Ordinary and Partial Differential Equations and Applications
Ordinary and Partial Differential Equations and Applications. Instructors: Dr. P. N. Agrawal and Dr. D. N. Pandey, Department of Mathematics, IIT Roorkee. Differential equation are used to express many general laws of nature and have many applications in physical, biological, social, economical and other dynamical systems. This course 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, Green's function, autonomous systems, phase plane, critical points and stability for linear and non-linear systems, eigenvalue problems, Sturm-Liouville problem. Classification of first order PDE, existence and uniqueness of solutions, Nonlinear PDE of first order, Cauchy method of characteristics, Charpit's method, PDE with variable coefficients, canonical forms, characteristic curves, Laplace equation, Poisson equation, wave equation, homogeneous and nonhomogeneous diffusion equation, Duhamel's principle. This course has tremendous applications in diverse fields of Engineering and Sciences such as control theory, numerical analysis and dynamical systems etc. (from nptel.ac.in)
| Lecture 10 - Solution of Homogeneous Linear System with Constant Coefficients (cont.) |
The method to find the solution of a homogeneous linear system with constant coefficients is discussed when the matrix A has a pair of complex roots.
Go to the Course Home or watch other lectures: