**A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields**

Featuring a thoroughly revised presentation of topics, *Beginning Partial Differential Equations, Third Edition* provides a challenging, yet accessible, combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems.

The *Third Edition* is organized around four themes: methods of solution for initial-boundary value problems; applications of partial differential equations; existence and properties of solutions; and the use of software to experiment with graphics and carry out computations. With a primary focus on wave and diffusion processes, *Beginning Partial Differential Equations, Third Edition* also includes:

Proofs of theorems incorporated within the topical presentation, such as the existence of a solution for the Dirichlet problem

The incorporation of Maple™ to perform computations and experiments

Unusual applications, such as Poe's pendulum

Advanced topical coverage of special functions, such as Bessel, Legendre polynomials, and spherical harmonics

Fourier and Laplace transform techniques to solve important problems

*Beginning of Partial Differential Equations, Third Edition* is an ideal textbook for upper-undergraduate and first-year graduate-level courses in analysis and applied mathematics, science, and engineering.

- Cover
- Half Title page
- Title page
- Copyright page
- Preface
- Chapter 1: First Ideas
- Chapter 2: Solutions of the Heat Equation
- Chapter 3: Solutions of the Wave Equation
- Chapter 4: Dirichlet and Neumann Problems
- Chapter 5: Fourier Integral Methods of Solution
- Chapter 6: Solutions Using Eigenfunction Expansions
- Chapter 7: Integral Transform Methods of Solution
- Chapter 8: First-Order Equations
- Chapter 9: End Materials
- Index