publication.
Reference 2. *H. Anton, I. Bivens and S. Davis, Calculus, 7th Edition, John Wiley & Sons
Books 3. *J. Stewart, Calculus, 5e, Thomson, Books / Cole
4. R.E. Johnson, F.L. Kiokemeister and E.S. Wolk, Calculus, Allyn & Bacon, Inc. Boston
5. D. V. Widder: Advanced Calculus, Prentice Hall of India Pvt. Ltd., New Delhi, 2nd Ed, 2012
6. N. Piskunov: Differential and Integral Calculus, CBS Publishers, New Delhi, 1996.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. I Semester approved in BOS: 17-05-2022
Course Title Two-dimensional Coordinate Geometry
Course Number MMBSMJ1002
Credits 2
Course Category Major/Core
Prerequisite Courses Introductory Co-ordinate Geometry
Contact Hours 2 Lectures/week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives The primary objective of this course is to introduce the basic tools of plane geometry and
geometric properties of different conic sections which are helpful to understand their
applications to the real-world problems.
Course Outcomes  This course will enable the students to:
 Basic knowledge about pair of straight lines
 Elementary properties of conic sections in the Cartesian and polar coordinate systems.
 General equation of second degree in two variables
Contents of Syllabus No. of Lectures
UNIT I: Pair of Straight Lines 6
General transformation (change of axes), Invariants, Removal of -term, Pair of straight lines:
Homogeneous equation of second degree, Angle between two lines, General equation of second
degree, Necessary and sufficient condition that general equation of second degree represents a pair
of straight lines, Lines joining the origin to the intersection of a curve and a line.
UNIT II: Conic Sections
Circle: General equation of a circle, Equation of a circle one of whose diameter is the line joining
( ) and ( ). The tangent to the circle Length of tangent to a circle from a
given point, common tangent to two circles.
Ellipse: Auxiliary circle for an ellipse, eccentric angle, parametric equation of an ellipse. The 6
director circle.
Hyperbola: Rectangular hyperbola, limiting case of the hyperbola, parameter equation of a
hyperbola, equation of hyperbola when the asymptotes are the coordinate axes. Equation of
tangent and normal at ( 𝑡 ) to the hyperbola
UNIT III: General Equation of Second degrees in two variables
Second degree equations representing a conic section; the intersection of a line and a conic
section; tangent at ( ) to a conic; pair of tangents from a given point; condition of tangency; 6
chord of contact of tangents drawn from a point ( ); pole and poler; conjugate points and
conjugate lines; condition of conjugacy; chord with a given middle point, centre and diameter of a
conic section conjugacy of diameters.
UNIT IV: Polar equations for Conic Sections 6
Polar coordinates, Polar equation of circle; Polar equation of a straight line; Polar equation of
conics when the focus is the pole; directrix; chord of conic joining two given points. Tangent and
normal.
Total No. of Lectures 24
Textbooks*/ 1. S. L. Loney: The Elements of Coordinate Geometry, AITBS Publishers.
Reference 2. *Ram Ballabh: A Textbook of Coordinate Geometry, Prakashan Kendra, Lucknow.
Books 3. Hari Kishan, Co-ordinate Geometry of two dimensions, Atlantic Publishers and distributors,
New Delhi, 2006
4. *C. Smith: An Elementary Treatise on Conic Sections, MacMillon & Co. Ltd
5. Robert J.T. Bell, An Elementary Treatise on Coordinate Geometry of Three Dimension,
MacMillan & Co. Ltd.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. I Semester approved in BOS: 17-05-2022
Course Title Set Theory
Course Number MMBSMJ1003
Credits 2
Course Category Major/Core
Prerequisite Courses None

Contact Hours 2 Lectures/week

Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives This course aims to introduce students to the following concepts and cognitive skills.
 This course will consist of the basics of mathematical set theory, including well-
ordering, cardinality, characteristic functions and choice functions, equipotent sets,
Cantor’s theorem, Schroeder Bernstein theorem, maximal and minimal elements,
axiom of choice.
Course Outcomes On successful completion of this course student will be able to:
 formalize mathematical statements in ZF set theory.
 Understand cardinal and ordinal arithmetic.
 apply variants of the axiom of choice.
 carry out proofs and constructions by transfinite induction and recursion.
 be familiar with various paradoxes in naive set theory and understand the need for
formalization of set theory.
 know independence results for the continuum hypothesis and the axiom of choice.
 present mathematical arguments to others.
Contents of Syllabus No. of Lectures
UNIT I: Relation and Functions
Revisit of relations and functions, Composition of relation, its matrix representation and 6
properties, Equivalence relation and partition, Fundamental theorem of equivalence relation,
cross partition.
UNIT II: Some Special Kinds of Functions
Functions and their restrictions and extensions, Invertible functions, Characteristic functions 6
and choice functions, Equipotent sets and their properties.
UNIT III: Countable Sets and Cardinality
Infinite sets, Denumerable sets, Countable sets, Continuum, Cardinals, Cardinal arithmetic, 6
Inequalities of cardinal numbers, Cantor’s theorem, Schroeder Bernstein theorem, Continuum
hypothesis.
UNIT IV: Ordered Sets and Their properties
Partially ordered sets, Hasse’s diagram, totally ordered sets, Similar sets, and well-ordered sets, 6
First and last elements, Maximal and minimal elements, Zorn’s lemma (statement), Axiom of
choice, Russel’s paradox.
Total No. of Lectures 24
Textbooks*/ 1. * Seymour Lipschutz: Set Theory and Related Topics, Schaum’s Outline Series.
Reference 2. P. R. Halmos: Naive Set Theory.
Books 3. E. Kamke: Theory of sets, Dover Publication.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. I Semester approved in BOS: 17-05-2022
Course Title Calculus of Single Variable
Course Number MMBSMN1004
Credits 4
Course Category Minor
Prerequisite Courses None
Contact Hours 4 Lectures/week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives The main objectives of this course are to deal with the following topics:
 Some topics of Calculus which are ignored in Class XII, namely, indeterminate
forms, improper integrals, integration by beta and gamma functions, expansion of
functions by Maclaurin’s theorem and Taylor’s theorem, and Curve sketching.
 Polar coordinate system and curvature
 Volume and surface of solids of revolution
Course Outcomes On successful completion of this course, student will be able to know:
 How to sketch the graph of functions
 Indeterminant forms, expansion of functions by Maclaurin’s theorem and Taylor’s
theorem and polar coordinates
 How to find the volume and surface of solids of revolution by using integral
Contents of Syllabus No. of Lectures
UNIT I: Indeterminate Forms, Improper Integrals, Expansion of Functions 12
Indeterminate forms, L’Hopital rule; Improper integrals, Integration by beta and gamma
functions; Successive differentiation (𝑛𝑡ℎ derivative) of well-known functions, Leibnitz’s
theorem; Expansion of functions: Maclaurin’s theorem and Taylor’s theorem.
UNIT II: Asymptotes and Curve Sketching 12
Asymptotes of the algebraic curves, parallel asymptotes, Asymptotes parallel to axes, Normal,
Cartesian subtangent and subnormal, Intercepts, Length of the tangent and normal, Lengths of
the polar subtangent and subnormal, Lengths of the perpendicular from the pole on tangent,
convexity and concavity of a curve, point of inflexion, Double points and their types, Equation
of the tangent(s) at the origin, Tracing of Cartesian curves.
UNIT III: Polar coordinates and Curvature 12
Parametric equations of plane curves; Polar coordinates and their relations with rectangular
coordinates; Asymptotes in polar coordinates; Graph of polar equation; Conics in polar
coordinates; Slope of tangent line in parametric and polar form; Area in polar coordinates;
Curvature: curvature, radius of curvature, arc length in parametric, Cartesian, and polar forms,
Intrinsic formula for radius of curvature; Cartesian, parametric and Polar formulae for radius of
curvature, Pedal formula for the radius of curvature.
UNIT IV: Volume and Surface of Solids of Revolution 12
Volume using cross-section (Slicing by parallel planes); Solids of revolution (Disk method and
Washer method); Volume by disks for rotation about x-axis and about y-axis; Volume using
cylindrical shell (slicing with cylinders); The shell formula for revolution about a vertical line;
Area of surface of revolution about x-axis and about y-axis.
Total No. of Lectures 48
Textbooks*/ 1. *G. B. Thomas Jr., M.D. Weir, J. Hass, Calculus, 12th Ed., Pearson Publication.
