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
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.