I am a 3rd year undergrad studying maths. I am undertaking a module for methods of PDE's and was wondering whether it would be possible for someone to recommend a suitable textbook for this topic, preferably one with plenty of practice questions and suitable explanations.
The topics covered are:
- Single first-order quasi-linear PDE: Characteristics, ground curves, the general method of solution.
- Classification of linear 2nd-order PDEs, canonical form, characteristics
- Well-posedness of problems, examples of ill-posed problems, the maximum principle for harmonic functions, uniqueness of solutions
- The wave equation for an elastic string, D’Alembert’s solution, initial and boundary-value problems, Goursat problem.
- The method of separation of variables for problems for hyperbolic, elliptic and parabolic equations.
- Solving 2D Laplace’s equation using the method of conformal mapping
- Systems of first-order PDEs, classification, canonical form, characteristics, Riemann invariants, simple waves