University of Madras - Syllabus of Bachelor of Science (BSc) Mathematics - Semester III - Paper IV - Calculus and Differential Geometry
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.)