SEMESTER II
VECTOR CALCULUS AND DIFFERENTIAL EQUATIONS
MA121
(2 – 1 – 0) 3 credits
Vector Calculus: scalar and vector fields – level surfaces – directional derivatives, gradient, curl,
divergence – Laplacian – line and surface integrals – theorems of Green, Gauss, and Stokes.
Sequences and Series of Functions: complex sequences – sequences of functions – uniform
convergence of series – test for convergence – uniform convergence for series of functions.
Differential Equations: first order ordinary differential equations – classification of differential
equations – existence and uniqueness of solutions of initial value problem – higher order linear
differential equations with constant coefficients – method of variation of parameters and
method of undetermined coefficients – power series solutions – regular singular point –
Frobenius method to solve variable coefficient differential equations.
Special Functions: Legendre polynomials, Bessel's function, gamma function and their properties
– Sturm‐Liouville problems.
Textbooks:
1. Ross, S. L., Differential Equations, Blaisedell (1995).
2. Kreyszig, E., Advanced Engineering Mathematics, 9th ed., John Wiley (2005).
3. Stewart, J., Calculus: Early Transcendentals, 5th ed., Brooks/Cole (2007).
References:
1. Greenberg, M. D., Advanced Engineering Mathematics, Pearson Education (2007).
2. Jain, R. K. and Iyengar, S. R. K., Advanced Engineering Mathematics, Narosa (2005).
PH121
PHYSICS