Description
Solution Techniques for Elementary Partial Differential Equations, Third Edition remains a top choice for a standard, undergraduate-level course on partial differential equations (PDEs). Making the text even more user-friendly, this third edition covers important and widely used methods for solving PDEs.
New to the Third Edition
- New sections on the series expansion of more general functions, other problems of general second-order linear equations, vibrating string with other types of boundary conditions, and equilibrium temperature in an infinite strip
- Reorganized sections that make it easier for students and professors to navigate the contents
- Rearranged exercises that are now at the end of each section/subsection instead of at the end of the chapter
- New and improved exercises and worked examples
- A brief Mathematica® program for nearly all of the worked examples, showing students how to verify results by computer
This bestselling, highly praised textbook uses a streamlined, direct approach to develop students’ competence in solving PDEs. It offers concise, easily understood explanations and worked examples that allow students to see the techniques in action.
Table of Contents
Ordinary Differential Equations: Brief Revision
First-Order Equations
Homogeneous Linear Equations with Constant Coefficients
Nonhomogeneous Linear Equations with Constant Coefficients
Cauchy–Euler Equations
Functions and Operators
Fourier Series
The Full Fourier Series
Fourier Sine and Cosine Series
Convergence and Differentiation
Series Expansion of More General Functions
Sturm–Liouville Problems
Regular Sturm–Liouville Problems
Other Problems
Bessel Functions
Legendre Polynomials
Spherical Harmonics
Some Fundamental Equations of Mathematical Physics
The Heat Equation
The Laplace Equation
The Wave Equation
Other Equations
The Method of Separation of Variables
The Heat Equation
The Wave Equation
The Laplace Equation
Other Equations
Equations with More Than Two Variables
Linear Nonhomogeneous Problems
Equilibrium Solutions
Nonhomogeneous Problems
The Method of Eigenfunction Expansion
The Nonhomogeneous Heat Equation
The Nonhomogeneous Wave Equation
The Nonhomogeneous Laplace Equation
Other Nonhomogeneous Equations
The Fourier Transformations
The Full Fourier Transformation
The Fourier Sine and Cosine Transformations
Other Applications
The Laplace Transformation
Definition and Properties
Applications
The Method of Green’s Functions
The Heat Equation
The Laplace Equation
The Wave Equation
General Second-Order Linear Equations
The Canonical Form
Hyperbolic Equations
Parabolic Equations
Elliptic Equations
Other Problems
The Method of Characteristics
First-Order Linear Equations
First-Order Quasilinear Equations
The One-Dimensional Wave Equation
Other Hyperbolic Equations
Perturbation and Asymptotic Methods
Asymptotic Series
Regular Perturbation Problems
Singular Perturbation Problems
Complex Variable Methods
Elliptic Equations
Systems of Equations
Appendix
Further Reading
Index
