FYUGP CURRICULAR FRAMEWORK FOR BACHELORS PROGRAMME WITH
MATHEMATICS/APPLIED MATHEMATICS AS MINOR
CREDITS
COURSE TYPE OF
SEMESTER TITLE OF COURSE
CODE COURSE
THEORY TUTORIAL
I MMT122N MINOR MATH/APP. MATH: CALCULUS-I 4 2
II MMT223N MINOR MATH/APP. MATH: CALCULUS-II 4 2
III MMT322N MINOR MATH/APP. MATH: THEORY OF MATRICES 4 2
IV MMT422N MINOR MATH/APP. MATH: REAL ANALYSIS -1 3 1
V MMT522N MINOR MATH/APP. MATH: ALGEBRA-I 3 1
VI MMT622N MINOR MATH/APP. MATH: GRAPH THEORY 3 1
VII MMT722N MINOR MATH/APP. MATH: LINEAR ALGEBRA 3 1
VIII MMT822N MINOR MATH/APP. MATH: COMPLEX ANALYSIS 3 1
HEAD OF THE DEPARTMENT / CONVENOR BOUGS
Bachelors with Mathematics as Minor
1st Semester
MMT122N: Mathematics/Applied Mathematics: Calculus - I
Credits: 4 THEORY + 2 TUTORIAL Theory: 60 Hours & Tutorial: 30 Hours
Course Objectives: (i) To study and understand the notions of differential calculus and to imbibe the
acquaintance for using the techniques in other sciences and engineering. (ii) To prepare the students for
taking up advanced courses of mathematics.
Course Outcome: (i) After the successful completion of the course, students shall be able to apply
differential operators to understand the dynamics of various real life situations. (ii) The students shall be
able to use differential calculus in optimization problems.
Theory: 4 Credits
Unit –I
Limits and infinitesimals, Continuity ϵ − δ definition , types of discontinuities of functions,
Differentiability of functions, Successive differentiation and Leibnitz theorem, Partial differentiation,
Total differentiation, Homogenous functions and Euler’s theorem.
Unit –II
Indeterminate forms, Tangents and normals (polar coordinates only), Angle between radius vector and
tangent, Perpendicular from pole to tangent, angle of intersection of two curves, polar tangent, polar
normal, polar sub-tangent, polar sub-normal.
Unit –III
Curvature and radius of curvature, Pedal Equations, lengths of arcs, Asymptotes, Singular points,
Maxima and minima of functions. Bounded functions, Properties of continuous functions on closed
intervals, Intermediate value theorem, Darboux theorem.
Unit –IV
Rolle’s theorem and mean value theorems (with proofs) and their geometrical interpretation, Taylor’s
theorem with Lagranges and Cauchy’s form of remainder, Taylor’s series, Maclaurin’s series of
sin 𝑥, cos 𝑥, 𝑒 ! , log 𝑥 , 1 + 𝑥 ! .Envelope of a family of curves involving one and two parameters.
Tutorial: 2 Credits
Unit –V
Examples of discontinuous functions, nth derivative of product of two functions, involutes and evolutes,
bounds of function (Supremum and infimum).
Unit –VI
Tracing of cartesian equations of the form y = f ( x ) , y 2 = f ( x ) , tracing of the parametric equations.
Recommended Books:
1. Shanti Narayan and P.K. Mittal, Differential Calculus, S. Chand, 2016.
2. S. D. Chopra, M. L. Kochar and A. Aziz, Differential Calculus, Kapoor Sons.
3. Schaums outline of Theory and problems of Differential and Integral Calculus, 1964.
1. H. Anton, I. Birens and S. Davis, Calculus, John Wiley and Sons, Inc. 2002.
2. T.M. Apostal, Calculus Vol. I, John Wiley & Sons Inc, 1975.
3. S. Balachandra Rao and C. K. Shantha, Differential Calculus, New Age Publication, 1992.
4. S. Lang, A First Course in Calculus, Springer-Verlag, 1998.
5. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 2008.
6. G.B. Thomas and R.L. Finney, Calculus, Pearson Education, 2007.
7. Suggestive digital platforms web links: NPTEL/ SWAYAM/ MOOCS.
