Solution Techniques for Elementary Partial Differential Equations, Third Edition

✍ Scribed by Constanda, Christian

• Publisher: Chapman and Hall/CRC
• Year: 2016
• Tongue: English
• Leaves: 378
• Edition: Third edition
• Category: Library

✦ Synopsis

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

Content: 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

✦ Subjects

Differential equations, Partial.