Differential Equations

Code: MA542 | L-T-P-C: 4-0-0-8

Review of fundamentals of Differential equations (ODEs); Existence and uniqueness theorems, Power series solutions, Systems of Linear ODEs, Stability of linear systems.

First order linear and quasi-linear partial differential equations (PDEs), Cauchy problem, Classification of second order PDEs, characteristics, Well-posed problems, Solutions of hyperbolic, parabolic and elliptic equations, Dirichlet and Neumann problems, Maximum principles, Green's functions.

Texts:

1. E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, Tata McGraw Hill, 1990.
2. S. L. Ross, Differential Equations, 3rd Edn., Wiley India, 1984.
3. I. N. Sneddon, Elements of Partial Differential Equations, Dover Publications, 2006.
4. F. John, Partial Differential Equations, Springer, 1982.

References:

1. S. J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Publications, 1993.
2. E. L. Ince, Ordinary Differential Equations, Dover Publications, 1958.
3. F. Brauer and J. A. Nohel, The Qualitative Theory of Ordinary Differential Equations: An Introduction, Dover Publications, 1969.