Ordinary Differential Equations

Code: MA548 | L-T-P-C: 3-1-0-8

Prerequisites: Nil

First order non-linear differential equations: Existence and Uniqueness problem, Gronwall’s inequality, Peano existence theorem, Picard existence and uniqueness theorem, interval of definition. Second order linear differential equations: general solution for homogeneous equations, superposition of solutions, methods of solution for non-homogeneous problems, undetermined coefficients, variation of parameters, series solutions for ODEs, types of singularity, solution at an ordinary point, solution at a singular point. nth order linear differential equations: system of equations, homogeneous system of equations, fundamental matrix, Abel-Liouville formula, system of non-homogeneous equations, stability of linear systems. Theory of two-point BVP: Green’s functions, properties of Green’s functions, Adjoint and self-adjoint BVP. Strum-Liouville’s problem, orthogonal functions, eigenvalues and eigen functions, completeness of the eigen functions.

Texts:

1. Boyce, W. E. and DiPrima, R. C., Elementary Differential Equation and Boundary Value Problems, 7th Edition, John Wiley & Sons (Asia), 2001.
2. Ross, S. L., Differential Equations, 3rd edition, Wiley 1984.

References:

1. Simmons, G. F., Differential Equations with Applications and Historical Notes, McGraw Hill, 1991
2. Coddington, E. A., An Introduction to Ordinary Differential Equations, Prentice- Hall, 1974.
3. Farlow, S. J., An Introduction to Differential Equations and Their Applications, McGraw-Hill International Editions, 1994.