NIT Agartala Mathematics-III Syllabus

M-301 MATHEMATICS III (3-1-0) 4

1. Mathematical Series:  Fourier Series; Half- Range series; Harmonic analysis. Solution in

Series Differentiation and integration of infinite series; Series solution of differential

equations; Bessel and Legendre equations, their  series solution, elementary properties of

Bessel functions and Legendre polynomials.

2. Complex Variables: Functions of complex variables; Exponential; Trigonometric; Hyperbolic

and logarithmic function; Differentiation; Analytic function; Cauchy Riemann equations;

Conjugate functions; Introduction to two  dimensional potential problem; Conformal

transformations; Schwartz- Christoffel transformational; Cauchy’s integral theorem; Taylor’s

and Laurent’s expansion; Branch points; Zeros; Poles and  residues; Simple problem on

contour integration.

3. Boundary Value Problem: Equations for vibration of strings; Heat flow and electrical

transmission lines; Laplace’s equation in cylindrical, Cartesian, polar and spherical polar

coordinates; Solution by separation of variables.

4. Integral Transforms: Fourier integral theorem; Fourier transforms; Convolution theorems;

Inversion theorems for Fourier and Laplace  transforms; Simple applications of these

transforms to one- dimensional problems.