Reference 2. *H. Anton, I. Bivens and S. Davis, Calculus, 7th Edition, John Wiley & Sons
Books 3. *J. Stewart, Calculus, 5e, Thomson, Books / Cole.
4. R.E. Johnson, F.L. Kiokemeister and E.S. Wolk, Calculus, Allyn & Bacon, Inc. Boston
5. N. Piskunov: Differential and Integral Calculus, CBS Publishers, New Delhi, 1996.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. I Semester approved in BOS: 17-05-2022
Course Title Basic Coordinate Geometry
Course Number MMBSMN1005
Credits 2
Course Category Minor
Prerequisite Courses None
Contact Hours 2 Lectures / week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives The primary objective of this course is to introduce the basic tools Two-Dimensional
Geometry and Three-Dimensional Geometry, their geometric properties which are helpful in
understanding their applications to the real-world problems.
Course Outcomes This course will enable the students to:
basic knowledge about Two-Dimensional Geometry and Three-Dimensional Geometry
● elementary properties of conic sections in the cartesian and polar coordinate
systems.
● encourage geometrical thinking of conic sections and its mathematical
properties.
Contents of Syllabus No. of Lectures
UNIT I: Basics of Two-Dimensional Geometry 6
Coordinate Systems and Coordinates Pair, General transformation, Invariants, Removal of
-term, Classification of conic section, Pair of straight Lines: Homogeneous equation of
second degree, Angle between two lines, General second degree equation, , General
equation of a circle, The tangent √ ) to the circle length
of tangent to a circle from a given point, common tangent and normal at ( 𝑡 𝑡);
UNIT II: Parabola, Ellipse and Hyperbola 6
Second degree equations representing a conic section and vice-versa; the intersection of a
line and a conic section; tangent at ( ) to a conic; pair of tangents from a given point;
condition of tangency; chord of contact of tangents drawn from a point ( ); pole and
polar; chord with a given middle point, Auxiliary circle for an ellipse, eccentric angle,
parametric equation of an ellipse. The director circle; Rectangle hyperbola, limiting case of
the hyperbola, parameter equation of a hyperbola, equation of hyperbola when the
asymptotes are the coordinates axis. Equation of tangent and normal at ( 𝑡 ) to the
hyperbola
UNIT III: Basics of Three-Dimensional Geometry and Conicoids 6
Vector and Cartesian equation of line and plane, angle between two lines, two planes, line
and plane in terms of direction ratios, General equation of Sphere with examples, Equation
of Cone and Cylinder with examples. Conicoid and plane section of conicoids, Central
conicoids.
UNIT IV: Polar equations for Conic sections 6
Polar equation of circle; Polar equation of a straight line; Polar equation of conics when the
focus is the pole, classification. Equation of tangent in polar form.
Total No. of Lectures 24
Textbooks*/ 1. Shanti Narayan, Analytical Solid geometry, S.Chand.
Reference 2. S. L. Loney: The Elements of Coordinate Geometry, AITBS Publishers.
Books 3. S. Series: Principles and Problems of Plane Geometry with Coordinate Geometry
4. C. Smith: An Elementary Treatise on Conic Sections, MacMillon & Co.Ltd
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. I Semester approved in BOS: 17-05-2022
Course Title Elementary Calculus
Course Number MMBSGE1006
Credits 4
Course Category Generic (Elective)
Prerequisite Courses None
Contact Hours 4 Lectures / week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives The primary objective of this course is to provide essential knowledge of
basic tools of set operations, number systems, differential calculus, integral
calculus, matrices, and determinants for those students who do not have
mathematical background at +2 level.
Course Outcomes This course will enable the students to provide understanding in different
topics of elementary algebra and elementary calculus.
Contents of Syllabus No. of Lectures
UNIT I: Revisit to Sets and Numbers
Sets and elements, Empty and Non-empty sets, Subset of a set, Union and intersection of
two sets, Venn diagram, Universal set, Revisit to number system (natural numbers, whole
numbers, integers, rational numbers and real numbers), Standard notations to represent the 11
sets of different class of numbers, Principle of mathematical induction and its simple
applications, Complex numbers, Real and imaginary parts of a complex numbers, Algebra
of complex numbers, Conjugate and modulus of a complex number, Cube roots of unity.
UNIT II: Relations and Functions
Definition and examples of a relation and function, Domain, Codomain and Range of a
function, Image and preimage of an element, One-one and Many-one functions, Onto and
into functions, Composite functions, Inverse of a function, Pictorial representation of a 11
function, Real valued function of a real variable, Some elementary real functions such as:
linear, quadratic, power, polynomial, rational, absolute value, signum and greatest integer
functions with their graphs, domains and ranges; Properties of trigonometric, logarithmic
and exponential functions, Even and odd functions, Periodic functions, Sum, difference,
product and quotients of real functions.
UNIT III: Differential Calculus
Limit of real functions, Left-hand and right-hand limits, Continuous functions, Derivative
of a function and its geometrical explanation and properties, Differentiation from the first 13
principle, Derivative of function of function, Algebra of derivatives, Differentiation by
substitution, Differentiation of implicit functions, Logarithmic differentiation, Parametric
differentiation, Higher order derivatives, Applications of derivative.
UNIT IV: Integral Calculus
Idea of integration of a function, Indefinite integration, Some basic formulas for
integration of functions, Integration by substitution, Integration of the functions of certain 13
forms, Integration by partial fractions, Integration by parts, Definite integration and its
properties, Applications of definite integral.
Total No. of Lectures 48

Textbooks*/ 1. *R. Steege and K. Bailey: Intermediate Algebra, Schaum’s Outline Series, 2nd Ed.
Reference 2. *G. B. Thomas Jr., M.D. Weir, J. Hass, Calculus, 12th Ed., Pearson Publication.
Books 3. *H. Anton, I. Bivens and S. Davis, Calculus, 7th Edition, John Wiley & Sons
4. *J. Stewart, Calculus, 5e, Thomson, Books / Cole
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. II Semester approved in BOS: 17-05-2022
Course Title Advanced Calculus
Course Number MMBSMJ2001
Credits 4
Course Category Major/Core
Prerequisite Courses Calculus
Contact Hours 4 Lectures / week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives To focus on functions of several variables, Cartesian, cylindrical and spherical coordinate
systems and the concepts of limit, continuity, partial derivatives, and double and triple
integrals of functions of several variables. To introduce directional derivative and its
physical and geometric interpretation with some applications. To discuss some applications
of multiple integrals. To introduce vector valued functions of a single variable and their
limit, continuity, and differentiability.
Course Outcomes On successful completion of this course, student will be able to:
1. Express some physical problems in the form of functions of several variables.
2. Understand the idea of different coordinates systems, partial and directional
derivatives, and their applications
3. Find area and volume of nonrectangular regions and ready to solve problems arise
in mathematical physics.
4. Know vector valued functions of single variable and the concept of limit,
continuity, differentiability of such functions.
Contents of Syllabus No. of Lectures
UNIT I: Directional derivatives and Applications of Partial Derivatives
Directional derivative and its properties, Gradient vectors, Tangent line to a level curve, Tangent
plane and normal line to a surface, Linearization and differentials, Extreme values and saddle 12
points, Local and absolute maxima / minima, Method of Lagrange multipliers (with one constraint
only), Taylor’s formula for function of two variables, Partial derivatives with constrained variables.
UNIT II: Multiple Integrals
Double integrals over rectangles, Double integrals as volumes, Iterated integrals, Double integrals
over general regions, Fubini’s Theorem, Area by double integration, Double integrals in Polar 12
form, Triple integrals in rectangular, cylindrical, and spherical coordinates, Applications of triple
integrals.
UNIT III: Further Topics on Multivariable Differentiation and Integration 12
Mean value theorem, Young’s theorem, Schwartz’s theorem, Differential of higher order,
Homogeneous functions and Euler’s theorem, Implicit function theorem, Jacobian of a
transformation, Functional dependence, Envelopes, Differentiation under the integral sign:
Leibnitz’s rule, Dirichlet’s theorem and its Liouville’s extension.
UNIT IV: Vector Valued Functions of Single Variable 12
Parametrized curves in plane and space; Limits, continuity, differentiation, indefinite integration,
and definite integration of a vector valued function of a single variable, and their physical
interpretation, Tangent vectors and normal vectors, Tangential and normal components of
acceleration, Arc length and curvature.
Total No. of Lectures 48
1. *G. B. Thomas Jr., J. Hass, C. Heil and M. D. Weir: Calculus, Pearson Education Services
Textbooks*/ Pvt Ltd, 12th Ed, 2009.
