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### Title-PDE (Code-09010302)

 S.N Unit Content of the topics Learning objects Teaching Guidelines Methodology Time (Hrs) 1 one 1.    Partial differential equations: Formation, order and degree, 2.    Linear and Non-Linear Partial differential equations of the first order: 3.    Complete solution, singular solution, General solution, 4.    Solution of Lagrange’s linear equations, Charpit’s general method of solution. 5.    Compatiblesystems of first order equations, Jacobi’s method. Students will be able to   1.       Boundedness of the set of real numbers; least upper bound, greatest lower bound of a set, 2.       Bolzano-Weiestrass theorem. 3.       Heine-Borel Theorem. Lecture should be effective so that student can grasp the topics easily. 1. Lecture. 2.  Seminar. 3. Discussion/Interaction with Students. 4. Assignment. 5.  Discussion on Assignment. 6. Evaluation of Assignment. 15 2 Two 1.    Linear PDE of second and higher orders, 2.    Linear and non-linear homogenous and non-homogeneous equations with constant co-efficients, 3.    PDE with variable co-efficients reducible to equations with constant coefficients, their complimentary functions and particular Integrals, 4.    Equations reducible to linear equations with constant co-efficients. 5.    Classification of linear partial differential equations of second order, 6.    Hyperbolic, parabolic and elliptic types, Reduction of second order linear partial differential equations to 7.    Canonical  (Normal) forms and their solutions, Solution of linear hyperbolic equations, 8.    Monge’s method for partial differential equations of second order. Students will be able to 1.       Linear partial differential equations of second and higher orders, Linear and non-linear, 2.       Homogenious and non-homogenious equations with constant co-efficients, 3.       Reduction of second order linear partial differential equations to Canonical, 4.       (Normal) forms and their solutions, Solution of linear hyperbolic equations, Monge’s method for partial differential equations of second order. Lecture should be effective so that student can grasp the topics easily. 1.    Lecture. 2.     Seminar. 3.    Discussion/Interaction with Students. 4.    Assignment. 5.    Discussion on Assignment. 6.    Evaluation of Assignment 15 3 Three 1.    Cauchy’s problem for second order partial differential equations, 2.    Characteristic equations and characteristic curves of second order partial differential equation, 3.    Method of separation of variables, 4.    Solution of Laplace’s equation, 5.    Wave equation (one and two dimensions), 6.    Diffusion (Heat) equation (one and two dimension) in Cartesian Co-ordinate system. To make students familiar with Cauchy’s problem for second order partial differential equations, Characteristic equations and characteristic curves of second order partial differential equation, Method of separation of Variables: Solution of Laplace’s equation, Wave equation (one and two dimensions), Diffusion (Heat) equation (one and two dimension) in Cartesian Co-ordinate system. Lecture should be effective sothat student can grasp the topics easily. 1.    Lecture. 2.    Seminar. 3.    Discussion/ Assignment. 4.    Discussion on Assignment. 5.    Evaluation of Assignment 15