Partial Differential Equations: Methods, Applications And Theories

This volume is an introductory level textbook for partial differential equations (PDE's) and suitable for a one-semester undergraduate level or two-semester graduate level course in PDE's or applied mathematics. Chapters One to Five are organized according to the equations and the basic PDE's are introduced in an easy to understand manner. 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. The equations in higher dimensions are also discussed in detail.This volume is application-oriented and rich in examples. Going through these examples, the reader is able to easily grasp the basics of PDE's.

This is a textbook for an undergraduate course in Math, Science, and Engineering. Also, this book can also be used as a textbook for graduate course in Science and Engineering, and as a textbook for the first semester in two-semester graduate level courses. Students learn basic knowlegde in partial differential equations. This includes First order equations, Second order linear equations, Fourier series, and Green functions.