BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, Pilani
Pilani Campus
AUGS/ AGSR Division
FIRST SEMESTER 2023-2024
Course Handout (Part II)
Date: 09/08/2023
In addition to part-I (General Handout for all courses appended to the timetable) this portion gives further
specific details regarding the course.
Course No. : MATH F111
Course Title : Mathematics-I
Instructor-in-charge : ANIRUDH SINGH RANA
Team of Instructors: Anirudh Rana, Balram Dubey, Devendra Kumar, Gaurav Dwivedi, Pradipkumar
Haribhau Keskar, Rahul Kumar, Sangita Yadav, Trilok Mathur, Shailesh Trivedi, Divyum Sharma, Pramod
Eyyunni, Jitender Kumar
1. Course Description: The course is intended as a basic course in calculus of several variables and vector
analysis. The geometry of objects in two- or three-dimensional spaces is studied: near a point on them (locally)
using differentiation and on the whole (globally) using integration. It includes polar coordinates, convergence
of sequences and series, Maclaurin and Taylor series, partial derivatives, vector calculus leading to theorems
of Green, Stokes and Gauss.
2. Scope and Objective of the Course:
● Calculus is fundamental to every branch of science and engineering, as all dynamics is modeled
through differential and integral equations.
● Functions of several variables appear frequently in science.
● The derivatives of the functions of several variables are more interesting because of the several degrees
of freedom available.
● The integrals of the functions of several variables occur in several places such as probability, fluid
dynamics, electrical sciences, just to name a few. All lead in a natural way to functions of several
variables.
● The objective of the course is to lay the foundations for these topics.
3. Textbook:
J. Hass, C. Heil and M. D. Weir: Thomas’ Calculus, 14th Edition, Pearson Education, 2018.
4. Reference Books:
(i) E. Kreyszig : Advanced Engineering Mathematics, 10th Edition John Wiley and Sons 2011.
(ii) T. M. Apostol : Calculus Vols I and II, 2nd Edition, John Wiley and Sons, 1967 and 1969.
5. Course Plan:
_
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BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, Pilani
Pilani Campus
AUGS/ AGSR Division
Module Number Lecture session/Tutorial Ref. to textbook: Learning Outcome
Session. chap/Sec.
1. Limits and Self-Study: Properties 2.3 to 2.6 Understanding of real
continuity of real of limits, infinity as a valued functions of one
valued function of limit, continuity real variable
one real variable
2. Vector-valued L1: Limit, continuity and 13.1-13.3 Understanding of vector
functions differentiability of vector (projectile motion valued functions of one
function excluded) variable, motion and its
L2: Arc length, velocity path in space
unit tangent vector
3. Motion in space L3: Curvature, normal 13.4, 13.5 The relation between the
vector, torsion dynamics and geometry of
L4: TNB frame, motion
tangential and normal
components of velocity
and acceleration
4. Polar coordinates L5: Polar coordinates 11.3 -11.5, 11.7 The curvilinear coordinate
L6-L7: Graphing in polar systems like polar
coordinates coordinates can be more
L8: Integration using natural than Cartesian
polar coordinates. coordinates many a times
L9: Polar equations of
conic sections
5. Functions of several L10: Functions of several 14.1, 14.2 Limits and continuity of
variables variables, level curves functions of several
L11: Limits, continuity variables is more intricate
6. Partial L12: Partial derivatives 14.3, 14.4 Difference between
differentiation L13: Differentiability ordinary and partial
L14: Chain rule derivatives
7. Directional L15: Directional 14.5, 14.6 Generalizations of
derivatives, derivatives, gradient partial derivatives and their
gradient vectors, vectors applications
tangent planes and L16: Tangent planes and
normal lines and normal lines and
linearization linearization
8. Extreme values L17: Maximum, Optimization (maximize or
and saddle point of a minimum and saddle 14.7, 14.8 minimize) functions of
function of several real points of functions of several variables locally as
variables several real variables well as globally
L18: Lagrange
multipliers
9. Double integrals L19: Double integrals Evaluation of area of
L20: Areas and 15.1-15.4 planar regions and
volumes volumes using iterated
L21: Change of integrals
integrals from rectangular
to polar coordinates
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BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, Pilani
Pilani Campus
AUGS/ AGSR Division
10. Triple integrals L22-L23: Triple Volumes of solids in
integrals in rectangular, 15.5, 15.7, 15.8 space using suitable
cylindrical and curvilinear coordinate
spherical coordinates system
L24: Substitution in
integrals
11. Line integrals of L25: Line integrals Different integrals of
vector fields and L26-L27: Work, 16.1-16.4 vector fields on objects
Green's theorem in circulation, flux, path in space; applications to
plane independence, Potential flow, flux, work etc.;
function, conservative their mutual
relationship via
field
Green's theorem
L28: Green's theorem
generalizing the
in plane fundamental theorem
of integral calculus
12. Surface integrals, L29-L32: Surface area 16.5-16.8 Divergence theorem and
Gauss' divergence and surface integral (from sec 16.8 Stokes' theorem further
theorem and Stokes' L33-L35: Gauss' laws of generalize Green's
theorem divergence theorem, theorem
electromagnetic
Stokes' theorem
theory and
hydrodynamics
excluded)
13. Infinite L36: Convergence of 10.1 - 10.8 Differentiate clearly
sequences and series sequences and series of (10.1 is for self between three types of
real numbers study) series convergence with
L37-L38: Different examples and counter
tests of convergence for examples,
the series of non Approximating
negative terms, Absolute functions with
and conditional polynomials
convergence,
alternating series
L39: Power series,
Maclaurin series,
Taylor series of
functions
Note: In tutorials, problems based on the lectures will be practiced, and tutorial tests will be conducted.
6. Evaluation Scheme:
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BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, Pilani
Pilani Campus
AUGS/ AGSR Division
Evaluation Weightage Duration Date of Evaluation
Components (Marks) (Minutes)
1 Midsemester Test 35% 90 As announced by
AUGSD
2 Quizzes 20% 20 Unannounced
3 Comprehensive Exam 45% 180 As announced by
AUGSD
7. Make-up Policy: Make-up for test will be given only for very genuine cases and prior permission
has to be obtained from I/C. No makeup will be given in tutorial tests under any circumstances.
8. Chamber consultation hour: To be announced by the respective Instructor. The chamber consultation
hour of all the instructors will be uploaded on Nalanda website.
9. Notices: The notices concerning this course will be displayed on Nalanda website.
Instructor-in-charge
MATH F111
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