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This volume is application-oriented and rich in examples. Going through these examples, the reader is able to easily grasp the basics of PDEs.\u003c\/p\u003e\u003cp\u003eChapters One to Five are organized to aid understanding of the basic PDEs. They include the first-order equations and the three fundamental second-order equations, i.e. the heat, wave and Laplace equations. Through these equations, we learn the types of problems, how we pose the problems, and the methods of solutions such as the separation of variables and the method of characteristics. The modeling aspects are explained as well. The methods introduced in earlier chapters are developed further in Chapters Six to Twelve. They include the Fourier series, the Fourier and the Laplace transforms, and the Green's functions. Equations in higher dimensions are also discussed in detail. In this second edition, a new chapter is added and numerous improvements have been made including the reorganization of some chapters. 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First-order and some common nonlinear PDEs arising in the physical and life sciences, with their solutions, are also covered.\u003c\/p\u003e\u003cp\u003eThis textbook includes an introduction to Fourier series and their properties, an introduction to regular Sturm-Liouville boundary value problems, special functions of mathematical physics, a treatment of nonhomogeneous equations and boundary conditions using methods such as Duhamel's principle, and an introduction to the finite difference technique for the numerical approximation of solutions. All results have been rigorously justified or precise references to justifications in more advanced sources have been cited. Appendices providing a background in complex analysis and linear algebra are also included for readers with limited prior exposure to those subjects.\u003c\/p\u003e\u003cp\u003eThe textbook includes material from which instructors could create a one- or two-semester course in PDEs. 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