Syllabus
|
Course Code: B-MAT 504 Course Name: Partial Differential Equations and Integral Transforms |
||
| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
|---|---|---|
| 1 | Classification of linear partial differential equations of second order, Hyperbolic, parabolic and elliptic types, Reduction of second order linear partial differential equations to Canonical (Normal) forms and their solutions. Characteristic equations and characteristic curves of second order partial differential equation. | |
| 2 | Solution of linear hyperbolic equations. Monge’s method for solving non-linear second order
partial differential equations. Laplace equation: elementary solutions of Laplace’s equation. Method of separation of variables: Solution of Laplace’s equation, Wave equation and Diffusion (Heat) equation in one and two dimensions Cartesian Co-ordinate system. |
|
| 3 | Laplace Transforms – Existence theorem for Laplace transforms, Linearity and shifting properties of the Laplace transforms, Laplace transforms of derivatives and integrals, Convolution theorem, Inverse Laplace transforms, solution of differential equations using Laplace transform. | |
| 4 | Fourier transforms: Linearity and shifting properties, Convolution Theorem, Fourier Transform of Derivatives, Parseval’s identity for Fourier transforms. Solving differential Equations using Fourier Transforms. | |