Reference 2. D. V. Widder: Advanced Calculus, Prentice Hall of India Pvt. Ltd., New Delhi, 2nd Ed, 2012.
Books 3. R. Larsen and B. Edwards, Calculus, 11e, Cengage Learning, 2016
4. N. Piskunov: Differential and Integral Calculus, Vol. I and II, CBS Publishers and
Distributors, New Delhi, 1996.
5. T.M. Apostol: Mathematical Analysis, 2nd Ed., Narosa Distributor, New Delhi, 2002.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. II Semester approved in BOS: 17-05-2022
Course Title Three-dimensional Coordinate Geometry
Course Number MMBSMJ2002
Credits 2
Course Category Major/Core
Prerequisite Courses Three-dimensional Coordinate Geometry
Contact Course 2 Lectures/week
Type of Hours Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives The main aim of this course to introduce the basic tools of space geometry.
Course Outcomes This course will enable the students to:
 understand about lines in 3D, projections and planes.
 basic knowledge about different types of conicoid such as: spheres, cone, cylinder,
ellipsoid, hyperboloid and paraboloid.
Contents of Syllabus No. of Lectures
UNIT I: Plane, Straight Lines, and Sphere
Plane: General equation of first degree, Transformation of first degree equation into normal
form, Direction cosines of the normal, Plane through three given points, Two sides of a plane,
Length of the perpendicular from a point to a plane, Angle between planes, Bisectors of angles
between two planes, 06
Straight lines in space: Equation of a straight line, Finding the coordinates of point intersection
of two lines, Symmetrical and unsymmetrical form of the equation, Angle between a line and a
plane, Condition for a line to lie in a plane, Coplanar lines,
Sphere: General equation of a sphere, Sphere through four given points, Plane section of a sphere,
Sphere through a given circle, Sphere on the join of two points as diameter, Tangent plane,
Condition of tangency.
UNIT II: Cone and Cylinder
Cone and its equation, Cone with vertex at origin, Condition for general equation of second degree
to represent a cone, Intersection of a cone with a plane, Tangent plane to a cone and condition of 06
tangency, Reciprocal cone, Rectangular cone, Right circular cone, Cylinder and right circular
cylinder with their equations,
UNIT III: Central Conicoid
General equation of second degree, Special cases (Paraboloid and central conicoids), , Paraboloid,
Elliptic and hyperbolic paraboloids, Intersection of a line with a paraboloid, Diameter of a 06
paraboloid, Tangent plane to a paraboloid, Condition of tangency,
Unit IV: Central Conicoid
Standard equation of central conicoid, Shapes of central conicoid Tangent plane to central
conicoid and condition of tangency, Director sphere, Normal to a central conicoid, Number of 06
normal from a given point, Enveloping cone of a central conicoid, Polar plane, Polar lines,
Diametral planes and conjugate diameters
Total No. of Lectures 24
Textbooks*/ 1. *Shanti Narayan, Analytical solid geometry, S.Chand and Company Ltd..
Reference 2. * N. Saran and R.S. Gupta, Analytical Geometry of three dimensions, Pothishala (P) Ltd.
Books 3. R. J. T. Bell: An Elementary Treatise on Coordinate Geometry, MacMillon & Co Ltd, 1960.
4. Charles Smith: An Elementary Treatise on Solid Geometry, MacMillon & Co Ltd, 1931.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. II Semester approved in BOS: 17-05-2022
Course Title Numerical Methods
Course Number MMBSMJ2003
Credits 2
Course Category Major/Core
Prerequisite Courses None
Contact Hours 2 Lectures/week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives Numerical Analysis is the study of algorithms using numerical approximations for the
problems of mathematical analysis.
This course is designed to achieve the following objectives:
1. The objectives of studying this module are to make the students familiarize with the ways
of solving complicated mathematical problems numerically.
2. Describing and understanding of the several errors and approximation in numerical
methods.
3. Obtaining numerical solutions to problems of mathematics. e.g. finding roots of
equations, numerical differentiation and integration, solution of ordinary differential
equations.
4. The studying of Curve Fitting and Interpolation.
Course Outcomes To explore complex systems, physicists, engineers, financiers and mathematicians require
computational methods since mathematical models are only rarely solvable algebraically.
Numerical methods, based upon sound computational mathematics, are the basic algorithms
underpinning computer predictions in modern systems science. Such methods include
techniques for simple optimization, interpolation from the known to the unknown, linear
algebra underlying systems of equations, ordinary differential equations to simulate
systems, and stochastic simulation under random influences.
Contents of Syllabus No. of Lectures
UNIT I: Numerical Solution of algebraic and transcendental Equations
Absolute, relative and percentage errors, General error formula, Solution of algebraic and
transcendental equations by iteration methods namely: Bisection method, Regulafalsi method, 6
Iterative method and Newton-Raphson method, Solution of system of linear equations using direct
methods such as matrix inversion, Gauss elimination and LU decomposition including some
iteration methods namely: Jacobi and Gauss-Siedel method.
UNIT II: Interpolation
Symbols of Δ,, E, E-1, D,  and and their relations, Newton-Gregory interpolation formulae,
Forward difference, Backward difference, (derivation of all formulae) Gauss’s Forward difference, 6
Gauss Backward difference, Stirling’s formulae, Bessel’s formulae and Lagrange’s interpolation
formula, Divided differences and their properties.
UNIT III: Numerical Differentiation and Integration
Numerical differentiation of tabular functions including error estimations, Numerical integration
using Gauss quadrature formulae, Trapezoidal, Simpson’s 1/3- and 3/8-Rule, Least squares curve 6
fitting procedures and Least squares polynomial approximation.
UNIT IV: Numerical Solution of Ordinary Differential Equations
Euler’s and modified Euler’s methods, Picard’s method, Taylor series method, Runge-Kutta
methods of 2nd and 4th order, Solution of boundary value problems of ordinary differential 6
equations using Finite Difference method.
Total No. of Lectures 24
Textbooks*/ 1. S. S. Sastry: Introductory Methods of Numerical Analysis, Prentice Hall of India, New
Reference Delhi, 5th Ed, 2012.
Books 2. M. K. Jain, S. R. K. Iyenger and R. K. Jain: Numerical Methods for Scientific and
Engineering Computation, New Age International (P) Ltd, 1999.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. II Semester approved in BOS: 17-05-2022
Course Title Calculus of Several Variables
Course Number MMBSMN2004
Credits 4
Course Category Minor
Prerequisite Courses Calculus
Contact Hours 4 Lectures / week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives To focus on functions of several variables, Cartesian, cylindrical and spherical coordinate
systems and the concepts of limit, continuity, partial derivatives, and double and triple
integrals of functions of several variables. To introduce directional derivative and its
physical and geometric interpretation with some applications. To discuss some applications
of multiple integrals
Course Outcomes On successful completion of this course, student should be able to:
5. Express some physical problems in the form of functions of several variables.
6. Understand the idea of different coordinates systems, partial and directional
derivatives, and their applications
7. Find area and volume of nonrectangular regions and ready to solve problems arise
in mathematical physics.
8. Geometric and physical meaning of line and surface integrals, their applications.
Contents of Syllabus No. of Lectures
UNIT I: Limit, Continuity and Differentiability
Functions of several variables, Contour curves, level curves and level surfaces, Cylindrical and
spherical coordinate systems and their relations with Cartesian coordinates, Limits and 12
continuity for functions of two variables, Partial derivatives, Relation between partial
derivatives and continuity, Differentiability, Chain rule for functions of two and three variables.
UNIT II: Applications of Partial Derivatives
Directional derivatives, Gradient vectors, Tangent line to a level curve, Tangent plane and
normal line to a surface, Linearization and differentials, Extreme values and saddle points, 12
Local and absolute maxima / minima, Method of Lagrange multipliers (with one constraint
only), Taylor’s formula for function of two variables, Partial derivatives with constrained
variables.
UNIT III: Double and Triple Integrals
Double integrals over rectangles, Double integrals as volumes, Iterated integrals, Double
integrals over general regions, Fubini’s Theorem, Area by double integration, Double integrals 12
in Polar form, Triple integrals in Rectangular, Cylindrical, Dirichlet integral.
UNIT IV: Line and surface integrals
Line integrals of scalar fields and vector fields, Applications of line integrals: Work, Circulation
and Flux; Green’s Theorem in the plane, Evaluation of line integral using Green’s Theorem, 12
Surfaces and Area, Surface integrals, Stoke’s Theorem.
