TitlePDE (Code09010302)
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 NonLinear 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. BolzanoWeiestrass theorem. 3. HeineBorel 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 nonlinear homogenous and nonhomogeneous equations with constant coefficients, 3. PDE with variable coefficients reducible to equations with constant coefficients, their complimentary functions and particular Integrals, 4. Equations reducible to linear equations with constant coefficients. 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 nonlinear, 2. Homogenious and nonhomogenious equations with constant coefficients, 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 Coordinate 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 Coordinate 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 