Could someone suggest me one or more good books on the following topics:
- Nonlinear systems: fixed point and Newton's method
- Optimization: steepest descent and Newton's-quasi newton methods
- ODE (IVPs-BVPs, explicit and implicit methods)
- PDE (Laplace Equation, Diffusion equation, finite difference method)
I'm looking for not-too formal (introductory) textbooks. I don't need theorems or proofs, but the general concepts should be clearly explained.
I'll appreciaty any help. Thank you.
Try "numerical analysis" by L. Ridgway Scott. Should easily cover the first 3 on your list, when it comes to numerical pde, go on the Oxford pde site, and look for the finite elements notes by Endre Suli, they're very good, the pdf is available, and hopefully you should find a pdf for the Scott book as well.