This is an introductory level textbook for partial differential equations (PDEs). It is suitable for a one-semester undergraduate level or two-semester graduate level course in PDEs or applied mathematics. This volume is application-oriented and rich in examples. Going through these examples, the reader is able to easily grasp the basics of PDEs.
Chapters 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. Extensions of nonlinear equations treated in earlier chapters are also discussed.
Partial differential equations are becoming a core subject in Engineering and the Sciences. This textbook will greatly benefit those studying in these subjects by covering basic and advanced topics in PDEs based on applications.
Contents: - First and Second Order Linear Equations - Preparation
- Heat Equation
- Wave Equation
- Laplace Equation
- First Order Equations
- Fourier Series and Eigenvalue Problems
- Separation of Variables in Higher Dimensions
- More Separation of Variables
- Fourier Transform
- Laplace Transform
- Green's Functions
- Applications
Readership: Undergraduate students in mathematics, science, and engineering.Partial Differential Equations;Wave Equation;Heat Equation;Laplace Equation;First-Order Equations;Separation of Variables;Method of Characteristics;Fourier Series;Fourier Transform;Laplace Transform;Green's Function0
Key Features:- Subjects are introduced through examples
- Detailed solutions are provided for the examples
- The first half of the book is organized by equations so that students can learn basic important PDEs. Essential methods are introduced as we go through those equations. The second half is organized by methods so that students can have more in-depth details of the important methods for PDEs
- Some prerequisite materials are listed in the Appendices to be used as quick references for students
