Course | Dual Degree (B. Tech + Master of Science / Master of Technology) |
Semester | Sem. II |
Subject Code | MA121 |
Subject Title | Vector Calculus and Differential Equations |
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.
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).
1. Greenberg, M. D., Advanced Engineering Mathematics, Pearson Education (2007).
2. Jain, R. K. and Iyengar, S. R. K., Advanced Engineering Mathematics, Narosa (2005).