Title: Partial Differential Equation (Code-09050302)
B.Sc. (Hons), Semester-III
|S.No.||Topic||Domain||Hours as per UGC|
|1||Partial Differential Equations: Formation, Order and Degree
Linear and Non-linear PDE of First Order, Complete Solution, Singular Solution, General Solution, Solution of Lagrange’s Linear Equations, Charpit’s General Method of Solution, Compatible systems of First Order Equation
Solution of Lagrange’s Linear Equations, Jacobi’s Method
|2||Linear PDEs of Second and Highers Orders, Linear and Nonlinear homogeneous and Nonhmogeneous PDEs with, Constant Coefficients, PDEs with variable coefficients reducible to Equations with Constant Coefficients, PDEs with variable coefficients reducible to equations with, variable coefficients reducible to equations with constant coefficients, Their Complimentary Functions and Particular Integrals||Must know||12|
|3||Classification of Linear Partial Differential Equations of, Second Order, Reduction of Second Order Linear PDEs to, Canonical (Normal) forms and their solutions, Solutions of Linear Hyperbolic Equations, Monge’s Method for PDEs of Second Order||Must know||10|
|4||Cauchy’s Problem for Second Order PDEs, Characteristic Equations and Characteristic Curves of Second Order PDEs, Method of Separation of variables, Solution of Laplace Equation, Solution ofWave equation (One and Two dimensions, Diffusion (Heat) Equation (one and two dimensions) in Cartesion Coordinate system||Nice to know||14|
- A.Murray: Introductory Course on Differential Equations, Orient Longman, (India),1967.
- Erwin Kreyszing : Advanced Engineering Mathematics, John Wiley & Sons, Inc., New York, 1999 Co. Ltd.
- Ian N.Sneddon : Elements of Partial Differential Equations, McGraw Hill Book company, 1988.
- Frank Ayres : Theory and Problems of Differential Equations, McGraw Hill Book Company, 1972.
- N. Sharma & Kehar Singh : Partial Differential Equations