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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.

Thanks!

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The reference book I normally use for the basics on PDEs is Partial Differential Equations, by Lawrence C. Evans. I think it covers most (maybe all) the topics you mention.

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