I have an exam in January and I want to prepare ODE and PDE section first as they carry good weightage. For ODE I have S.L. Ross' book, which I like and have always referred to. But I haven't done PDE yet and I have to prepare it now. My syllabus consists of these topics-
- Linear and quasilinear first order partial differential equations
- method of characteristics; second order linear equations in two variables and their classification
- Cauchy, Dirichlet and Neumann problems; solutions of Laplace
- wave in two dimensional Cartesian coordinates
- Interior and exterior Dirichlet problems in polar coordinates
- Separation of variables method for solving wave and diffusion equations in one space variable
- Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations.
My main and only focus is these topics with as many problems I can try on them. Can someone recommend a good book/s which covers all these topics.