UNIVERSITY OF MADRAS
B.Sc. DEGREE COURSE IN MATHEMATICS
SEMESTER SYSTEM WITH CREDITS
(Effective from the Academic Year 2003-2004)

SYLLABUS

Semester III - Paper IV - Calculus and Differential Geometry

Duration of Examination: 3 hrs
Maximum Marks: 100
Credits: 4

Curvature :-

Curvature; radius of curvature in Cartesian coordinates; polar coordinates; equation of a straight line, circle and conic; radius of curvature in polar coordinates; p-r equations; evolutes; envelopes;

Asymptotes :

Methods (without proof) of finding asymptotes of rational algebraic curves with special cases.

Beta and Gamma functions, properties and simple problems.

Double Integrals; change of order of integration; triple integrals; applications to area, surface area and volume.

Reference books :-

1. Calculus : S. Narayanan and others (S. Viswanathan publishers)

2. Integral Calculus and differential equations : Dipak Chatterjee (TATA McGraw Hill Publishing company ltd.)