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  • 11:45 AM, Wednesday, 20 Nov 2019


Course Undergraduate
Semester Sem. II
Subject Code MA121
Subject Title Vector Calculus and Ordinary Differential Equations

Syllabus

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.

Ordinary 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.

Text Books

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

2. Jain, R. K. and Iyengar, S. R. K., Advanced Engineering Mathematics, Narosa (2005).