I am looking for an introductory book on Numerical Analysis and Differential Equations. I have done my B.Sc. in Math and I'm preparing for M.Sc entrance exams. The syllabus for the exam contains the following topics:
- Existence and Uniqueness of solutions of initial value problems for first order ordinary differential equations, singular solutions of first order ordinary differential equations, System of first order ordinary differential equations, General theory of homogeneous and non- homogeneous linear ordinary differential equations, Variation of parameters, Sturm Liouville boundary value problem, Green’s function.
- Lagrange and Charpit methods for solving first order PDEs, Cauchy problem for first order PDEs, Classification of second order PDEs, General solution of higher order PDEs with constant coefficients, Method of separation of variables for laplace. Heat and Wave equation.
- Numerical solutions of algebraic equation, Method of iteration and Newton-Raphson method, Rate of convergence, Solution of systems of linear algebraic equations using Guass elimination and Guass-Seidel method, Finite differences, Lagrange, Hermite and Spline interpolation, Numerical integration, Numerical solutions of ODEs using Picard, Euler, modified Euler and second order Runge- Kutta methods.
I've had an introduction to ODE from Pollard and Tenenbaum but I have no prior experience with PDE and Numerical Analysis. This exam only contains MCQ so I am more interested in getting to know how to apply a particular method fast, rather than the proofs and justifications behind it, something like Stewart's Calculus that has lots of solved problems, skips the harder proofs and is very concise and suitable for self study.