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

SYLLABUS

Semester IV - Paper VII - Vector Calculus Fourier Series and Fourier Transforms

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

Vector Differentiation:

gradient, divergence, curl, directional derivative, unit normal to a surface.

Vector integration:

line surface and volume integrals; theorems of Gauss, Stokes and Green (without proof) - simple problems.

Fourier Series:

Expansions of periodic function of period 2π expansion of even and odd functions: half range series.

Fourier transforms:

Infinite Fourier transform (Complex form, no derivation); sine and cosine transforms; simple properties of Fourier Transforms; Convolution theorem; Parseval's Identity.

Reference Books :-

1. Engineering Mathematics Volume 3: M. K. Venkataraman (National Publishing Co.)

2. Engineering Mathematics Volume 3: P. Kandasamy and others (S. Chand and Co.)

3. Vector Analysis: Murray Spiegel (Schaum Publishing company, New York)

4. Vector Analysis: P. Duraipandian and Laxmi Duraipanciian (Emerald Publishers)