Ordinary Differential Equations: Initial and boundary value problems, Basic existence, Uniqueness theorems for a system of ODE, Gronwall’s lemma, Continuous dependence on initial data, Linear systems with variable coefficients, Variation of parameter formula, Floquet theory, Systems of linear equations with constant coefficients, Stability of equilibrium positions.Partial Differential Equations: Single and systems of PDE, First order PDE, Semi-linear and nonlinear equations (Monge’s method), Four important linear PDE, Transport equations, Laplace equations, Fundamental solution, Mean value formulas, Green’s functions, Energy methods, Heat equation, fundamental solution, Mean value formula, Energy methods, Wave equations, Solutions by spherical mean, Energy method, Maximum principle for elliptic and parabolic equations with applications.
- V. I. Arnold, Ordinary Differential Equations , Prentice Hall of India.
- Brauer and Nohel, Qualitative Theory of Differential Equations, Dover Publications.
- Coddington and Levinson, Ordinary Differential Equations, Tata Mcgraw-Hill.
- Fritz John, Partial Differential Equation, Narosa Publications.
- M. Renardy and R. C. Rogers, An Introduction to Partial Differential Equations, Springer International Edition.
- L. C. Evans, Partial Differential Equations, AMS Graduate Studies in Mathematics, Vol 19.