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 Burgers equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems.

TheThird 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 problemThe incorporation of Maple to perform computations and experimentsUnusual applications, such as Poes pendulumAdvanced topical coverage of special functions, such as Bessel, Legendre polynomials, and spherical harmonicsFourier 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.

PETER V. ONEIL, PHD, is Professor Emeritus in the Department of Mathematics at the University of Alabama at Birmingham. He has over forty years of experience in teaching and writing and is the recipient of the Lester R. Ford Award from the Mathematical Association of America. Dr. ONeil is also a member of the American Mathematical Society, the Mathematical Association of America, the Society for Industrial and Applied Mathematics, and the American Association for the Advancement of Science.

1 First Ideas 1

1.1 Two Partial Differential Equations 11.2 Fourier Series 101.3 Two Eigenvalue Problems 281.4 A Proof of the Fourier Convergence Theorem 302. Solutions of the Heat Equation 392.1 Solutions on an Interval (0, L) 392.2 A Nonhomogeneous Problem 642.3 The Heat Equation in Two space Variables 712.4 The Weak Maximum Principle 753. Solutions of the Wave Equation 813.1 Solutions on Bounded Intervals 813.2 The Cauchy Problem 1093.3 The Wave Equation in Higher Dimensions 1374. Dirichlet and Neumann Problems 1474.1 Laplaces Equation and Harmonic Functions 1474.2 The Dirichlet Problem for a Rectangle 1534.3 The Dirichlet Problem for a Disk 1584.4 Properties of Harmonic Functions 1654.5 The Neumann Problem 1874.6 Poissons Equation 1974.7 Existence Theorem for a Dirichlet Problem 2005. Fourier Integral Methods of Solution 2135.1 The Fourier Integral of a Function 2135.2 The Heat Equation on a Real Line 2205.3 The Debate over the Age of the Earth 2305.4 Burgers Equation 2335.5 The Cauchy Problem for a Wave Equation 2395.6 Laplaces Equation on Unbounded Domains 2446. Solutions Using Eigenfunction Expansions 2536.1 A Theory of Eigenfunction Expansions 2536.2 Bessel Functions 2666.3 Applications of Bessel Functions 2796.4 Legendre Polynomials and Applications 2887. Integral Transform Methods of Solution 3077.1 The Fourier Transform 3077.2 Heat and Wave Equations 3187.3 The Telegraph Equation 3327.4 The Laplace Transform 3348 First-Order Equations 3418.1 Linear First-Order Equations 3428.2 The Significance of Characteristics 3498.3 The Quasi-Linear Equation 3549 End Materials 3619.1 Notation 3619.2 Use of MAPLE 3639.3 Answers to Selected Problems 370Index 434