Review of power series and analytic functions. Power series solutions about regular and singular points (Frobenius method). Special functions: Gamma, Bessel, Legendre and Hermite functions.



Boundary value problems for linear second order equations. Regular and singular Sturm-Liouville eigenvalue problems and their properties. Adjoint and selfadjoint.



Quantitative method for autonomous equations. Equilibria and phase line. Stability of linear systems. Linearization and local stability.



Numerical methods: Euler and improved Euler methods. Errors in numerical method, local truncation error (discretization error). Runge-Kutta methods.



References:

1.Nagle, K.B., Saff, E.B. & Snider, A.D. (2003). Fundamentals of Differential Equations and Boundary Value Problems (4th Edition). Addison Wesley.

2.Edwards, C.H., Penney, D.E. & Edwards, H.C. (2003). Differential Equations and Boundary Value Problems: Computing and Modeling (3rd Edition). Prentice Hall.

3.Polking, J., Boggess, A. & Arnold, D. (2002). Differential Equations With Boundary Value Problems (1st Edition). Prentice Hall.