Ordinary and Partial Differential Equations and Applications

This course is a basic course offered to UG/PG students of Engineering/Science background. It contains existence and uniqueness of solutions of an ODE, homogeneous and non-homogeneous linear systems of differential equations, power series solution of second order homogeneous differential equations. Frobenius method, boundary value problems for second order ODE, Greens function, autonomous systems, phase plane, critical points and stability for linear and non-linear systems, eigen value problems, Sturm-Liouville problem. Classification of first order PDE, existence and uniqueness of solutions, Nonlinear PDE of first order, Cauchy method of characteristics, Charpits method, PDE with variable coefficients, canonical forms, characteristic curves, Laplace equation, Poisson equation, wave equation, homogeneous and nonhomogeneous diffusion equation, Duhamels principle. This course has tremendous applications in diverse fields of Engineering and Sciences such as control theory, numerical analysis and dynamical systems etc.INTENDED AUDIENCE : UG and PG students of technical institutions/ universities/colleges.PREREQUISITES : NILINDUSTRY SUPPORT : NIL

Week 1: Existence and uniqueness of solutions of ODE
Week 2: Linear system
Week 3: Power Series solution
Week 4: Fronius Series solution
Week 5: Stability of systems
Week 6: Boundary Value Problems
Week 7: Introduction to First order PDE
Week 8: Nonlinear PDE of 1st Order
Week 9: Classification and Canonical forms of Second order PDE
Week 10: Laplace equation
Week 11: Wave equation
Week 12: Heat equation