Title- Partial Differential Equation (Code-09050302)
B.Sc. (Hons) Mathematics (3^{rd} Semester)
S.No. | Contents of the topics | Learning Objectives | Teaching Guidelines | Methodology | Time
(Hour) |
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 |
Students will be able to understand about PDEs and their solutions | Lecture should be effective so that student can grasp the topics easily | Assignments/ seminars/ Class tests/ Presentations | 14 |
2 | · Linear PDEs of Second and Highers Orders,
· Linear and Nonlinear homogeneous and Non homogeneous PDEs with, Constant Coefficients, · PDEs with variable coefficients reducible to Constant Coefficients, · PDEs with variable coefficients, constant coefficients, Their Complimentary Functions and Particular Integrals |
Students will be able to understand difference between linear and non linear PDEs | Lecture should be effective so that student can grasp the topics easily | Assignments/ seminars/ Class tests/ Presentations | 12 |
3 | · Classification of Linear PDEs 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 |
Students will be able to understand Canonical form s and Monge’s Method | Lecture should be effective so that student can grasp the topics easily | Assignments/ seminars/ Class tests/ Presentations | 10 |
4 | · Cauchy’s Problem for Second Order PDEs,
· Characteristic Equations and Characteristic Curves of 2^{nd} Order PDEs, · Method of Separation of variables, · Solution of Laplace Equation, Solution of Wave equation (One and Two dimensions, · Diffusion (Heat) Equation (one and two dimensions) in Cartesion Coordinate system |
Students will be able to understand about Laplace, Heat and Wave equations | Lecture should be effective so that student can grasp the topics easily | Assignments/ seminars/ Class tests/ Presentations | 14 |
Books Recommended:
- 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