MALAVIYA NATIONAL INSTITUTE OF TECHNOLOGY, JAIPUR.
DEPARTMENT OF MATHEMATICS
SYLLABUS
MAT-623 Partial Differential Equations
4 Credits( 3L+1T+0P)
Formulation and classification of Linear and Quasi- Linear Partial Differential Equation of
the First Order, Lagrange’s Method for Linear Partial Differential Equation of the First Order
, Pfaffian Equation, Cauchy Problems, Complete Integrals of Non Linear Equations of First
Order, Four Standard Forms, Charpit’s Method, Monge’s Method. Linear Equations with
Constant Coefficients, Classification of Second Order Linear PDE and Reduction to
Canonical Forms, Laplace, Poisson’s and Helmholtz, Wave and Diffusion Equations in
Various Coordinate Systems and their Solutions Under Different Initial and Boundary
Conditions. Green’s Functions and Properties. Existence Theorem by Perron’s Method. Heat
Equation, Maximum Principle. Uniqueness of Solutions via Energy Method. Uniqueness of
Solutions of IVPs for Heat Conduction Equation.
Books Recommended:
1. Introduction to Partial Differential Equations, K.Sankara Rao, PHI learning Pvt. Ltd.
2. Partial Differential Equations, P Prasad and R Ravindran, New Age International, 2011.
3. T. Amaranath , An Elementary Course in Partial Differential Equations, Narosa, New
Delhi.
4. I. N. Sneddon, Elements of Partial Differential Equation McGraw – Hill, New York.
5. J N Sharma and K Singh, Partial Differential Equations for engineers and scientists, 2nd
Edition, Narosa, New Delhi.