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 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, 3rd ed., John Wiley (2004).
2. Kreyszig, E., Advanced Engineering Mathematics, 10th ed., John Wiley (2011).
3. Stewart, J., Calculus: Early Transcendentals, 7th ed., Cengage Learning (2010).

1. Greenberg, M. D., Advanced Engineering Mathematics, Pearson Education (2007).
2. Jain, R. K. and Iyengar, S. R. K., Advanced Engineering Mathematics, 4th ed., Alpha
Science Intl. Ltd. (2013).