Total No. of Lectures 48
1. *G. B. Thomas Jr., J. Hass, C. Heil and M. D. Weir: Calculus, Pearson Education Services
Textbooks*/ Pvt Ltd, 12th Ed, 2009.
Reference 2. *D. V. Widder: Advanced Calculus, Prentice Hall of India Pvt. Ltd., New Delhi, 2 nd Ed,
Books 2012.
3. N. Piskunov: Differential and Integral Calculus, Vol. I and II, CBS Publishers and
Distributors, New Delhi, 1996.
4. H. Anton, I. Bivens, and D. Stephens, Calculus, Wiley, 10th Ed., 2015.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. III Semester approved in BOS: 17-05-2022
Course Title Basic Numerical Methods
Course Number MMBSMN2005
Credits 2
Course Category Minor
Prerequisite Courses None
Contact Hours 2 Lectures/week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives Numerical Analysis is the study of algorithms using numerical approximations for the
problems of mathematical analysis.
This course is designed to achieve the following objectives:
1. The objectives of studying this module are to make the students familiarize with the ways
of solving complicated mathematical problems numerically.
2. Describing and understanding of the several errors and approximation in numerical
methods.
3. Obtaining numerical solutions to problems of mathematics. e.g. finding roots of equations,
numerical differentiation and integration, solution of ordinary differential equations.
4. The studying of Curve Fitting and Interpolation.
Course Outcomes To explore complex systems, physicists, engineers, financiers and mathematicians require
computational methods since mathematical models are only rarely solvable algebraically.
Numerical methods, based upon sound computational mathematics, are the basic algorithms
underpinning computer predictions in modern systems science. Such methods include
techniques for simple optimization, interpolation from the known to the unknown, linear
algebra underlying systems of equations, ordinary differential equations to simulate systems,
and stochastic simulation under random influences.
Contents of Syllabus No. of Lectures
UNIT I: Numerical Solution of algebraic and transcendental equations
Absolute, relative and percentage errors, General error formula, Solution of algebraic and
transcendental equations by iteration methods namely: Bisection method, Regulafalsi 6
method, Iterative method and Newton-Raphson method, Solution of system of linear
equations using some iteration methods namely: Jacobi and Gauss-Siedel method.
UNIT II: Interpolation
Symbols of Δ,, E, E-1, D,  and and their relations, Newton-Gregory interpolation
formulae, Forward difference, Backward difference, Gauss’s Forward difference, Gauss 6
Backward difference, Stirling’s formulae, and Lagrange’s interpolation formula, Divided
Differences, and their properties.
UNIT III: Numerical Differentiation and Integration
Numerical differentiation of tabular functions including error estimations, Numerical
integration using Gauss quadrature formulae, Trapezoidal, Simpson’s 1/3- and 3/8-Rule, 6
Least squares curve fitting procedures and Least squares polynomial approximation.
UNIT IV: Numerical Solution of Ordinary Differential Equations
Euler’s and modified Euler’s methods, Picard’s method, Taylor series method, Runge-Kutta
methods of 2nd order, Solution of boundary value problems of ordinary differential equations 6
using Finite Difference method.
Total No. of Lectures 24
Textbooks*/ 1. S. S. Sastry: Introductory Methods of Numerical Analysis, Prentice Hall of India, New
Reference Delhi, 5th Ed, 2012.
Books 2. M. K. Jain, S. R. K. Iyenger and R. K. Jain: Numerical Methods for Scientific and
Engineering Computation, New Age International (P) Ltd, 1999.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. II Semester approved in BOS: 17-05-2022
Course Title Matrices and Linear Programming
Course Number MMBSGE2006
Credits 4
Course Category Generic (Elective)
Prerequisite Courses None
Contact Hours 4 Lectures/week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives This course aims to introduce the following concepts and cognitive skills:
The course is divided into two parts. The first two units of this course consists of Matrices and
Determinants with their applications. The aim of this part is to introduce all the basic
properties and types of matrices and determinants by using its properties, evaluation of the
inverse of a matrix, as an application of how to solve a system of linear equations using
matrices and determinants. The next two units of this course begin with applications and scope
of O.R. formulation of linear programming problems, different methods to solve LPP, the
notion of Duality in LPP.
Course Outcomes Upon successful completion of this course, the student will be able to:
 Gain the knowledge of matrix and their properties.
 Know the system of a linear equation and its solution sets
 Know the use of properties of determinant and their calculations
 Use the method of Gauss-Jordan elimination to find the solution to a system of simultaneous
linear equations.
 Students will understand the concept of LPP
 Students will be able to solve some real-life problems using optimization techniques.
Contents of Syllabus No. of Lectures
UNIT I: Matrices 12
Types of matrices, Equality of matrices, Matrix addition and scalar multiplication, Matrix
multiplication, Transpose and adjoint of a matrix, The inverse of a matrix, solution of simultaneous
linear equations by matrix inversion method, Elementary transformations, Solution of linear
equations by Gauss Jordan elimination method
UNIT II: Determinants 12
Formation of determinants, The difference between matrix and determinant, Minors and cofactors of
the elements of a determinant, Properties of determinant, Cramer’s rule and Application of
determinants in finding the solutions of the system of linear equations.
UNIT III: Linear Programming Problems and Transportation Problems 12
Definition of operational research, Formulation of a linear programming problem, Linear
programming problem with applications, Graphical solution of a linear programming problem,
Some exceptional cases, General, standard and canonical forms of a linear programming problem,
Transportation problems
UNIT IV: Simplex Method 12
Basic feasible solutions, Simplex method, Big-M method, Two-phase simplex method, Revised
simplex method, Degeneracy and cycling problem, Duality and duality theorems, Dual simplex
method.
Total No. of Lectures 48
1. *Frank, Ayres: Theory and Problems of Matrices, Schaum’s outline series
Textbooks*/ 2. *Kanti Swarup, P.K. Gupta, Man Mohan, Operations Research, Sultan Chand & Sons, 2009.
Reference
3. H. A. Taha: Operational Research: An Introduction, 10th Edition, Pearson Publication
Books
4. M.S. Bazarra, John J. Jarvis and H. D. Sherali, Linear Programming and Network Flows.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. III Semester approved in BOS: 17-05-2022
Course Title Real Analysis
Course Number MMBSMJ3001
Credits 4
Course Category Major/Core
Prerequisite Courses Calculus
Contact Hours 4 Lectures/week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives The course will develop a deep and rigorous understanding of real line ℝ and of defining
terms to prove the results about convergence and divergence of sequences and series of real
numbers.
Course Outcomes On successful completion of this course, student should be able to:
● Understand many properties of the real line, especially axiomatic theory and point
set topology on ℝ.
● Recognize bounded, convergent, divergent, Cauchy and monotonic sequences and
to calculate their limit superior, limit inferior, and the limit of a bounded sequence.
● Apply the ratio, root, alternating series and limit comparison tests for convergence
and absolute convergence of an infinite series of real numbers.
Contents of Syllabus No. of Lectures
UNIT I: Fundamental Properties of Real Numbers
Bounded and unbounded sets, Supremum and infimum, Field axioms, Order axioms and
Completeness axioms on ℝ, Nested interval property, Archimedean property of real numbers and 12
representation of real numbers, Denseness property of rational numbers in ℝ, Dedekind theory of
real numbers, Dedekind-Cantor axioms, Inequalities of Cauchy-Schwartz, Minkowski and Holder,
Extended real number system.
UNIT II: Elements of Point Set Topology on ℝ
Neighbourhood of a point, Interior, exterior and boundary points, Open sets, Limits points and
derived set, Bolzano-Weierstrass Theorem, Adherent point and Closure of a set, Closed sets, 12
Compact sets, Heine-Borel Theorem, Connected sets, Dense sets, Perfect sets, Cantor sets.
UNIT III: Sequence of Real Numbers
Concept of sequence, Convergent and divergent sequences, Limit inferior and superior, Bounded
and unbounded sequences, Monotone sequences, Subsequences, Bolzano Weierstrass theorem for 12
sequence, Cauchy’s general principle of convergence, properly divergent sequences, Sequential
criterion of closed sets and compact sets, Cantor’s theory of real numbers.
UNIT IV: Series of Real Numbers
Introduction to series of real numbers, Sequence of partial sums and convergence of infinite series,
Necessary condition for the convergence of an infinite series, Positive term series, Comparison 12
tests (first type and limit form), Cauchy root test, D’Alembert’s ratio test with their applications,
Alternating series, Leibnitz test, Absolute and conditional convergence, Series of arbitrary terms,
Abel’s and Dirichlet’s tests, Rearrangement of series, Logarithmic and Condensation tests.
