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Title-PDE (Code-09010302)

S.No. Unit Contents Domain Time(Hrs)
1 One 1.       Partial Differential Equations: Formation

2.       Order and Degree

3.       Linear and Non-linear PDE of First Order

4.       Complete Solution, Singular Solution, General Solution

5.       Solution of Lagrange’s Linear Equations

6.       Charpit’s General Method of Solution

7.       Compatible systems of First Order Equation

8.       Solution of Lagrange’s Linear Equations

Must know

Nice to know

2 Two 1.       Linear PDEs of Second and Highers Orders

2.       Linear and Nonlinear homogeneous and Non homogeneous PDEs with Constant Coefficients

3.       PDEs with variable coefficients reducible to Equations with Constant Coefficients

4.       PDEs with variable coefficients reducible to equations with variable coefficients reducible to equations with constant coefficients

5.       Their Complimentary Functions and Particular Integrals

6.       Classification of Linear Partial Differential Equations of Second Order

7.       Reduction of Second Order Linear PDEs to Canonical (Normal) forms and their solutions

8.       Solutions of Linear Hyperbolic Equations

9.       Monge’s Method for PDEs of Second Order

Must know 15
3 Three 1.       Cauchy’s Problem for Second Order PDEs

2.       Characteristic Equations and Characteristic Curves of Second Order PDEs

3.       Method of Separation of variables

4.       Solution of Laplace Equation

5.       Solution ofWave equation (One and Two dimensions

6.       Diffusion (Heat) Equation (one and two dimensions) in Cartesion Coordinate system

Must know

Nice to know


Books Recommended:

  1. Murray, D.A. Introductory Course on Differential Equations. New Delhi : Orient Longman (India), 1967.
  2. Kreyszing, Erwin. Advanced Engineering Mathematics. New York:  John Wiley, 1999.
  3. Sneddon, Ian N. Elements of Partial Differential Equations. New York: McGraw-Hill, 1988.