### MA2102 Differential Equations - [Only for 2024 batch onwards]

#### Course Details

**Ordinary Differential Equations:**

Geometrical meaning of a first order ODE, First order linear and exact equations, integrating factors, homogeneous linear equations with constant coefficients of higher order, non-homogeneous linear equations with constant coefficients of higher order, linear independence of solutions and Wronskian, complex roots and repeated roots of characteristic equation, solution of non- homogeneous equations using Method of variation of parameters.

**Series solution of ODE:**

Power series method, Legendre's equation, Orthogonality of Legendre polynomials, Frobenius method, Bessel's equation, Orthogonality of Bessel functions.

**Partial differential equations:**

First order equations using Lagrange’s method, classification of second order equations, D'Alembert's solution of wave equation, solutions of heat equation, wave equation and Laplace equation (Cartesian coordinates) using separation of variables.

#### Course References:

Text:

E. Kreyszig, Advanced Engineering Mathematics, 10th Ed., John Willey & Sons, 2010.

References:

1. W.E. Boyce and R.C. DiPrima, Elementary Differential Equations, 7th Ed., John Wiely& Sons, 2002.

2. S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover, 2006.

3. N. Piskunov, Differential and Integral Calculus Vol. I & II, Mir Publishers, 1974.