Total No. of Lectures 48
1. *R. G. Bartle and D. R. Sherbert: Introduction to Real Analysis, John Wiley and Sons,
Textbooks*/ Singapore, 3rd Ed, 2003.
References 2. *S. C. Malik and S. Arora: Mathematical Analysis, New Academic Science Ltd, 5th Ed,
Books 2017.
3. W. Rudin: Principles of Mathematical Analysis, Third Edition, McGraw Hill, New York,
3rd Ed, 1976.
4. T.M. Apostol: Mathematical Analysis, 2nd Ed., Narosa Distributor, New Delhi, 2002.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. III Semester approved in BOS: 17-05-2022
Course Title Ordinary Differential Equations
Course Number MMBSMJ3002
Credits 2
Course Category Major/Core
Prerequisite Course(s) Calculus
Contact Hours 2 Lectures/week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives The main objectives of this course are to introduce the students to the
exciting world of Differential Equations, Mathematical Modelling, and
their applications.
Course Outcomes On successful completion of this course, student should be able to
solve first order nonlinear differential equation, second order boundary
value problems and linear differential equations of higher order using
various techniques.
Contents of Syllabus No. of Lectures
UNIT I: First Order ODE
Exact differential equations; Integrating factors; Change of variables; Bernoulli
equation; Orthogonal trajectory of a family of curves; Equations of the first order and 6
higher degree; Equations solvable for p, y and x; Clairaut’s equation; Lagrange’s
equation; Singular solutions.
UNIT II: Higher Order ODE with Constant Coefficients
Homogeneous and non-homogeneous linear differential equations of order n with
constant coefficients; Complementary functions; particular integrals of certain well- 6
known functions; Variation of parameters.
UNIT III: Higher Order ODE with Variable Coefficients
Linear differential equations of second order with variables coefficients: Reduction
of order; Cauchy-Euler and Legendre linear differential equations; Series solution of 6
differential equations: Frobenius method. (Bessel’s linear Differential Equations
for HA).
UNIT IV: Differential Equations in Three Variables
Total differential equations; Condition for integrability; Simultaneous total
differential equations; Methods of grouping and multipliers; System of linear 6
differential equations with constant coefficients; Triangular system of linear
differential equations; Degenerate system of linear differential equations.
Total No. of Lectures 24
1. *Zafar Ahsan: Differential Equations and their Applications, Prentice Hall of India,
Textbook*/ New Delhi, 3rd Ed, 2016.
Reference 2. Frank Ayres Jr: Theory and Problems of Differential Equations, McGraw-Hill
Books Book Company, 1972.
3. George F. Simmons: Differential Equations with Applications and Historical
Notes, Tata McGraw Hill Comp Ltd, New Delhi, 1974.
4. Dennis G. Zill: A first course in differential equations, Cengage Learning, 2008.
5. M. D. Raisinghania: Ordinary and Partial Differential Equations, S. Chand, New
Delhi, 18th Ed., 2016.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. III Semester approved in BOS: 17-05-2022
Course Title Number Theory
Course Number MMBSMJ3003
Credits 2
Course Category Major/Core
Prerequisite Set Theory
Courses
Contact Hours 2 Lectures/week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives This course aims to introduce the following concepts and cognitive skills.
It consists of mathematical induction, divisibility, prime numbers, congruences,
factorization, an arithmetic functions, primitive roots, Chinese remainder
theorem, Algebraic congruence (mod p), Lagrange’s theorem, Wilson’s theorem
and their applications.
Course Outcomes On successful completion of this course, students will be able to:
 Demonstrate knowledge of the basic definitions and theorems in number
theory.
 apply number theory algorithms and procedures to basic problems
 think and reason about abstract mathematics skills at writing
mathematical proofs.
 analyze and solve problems involving the distribution of primes.
 analyze and solve problems involving primitive roots.
 solve system of linear congruences using the Chinese remainder theorem.
 understand the basics of modular arithmetic.
 state and prove Lagrange’s theorem, Wilson theorem and its
generalization using Euler's function.
Contents of Syllabus No. of Lectures
UNIT I: Divisibility of Integers
Division algorithm and derived results, least common multiple, Greatest common 6
divisor, Euclid’s algorithm, Prime numbers, Relatively prime integers and related
results.
UNIT II: Factorization in integers and an Arithmetic function
Fundamental theorem of arithmetic and its applications, Euler’s phi function and its 6
properties including multiplicative property, Gauss’s theorem and related problems.
UNIT III: Linear Congruences
Congruences, Euler’s theorem, Fermat’s theorem, Order of an integer (mod m), Linear 6
congruences, Chinese remainder theorem, Primitive roots
UNIT IV: Algebraic Congruences
Algebraic congruence (mod p), Lagrange’s theorem, Wilson theorem, Algebraic 6
congruences with composite modulus.
Total No. of Lectures 24
Textbook* / 1. *J. Hunter: Number Theory.
Reference Books 2. David M. Burton: Elementary Number Theory, 6th Ed.
3. G. B. Mathews: Theory of Number Part-I.
4. M. Erickson and A. Vazzana: Introduction to Number theory, Chapman &
Hall/ CRC.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. III Semester approved in BOS: 17-05-2022
Course Title Basic Real Analysis
Course Number MMBSMN3004
Credits 4
Course Category Minor
Prerequisite Courses Calculus
Contact Hours 4 Lectures / week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives The course will develop a deep and rigorous understanding of real line ℝ and of
defining terms to prove the results about convergence and divergence of sequences
and series of real numbers.
Course Outcomes On successful completion of this course, student should be able to:
● Understand many properties of the real line, especially axiomatic theory
and point set topology on ℝ.
● Recognize bounded, convergent, divergent, Cauchy and monotonic
sequences and to calculate their limit superior, limit inferior, and the limit
of a bounded sequence.
● Apply the ratio, root, alternating series and limit comparison tests for
convergence and absolute convergence of an infinite series of real numbers.
Contents of Syllabus No. of Lectures
UNIT I: Real Number system and Countability of sets
Bounded and unbounded sets, Supremum and infimum, Field axioms, Order axioms and
Completeness axioms on ℝ, Nested interval property, Archimedean property of real 12
numbers and representation of real numbers, Denseness property of rational numbers in
R, Finite and infinite sets, Countable and uncountable sets.
UNIT II: Open, Closed sets and related results
Neighbourhood of a point, Interior, exterior and boundary points, Open sets, Limits
points and derived set, Bolzano-Weierstrass Theorem, Adherent point and Closure of a 12
set, Closed sets, Compact sets(definition and examples), Dense sets (using concept of
open sets and in terms of limit point), Heine-Borel Theorem, Connected sets(definition
and examples).
UNIT III: Sequence of Real Numbers
Concept of sequence, Convergent and divergent sequences, Limit inferior and superior,
Bounded and unbounded sequences, Monotone sequences, Subsequences, Bolzano 12
Weierstrass theorem for sequence, Cauchy’s general principle of convergence, properly
divergent sequences.
UNIT IV: Series of Real Numbers
Introduction to series of real numbers, Sequence of partial sums and convergence of
infinite series, Necessary condition for the convergence of an infinite series, Positive
term series, Comparison tests (first type and limit form), Cauchy root test, D’Alembert’s 12
ratio test with their applications, Alternating series, Leibnitz test, Absolute and
conditional convergence, Series of arbitrary terms, Abel’s and Dirichlet’s tests,
Rearrangement of series.
Total No. of Lectures 48
1. *R. G. Bartle and D. R. Sherbert: Introduction to Real Analysis, John Wiley and
Textbooks*/ Sons, Singapore, 3rd Ed, 2003.
References 2. *S. C. Malik and S. Arora: Mathematical Analysis, New Academic Science Ltd, 5th
Books Ed, 2017.
3. G.F. Simmons, Calculus with Analytical Geometry, McGraw Hill
4. T.M. Apostol: Mathematical Analysis, 2nd Ed., Narosa Distributor, New Delhi, 2002.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. III Semester approved in BOS: 17-05-2022
Course Title Elements of Ordinary Differential Equations
Course Number MMBSMN3005
Credits 2
Course Category Minor
Prerequisite Courses Calculus
Contact Hours 2 Lectures / week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives The main objectives of this course are to introduce the students to the exciting
world of Differential Equations, Mathematical Modelling, and their
applications to sciences, engg., social sciences etc.
