Classifications of Differential Equations: origin and applications, family of curves, isoclines. First order equations: separation of variable, exact
equation, integrating factor, Bernoulli equation, separable equation, homogeneous equations, orthogonal trajectories, Picard’s existence and uniqueness theorems. Second order equations: variation of parameter, annihilator methods. Series solution: power series solutions about regular and singular points. Method of Frobenius, Bessel’s equation and Legendre equations. Wronskian determinant, Phase portrait analysis for 2nd order system, comparison and maximum principles for 2nd order equations. Linear system: general properties, fundamental matrix solution, constant coefficient system, asymptotic behavior, exact and adjoint equation, oscillatory equations, Green’s function. Sturm-Liouville theory. Partial Differential Equations: Classifications of PDE, method of separation of variables, characterstic method.
- S. L. Ross, “Differential Equations”, Wiley-India Edition, 2009.
- E. A. Coddington, “An Introduction to Ordinary Differential Equations”, Prentice Hall of India, 2012
- G. F. Simmons, S. G. Krantz, “Differential Equations”, Tata Mcgraw-Hill Edition, 2007.
- B. Rai, D. P. Choudhury, “A Course in Ordinary Differential Equation”, Narosa Publishing House, New Delhi, 2002.
- R. P. Agarwal, D. O Regan, “Ordinary and Partial Differential Equations”, Univer sitext. Springer, 2009.