Differential Equation

Ordinary Differential Equations:


Unit I: First order differential equations, statement of existence and uniqueness theorem, exact, linear and Bernoulli equations, orthogonal trajectories, applications.

Unit II: Second and higher order linear differential equations with constant coefficients, method of undetermined coefficients, variation of parameters, operator method, Power series solutions, Legendre and Bessel equations.

Partial Differential Equations:


Unit III: Formulation of partial differential equations by eliminating arbitrary constants and functions, Lagrange’s linear equation, Charpit’s method, classification of second order PDEs.

Unit IV: Method of separation of variables, wave equation, heat equation, Laplace equation, Fourier series solutions.