Course Outcomes On successful completion of this course, student should be able to solve first
order nonlinear differential equation, second order boundary value problems
and linear differential equations of higher order using various techniques.
Contents of Syllabus No. of Lectures
UNIT I: First Order ODE
Bernoulli equation; Exact differential equations; Integrating factors; Change of 6
variables; Orthogonal trajectory of a family of curves; Equations of the first order
and higher degree; Equations solvable for p, y and x; Clairaut’s equation; Lagrange’s
equation.
UNIT II: Higher Order ODE with Constant Coefficients
Linear differential equations of order n with constant coefficients and their types; 6
Complementary functions; particular integrals of certain well-known functions;
Variation of parameters.
UNIT III: Higher Order ODE with non-constant Coefficients
Linear differential equations of second order with variables coefficients: Reduction 6
of order; Cauchy-Euler and Legendre linear differential equations; Frobenius
method for series solution of differential equations.
UNIT IV: Differential Equations in More Than Two Variables
Total differential equations; Condition for integrability; Simultaneous total
differential equations; Methods of grouping and multipliers; System of linear 6
differential equations with constant coefficients; Triangular system of linear
differential equations; Degenerate system of linear differential equations.
Total No. of Lectures 24
1. *Zafar Ahsan: Differential Equations and their Applications, Prentice Hall of
Textbooks*/ India, New Delhi, 3rd Ed, 2016.
Reference 2. Frank Ayres Jr: Theory and Problems of Differential Equations, McGraw-Hill
Books Book Company, 1972.
3. George F. Simmons: Differential Equations with Applications and Historical
Notes, Tata McGraw Hill Comp Ltd, New Delhi, 1974.
4. Dennis G. Zill: A first course in differential equations, Cengage Learning, 2008.
5. M. D. Raisinghania: Ordinary and Partial Differential Equations, S. Chand, New
Delhi, 18th Ed., 2016.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. III Semester approved in BOS: 17-05-2022
Course Title Functions of Several Variables
Course Number MMBSGE3006
Credits 4
Course Category Generic (Elective)
Prerequisite Courses Calculus
Contact Hours 4 Lectures / week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives To focus on general concepts of limit, continuity, and differentiability. To
introduce the idea of double and triple integrals.
Course Outcomes On successful completion of this course, the student will be able to:
1. Express the physical problems containing more variables.
2. Understand the idea of local and absolute maxima, local and
absolute minima.
3. Find the area and volume of nonrectangular regions and be
ready to solve problems that arise in mathematical physics.

Contents of Syllabus No. of Lectures

UNIT I: Limit, Continuity and Differentiability
Functions of several variables, level curves and level surfaces, Limits, and continuity
for functions of two variables, Partial derivatives, Relation between partial derivatives 12
and continuity, Cylindrical and spherical coordinates, Differentiability, Chain rule for
functions of two and three variables.
UNIT II: Applications of Partial Derivatives
Linearization and differentials, Extreme values and saddle points, Local and absolute
maxima, Local and absolute minima, Taylor’s formula for the function of two 12
variables, Partial derivatives with constrained variables.
UNIT III: Double Integrals
Double integrals over rectangular regions, Double integrals as volumes, Iterated
integrals, Double integrals over general regions, Fubini’s Theorem, Area by double 12
integration, Double integrals in Polar form.
UNIT IV: Triple Integrals
Triple integrals, Triple integrals in cylindrical and spherical coordinates, Equations of
well-known surfaces in cylindrical and spherical coordinates, Applications of triple 12
integrals, Dirichlet Integral formula.
Total No. of Lectures 48
1. *G. B. Thomas Jr., J. Hass, C. Heil, and M. D. Weir: Calculus, Pearson Education
Textbooks*/ Services Pvt Ltd, 12th Ed, 2009.
Reference 2. D. V. Widder: Advanced Calculus, Prentice Hall of India Pvt. Ltd., New Delhi, 2nd Ed,
Books
2012.
3. H. Anton, I. Bivens, and D. Stephens, Calculus, Wiley; Tenth edition (2015).
4. N. Piskunov: Differential and Integral Calculus, Vol. I and II, CBS Publishers and
Distributors, New Delhi, 1996.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. III Semester approved in BOS: 17-05-2022
Course Title Mathematical Logic and Reasoning
Course Number MMBSVO3007
Credits 2
Course Category Vocational and skill enhancement course
Prerequisite Courses Elementary set theory and plane geometry
Contact Hours Two lectures per week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives The ideas which are, essentially, well understood may need to be reformulated
before we proceed to prove or disprove anything. Therefore, the students need to
understand
1. The frame work under which a mathematical problem is addressed.
2. The deductive logic is applied only after assuming the postulates and
established properties of the given system.
3. Similarly, the criteria when inductive logic is to be applied.

Course Outcomes After the completion of the course, the students will be able to develop a holistic
approach to study all the system satisfying the given set of postulates.
Content of Syllabus No. of Lectures
UNIT I: Tautologies
Law of excluded middle, Truth table, Equivalents, Lexicographic ordering, Logically 6
equivalent statements, Conditional disjunctions, Demorgan law, examples
UNIT II: Inductive and Deductive Reasoning
Real numbers; The ordering of real numbers; The positive integers and induction 6
principle; The well ordering principle; Axiomatization of the properties.
UNIT III: Axiomatic System
Axiomatic system; Consistency of the system; Independence; Completeness and 6
Categoricalness; Models of deductions; Archimedian postulate and Euclidean
completeness.
UNIT IV: Set Theoretic Foundation of Mathematical Reasoning:
The language and notations of sets; The idea of functions; The set theoretic
interpretation of function and relation; The distance function; ,The ruler postulates; 6
The ruler placement theorem; Betweenness; Segments, rays, Angles and triangles;
Congruence of segments; Segment addition theorem.
Total No. of Lectures 24
Textbooks*/ 1. Edwin E. Moise: Elemetary Geometry from an advanced standpoint,
References Books secondt Edition. Addison-Wesley Publishing, California, 1973
2. Bertrand Russell: Introduction to Mathematical Philosophy; George Allen
& Unwin Ltd., Newyork.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. III Semester approved in BOS: 27.05.2023
Course Title Mathematics of Finance
Course Number
Credits 2
Course Category Value Added course
Prerequisite Courses None
Contact Hours 2 Lectures/week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives The purpose of this course is to aware students with the elementary financial
terms, namely, different kind of interests and their relations, which we use in
our daily life. The course objective is also to provide the knowledge of
counting principle, permutations and probability which we use in our daily life.
Course Outcomes On successful completion of this course, student will be able to know daily life
problems of calculating different kinds of interest, namely, compound interest,
effective interest, negative interest and their comparison.
Students will also be able to know the fundamentals of counting principle,
permutations and probability, and their applications in our daily life.
Contents of Syllabus No. of Lectures
UNIT I: Mathematics of Finance
Compound interest, Boubling money, Effective rate, Comparing interest rates, negative
interest rates, Present value, Single-payment trust funds, Equations of value, Comparing 6
investments, Net present values, Interest compounded continuously, effective rate under
continuous interest, Trust fund.
UNIT II: Annuities
Present value of annuities, periodic payment of an annuity, Future value of an annuity, 6
sinking fund, Amortization of loans, period of a loan, Perpetuities: present value of
perpetuities, limits
UNIT III: Basic Counting Principle and Permutations
Basic counting principle, travel routes, coin tosses and roll of dice, answering a quiz, 6
combination and other counting principles, sample space and events.
UNIT IV: Probability
Probability, conditional probability and stochastic processes, independent event Bayes 6
formula.
Total No. of Lectures 24
Textbooks*/ 1. Ernest F. Haeussler, Richard S. Paul and Richard J. Wood, Introductory
Reference Books Mathematical Analysis, 14th Edition.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A. / B.Sc. IV Semester approved in BOS: May 17, 2022
Course Title Linear Algebra
Course Number MMBSMJ4001
Credits 4
Course Category Major/Core
Prerequisite Courses Sets, relations, and functions
Contact Hours 4 Lectures/week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives This course aims to introduce the following concepts and cognitive skills.
In this course, the students understand real vector spaces and subspaces and apply their
properties. Understand linear independence and dependence. Find the basis and
dimension of a vector space and understand the change of basis. Find a basis for the row
space, column space and null space of a matrix, also find the rank and nullity of a matrix.
