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#### B.Sc. (Hons) Mathematics (3rd 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 2nd  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:

1. A.Murray: Introductory Course on Differential Equations, Orient Longman, (India),1967.
2. Erwin Kreyszing : Advanced Engineering Mathematics, John Wiley & Sons, Inc., New York, 1999 Co. Ltd.
3. Ian N.Sneddon : Elements of Partial Differential Equations, McGraw Hill Book company, 1988.
4. Frank Ayres: Theory and Problems of Differential Equations, McGraw Hill Book Company, 1972.
5. N. Sharma & Kehar Singh : Partial Differential Equations