Compute linear transformations, kernel, range, inverse of linear transformations, and find
matrices of general linear transformations. Find the dimension of spaces such as those
associated with matrices and linear transformations. Solve systems of linear equations
using various methods. Perform matrix algebra, invertibility, and transpose and
understand vector algebra in Rn. Determine the relationship between coefficient matrix
invertibility, solutions to a system of linear equations and the inverse of matrices.
Verification of Caley Hamilton’s theorem for matrices, Find the characteristic equation,
the eigenvalues and corresponding eigenvectors of a given matrix and use them in
applications. Students are also expected to gain an appreciation for the applications of
linear algebra to areas such as computer science, engineering, biology, and economics.
Course Outcomes Upon successful completion of this course, student should be able to:
1. explain the concepts of vector space and subspace.
2. define vector operations for vectors in Rn.
3. analyze whether a set S of vectors in a vector space V is a spanning set of V.
4. analyze whether a finite set of vectors in a vector space V is linearly independent.
5. explain the concepts of basis and dimension of a vector space.
6. explain the properties of vectors in the bases.
7. express row and column spaces of a matrix.
8. explain some functions defined between vector spaces.
9. express required conditions for a transformation to be a linear transformation.
10. find the kernel, range, rank and nullity of a linear transformation.
11. express some of the algebra operations between linear transformations.
12. able to find the matrix representation of a linear transformation.
13. explain whether a system of linear equations is consistent or inconsistent and find the
general solution to a consistent system.
14. explain the characteristic equations, eigenvalues and corresponding eigenvectors of a
given matrix.
Contents of Syllabus No. of Lectures
UNIT I: Vector Spaces
Binary operations, Definition of field with examples, Definition of vector space with examples, 12
Subspaces, Span of a set, Sum of subspaces, Linear dependence and independence, Basis and
dimension of a vector space, Coordinates of a vector relative to an ordered basis, Dimension
theorem.

UNIT II: Linear Transformations

Linear transformation and its properties, Range and kernel of a linear transformation, Rank and 12
nullity of a linear transformation, Rank-nullity Theorem, Inverse of a linear transformation.
UNIT III: Space L(U, V) and Matrix Representation of Linear Maps
Vector space L(U, V) and its dimension, Composition of linear transformations, Matrix 12
associated with a linear transformation, Linear transformation associated with a matrix, Rank
and nullity of a matrix.
UNIT IV: Elementary operations and Eigenvalues
Elementary row operations and row-reduced echelon form, Inverse of a matrix through 12
elementary row operations, Solution of a system of linear equations, Eigenvalues and
Eigenvectors of matrices.
Total No. of Lectures 48
1. *V. Krishnamurty, V. P. Mainra and J. L. Arora: An introduction to Linear Algebra, East-
Textbook*/ West Press, New Delhi, 2002.
References 2. S Lang, Introduction to Linear Algebra (2nd edition), Springer, 2005
books 3. S. Kumaresan: Linear Algebra- A Geometric Approach, Prentice Hall of India, 1999.
4. S. Lipschutz and M. Lipson: Linear Algebra, Schuam’s Outline Series.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. IV Semester approved in BOS: 17-05-2022
Course Title Partial Differential Equations
Course Number MMBSMJ4002
Credits 2
Course Category Major (Compulsory)
Prerequisite Courses Advanced Calculus and Ordinary Differential Equations
Contact Course 2 Lectures / week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives The main objectives of this course are to teach students to form and solve partial
differential equations and use them in solving some physical problems.
Course Outcomes On successful completion of this course, student should be able to:
 Formulate and classify partial differential equations.
 Solve linear and nonlinear partial differential equations using various
methods.
Contents of Syllabus No. of Lectures
UNIT I: Basic Concepts 6
Definition; order and degree of a partial differential equation; Formation of partial
differential equations by elimination of arbitrary constants and arbitrary functions;
Solution of a partial differential equation and its different kinds (complete, general
and particular solutions); Equations easily integrable; Classification of partial
differential equations.
UNIT II: First order PDE 6
Solution of quasilinear partial differential equations by Lagrange’s method; Integral
surfaces through a given curve; Standard forms of first order partial differential
equation; Charpit’s method; Cauchy’s problem and method of characteristics;
Compatible system of first order partial differential equations.
UNIT III: Second order PDE 6
Standard forms of second order linear partial differential equations; Classification;
characteristic curves of semilinear partial differential equations; Solution of
quasilinear partial differential equations by Monge’s method.
UNIT IV: Higher order linear PDE 6
Homogeneous linear partial differential equations with constant coefficients and
their solutions; Nonhomogeneous linear partial differential equations with constant
coefficients: Different cases of complementary functions and particular integrals;
Equations reducible to linear partial differential equations with constant
coefficients.
Total 24
Textbooks*/ 1. *N. Sneddon: Elements of Partial Differential Equations, McGraw Hill Book
Reference Company, 1957.
Books 2. Tyn Myint U: Partial Differential Equations of Mathematical Physics, American
Elsevier Pub Co, 1973.
3. M. D. Raisinghania: Ordinary and Partial Differential Equations, S. Chand, New
Delhi, 18th Ed., 2016.
4. T. Amarnath: A Elementary Course in Partial Differential Equations, Narosa
Publishing House, New Delhi, 2nd Ed., 2003.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. IV Semester approved in BOS: 17-05-2022
Course Title Vector Calculus
Course Number MMBSMJ4003
Credits 2
Course Category Major/Core
Prerequisite Courses Calculus, Coordinate Geometry & Advanced Calculus
Contact Course 2 Lectures / week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives The main objective of this course is to study the differential and integral
calculus of vector valued functions of several variables and the concept of
curvilinear coordinate systems
Course Outcomes On successful completion of this course, student will be able to know:
1. The conceptual variations when advancing in calculus from single
valued functions to vector valued functions.
2. Applications of vector calculus tools in geometry and physics.
3. Inter-relationship amongst the line & surface integrals with double
& triple integrals (Green’s, Gauss’s and Stoke’s theorems).
4. Curvilinear coordinate systems.
Contents of Syllabus No. of Lectures
UNIT I: Vector valued Function of Several variables 6
Functions from Rn to Rm: Limit, Continuity, Directional derivatives, Differentiability,
Jacobian matrix, General chain rule, Vector fields in plane and space, Conservative
fields and potential functions, Curl, and divergence of a vector field, Irrotational
fields, Solenoidal fields, Compatible identities of gradient, divergence and curl.
UNIT II: Line Integrals 6
Line integrals of scalar and vector fields, Applications of line integrals: Mass and
Work; Line integrals in differential forms, Line integrals of conservative fields,
Fundamental theorem for line integrals, Independence of path, Green's theorem,
Finding area by line integrals.
UNIT III: Surface Integrals 6
Parametrized surfaces, Area of a parametrized surface, Surface integrals, Orientation
of a surface, Flux integrals, Gauss divergence theorem, Stokes' theorem.
UNIT IV: Curvilinear Coordinates 6
Orthogonal curvilinear coordinates, Gradient, divergence, and Curl in orthogonal
curvilinear coordinates, cylindrical coordinates, and spherical coordinates; Potential,
line integral and circulation of a vector field in curvilinear coordinates, cylindrical
coordinates, and spherical coordinates; Laplace operator in orthogonal coordinates.
Total 24
1. *R. Larson and B. Edwards: Multivariable Calculus, Cengage Learning, 10th
Textbooks*/ Ed, 2016
Reference 2. *Daniel Miranda, Vector and Tensor Calculus, Frankenstein’s Note, Version
Books 0.76.
3. J. E. Marsden and A. Tromba: Vector Calculus, W. H. Freeman & Co, New
York, 6th Ed, 2012.
4. M. L. Krasnov, A. I. Kiselev and G. I. Makarenko: Vector Analysis, Mir
Publishers, Moscow, 1983.
5. M. Spiegel, S. Lipschutz and D. Spellman: Vector Analysis: Schaum’s
Outlines Series, McGraw Hill Education, 2nd Ed, 2017.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A. / B.Sc. IV Semester approved in BOS: May 17, 2022
Course Title Basic Linear Algebra
Course Number MMBSMN4004
Credits 4
Course Category Minor
Prerequisite Courses Sets, relations and functions
Contact Course 4 Lectures/ week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives This course aims to introduce the following concepts and cognitive skills.
The students will understand real vector spaces, subspaces, and their properties in this
course. Understand linear independence and dependence. Find the basis and dimension of
a vector space and understand the change of basis. Find a basis for the row space, column
space and null space of a matrix and find the rank and nullity of a matrix. Compute linear
transformations, kernel, range and inverse of linear transformations, also find matrices of
general linear transformations. Find the dimension of spaces such as those associated
with matrices and linear transformations. Solve systems of linear equations using various
methods. Perform matrix algebra, invertibility, transpose and understand vector algebra in
Rn. Determine the relationship between coefficient, matrix invertibility, solutions to a
system of linear equations and 0inverse matrices. Calculate the characteristic equation,
eigenvalue and corresponding eigenvector of a given matrix and use them in applications.
Students are also expected to gain an appreciation for the applications of linear algebra to
areas such as computer science, engineering, biology and economics.
Course Outcomes On successful completion of this course, student will be able to know:
Upon successful completion of this course student will be able to:
1. explain the concepts of vector space and subspace.
2. define vector operations for vectors in Rn.
3. analyze whether a set S of vectors in a vector space V is a spanning set of V.
4. analyze whether a finite set of vectors in a vector space V is linearly independent.
5. explain the concepts of basis and dimension of a vector space.
6. explain the properties of vectors in the bases.
7. express row and column space of a matrix.
8. explain some functions defined between vector spaces.
9. express required conditions for a transformation to be a linear transformation.
10. find the kernel, range, rank and nullity of a linear transformation.
11. express some of the algebra operations between linear transformations.
12. able to find the matrix representation of a linear transformation.
13. explain whether a system of linear equations is consistent or inconsistent and find
the general solution to a consistent system.
14. explain the characteristic equations, eigenvalues and corresponding eigenvectors of
a given matrix.
Contents of Syllabus No. of Lectures
UNIT I: Vector Spaces
Binary operations, Definition of field with examples, Definition of vector space with examples, 12
Subspaces, Span of a set, Sum of subspaces, Linear dependence, and independence, Basis and
Dimension of a vector space, Coordinates of a vector relative to an ordered basis, Dimension
Theorem (without proof).
UNIT II: Linear Transformations
Linear transformation and its properties, Range and kernel of a linear transformation, Rank and 12
nullity of a linear transformation, Rank-nullity theorem(without proof), Inverse of a linear
transformation.
UNIT III: Matrix Representation of Linear Maps
Algebra of linear transformations, Composition of linear transformations, Matrix associated 12
with a linear transformation, Linear transformation associated with a matrix, Rank and nullity
of a matrix.
UNIT IV: Elementary operations and Eigenvalues
Elementary row operations and row-reduced echelon form, Inverse of a matrix through 12
elementary row operations, Solution of a system of linear equations, Verification of Cayley
Hamilton’s theorem, Eigenvalues and Eigenvectors of matrices.
Total No. of Lectures 48

1. *V. Krishnamurty, V. P. Mainra and J. L. Arora: An introduction to Linear Algebra,

Textbook*/ East-West Press, New Delhi, 2002.
References books 2. S. Lang, Introduction to Linear Algebra (2nd edition), Springer, 2005.
3. S. Kumaresan: Linear Algebra- A Geometric Approach, Prentice Hall of India, 1999.
4. S. Lipschutz and M. Lipson: Linear Algebra, Schuam’s Outline Series.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. IV Semester approved in BOS: 17-05-2022
Course Title Elements of Partial Differential Equations
Course Number MMBSMN4005
Credits 2
Course Category Minor
Prerequisite Courses Advanced Calculus and Ordinary Differential Equations
Contact Course 2 Lectures / week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives The main objectives of this course are to teach students to form and solve
partial differential equations and use them in solving some physical problems.
Course Outcomes On successful completion of this course, student should be able to:
 Formulate and classify partial differential equations.
 Solve linear and nonlinear partial differential equations using various
methods.
Contents of Syllabus No. of Lectures
UNIT I: Basic Concepts 6
Definition, order and degree of a partial differential equation, Formation of partial
differential equations by elimination of arbitrary constants as well as arbitrary
functions, Solution of a partial differential equation and its different kinds (complete,
general and particular solutions), Equations easily integrable.
UNIT II: First order PDE 6
Classification of partial differential equations; Solution of quasilinear partial
differential equations by Lagrange’s method, Integral surfaces through a given curve,
Standard forms of first order partial differential equation, Charpit’s method, Cauchy’s
problem and method of characteristics, Compatible system of first order partial
differential equations.
UNIT III: Second order PDE 6
Standard forms of second order linear partial differential equations, Classification,
Characteristic curves of semilinear partial differential equations, Solution of
quasilinear partial differential equations by Monge’s method.
UNIT IV: Higher order linear PDE 6
Homogeneous linear partial differential equations with constant coefficients and their
solutions, Nonhomogeneous linear partial differential equations with constant
coefficients: Different cases of complementary functions and particular integrals;
Equations reducible to linear partial differential equations with constant coefficients.
Total 24
Textbooks*/ 1. *Tyn Myint U: Partial Differential Equations of Mathematical Physics, American
Reference Elsevier Pub Co, 1973.
Books 2. N. Sneddon: Elements of Partial Differential Equations, McGraw Hill Book
Company, 1957.
3. T. Amarnath: A Elementary Course in Partial Differential Equations, Narosa
Publishing House, New Delhi, 2nd Ed., 2003.
 DEPARTMENT OF MATHEMATICS
ALIGARH MUSLIM UNIVERSITY, ALIGARH
Syllabus of B.A./B.Sc. IV Semester approved in BOS: 17-05-2022
Course Title Differential Equations
Course Number MMBSGE4006
Credits 4
Course Category Generic (Elective)
Prerequisite Courses Calculus of single and several variables
Contact Hours 4 Lectures/week
Type of Course Theory
Course Assessment Sessional Tests 30%
Semester Examination 70%
Course Objectives The main objectives of this course are to introduce the students to the exciting world of
differential equations, solutions of standard ordinary and partial differential equations, and
some of their applications.
Course Outcomes On successful completion of this course, student should be able to:
1. recognize ordinary differential equations of first order that can be solved by each of
methods: Separation of variables, integrating factor method, Bernoulli’s cases,
Clairaut’s form and use the appropriate one to solve them.
2. analyze real world scenarios to recognize when ordinary differential equations are
appropriate and formulate problems about scenarios.
3. solve homogeneous and non-homogeneous linear ordinary differential equations of
higher orders with constant and variable coefficients.
4. apply a range of techniques to find solutions of standard partial differential equations.
5. understand basic properties of standard partial differential equations.
6. know the techniques how to solve homogeneous and non-homogeneous linear partial
differential equations of higher orders with constant coefficients.
7. classify partial differential equations, apply analytical methods, and physically interpret
the solutions.
Contents of Syllabus No. of Lectures
UNIT I: First Order Ordinary Differential Equations 12
Ordinary differential equations, Order, degree and solutions of differential equations, Formation
of differential equations, Method of separataion of variables, Homogeneous differential
equations, Linear differential equations, Integrating factor, Bernoulli’s equation, Exact
differential equations, Integrating factors, Change of variables, Equations of first order and
higher degree, Equations solvable for p, x and y, Clairaut’s equation.
UNIT II: Higher Order Ordinary Differential Equations 12
Homogeneous and non-homogeneous linear differential equations of order n with constant
coefficients, Complementary functions, Particular integrals, Variation of parameters, Linear
differential equations of second order with variable coefficients: Reduction of order, Cauchy-
Euler and Legendre linear differential equations.
UNIT III: Basics of Partial Differential Equations 12
Definition, order and degree of a partial differential equation, Formation of partial differential
equations by elimination of arbitrary constants and arbitrary functions, Equations easily
integrable, Solution of first order partial differential equations and its different kinds (general,
complete, and particular solutions), Classification of first order partial differential equations,
Solution of first order partial differential equations by Lagrange’s method and Charpit’s method.
UNIT IV: Higher Order Linear Partial Differential Equations 12
Homogeneous linear partial differential equations with constant coefficients and their solutions,
Nonhomogeneous linear partial differential equations with constant coefficients: Different cases
of complementary functions and particular integrals; Equations reducible to linear partial
differential equations with constant coefficients.
Total No. of Lectures 48
 1. *Zafar Ahsan: Differential Equations and their Applications, Prentice Hall of India, New
Textbook*/ Delhi, 3rd Ed, 2016.
Reference 2. Frank Ayres Jr: Theory and Problems of Differential Equations, McGraw-Hill Book Company,
Books 1972.
3. Dennis G. Zill: A first course in differential equations, Cengage Learning, 2008.
4. M. D. Raisinghania: Ordinary and Partial Differential Equations, S. Chand, New Delhi, 18th
Ed., 2016.