Research Catalog

Title

Solution techniques for elementary partial differential equations / Christian Constanda.

Author

Constanda, C. (Christian)

Publication

Boca Raton, FL : Chapman & Hall/CRC, ©2010.

Items in the Library & Off-site

Details

Description

xviii, 325 pages : illustrations; 24 cm.

Summary

"This concise, well-written book, which includes a profusion of worked examples and exercises, serves both as an excellent text in undergraduate and graduate learning and as a useful presentation of solution techniques for researchers and engineers interested in applying partial differential equations to real-life problems."--Barbara Zubik-Kowal, Boise State University, Idaho, USA<BR><BR>"... In my opinion, this is quite simply the best book of its kind that I have seen thus far. The book not only contains solution methods for some very important classes of PDEs, in an easy-to-read format, but is also student-friendly and teacher-friendly at the same time. It is definitely a textbook that should be adopted."--From the Foreword by Peter Schiavone, University of Alberta, Edmonton, Canada<BR><BR>Winner of the 2002 Choice Outstanding Academic Title Award, Solution Techniques for Elementary Partial Differential Equations presents some of the most important and widely used methods for solving PDEs. Along with a new chapter on complex variable methods, this second edition includes new sections on Cauchy-Euler equations, Bessel functions, Legendre polynomials, spherical harmonics, applications of Fourier transformations, and general hyperbolic equations. It lists additional mathematical models based on PDEs and shows how the methods of separation of variables and eigenfunction expansion work for equations other than heat, wave, and Laplace. The author also added many new examples and exercises. With concise, easily understood explanations and worked examples that illustrate the techniques in action, this edition continues to provide a streamlined, direct approach to developing readers' competence in solving PDEs. --Book Jacket.

Series Statement

Chapman & Hall/CRC mathematics ; 22

Subject

• Differential equations, Partial > Numerical solutions
• Partielle Differentialgleichung

Bibliography (note)

• Includes bibliographical references and index.

Contents

• Machine generated contents note: ch. 1 Ordinary Differential Equations: Brief Review -- 1.1. First-Order Equations -- 1.2. Homogeneous Linear Equations with Constant Coefficients -- 1.3. Nonhomogeneous Linear Equations with Constant Coefficients -- 1.4. Cauchy-Euler Equations -- 1.5. Functions and Operators -- Exercises -- ch. 2 Fourier Series -- 2.1. Full Fourier Series -- 2.2. Fourier Sine Series -- 2.3. Fourier Cosine Series -- 2.4. Convergence and Differentiation -- Exercises -- ch. 3 Sturm -- Liouville Problems -- 3.1. Regular Sturm -- Liouville Problems -- 3.2. Other Problems -- 3.3. Bessel Functions -- 3.4. Legendre Polynomials -- 3.5. Spherical Harmonics -- Exercises -- ch. 4 Some Fundamental Equations of Mathematical Physics -- 4.1. Heat Equation -- 4.2. Laplace Equation -- 4.3. Wave Equation -- 4.4. Other Equations -- Exercises -- ch. 5^ Method of Separation of Variables -- 5.1. Heat Equation -- 5.2. Wave Equation -- 5.3. Laplace Equation -- 5.4. Other Equations -- 5.5. Equations with More than Two Variables -- Exercises -- ch. 6 Linear Nonhomogeneous Problems -- 6.1. Equilibrium Solutions -- 6.2. Nonhomogeneous Problems -- Exercises -- ch. 7 Method of Eigenfunction Expansion -- 7.1. Heat Equation -- 7.2. Wave Equation -- 7.3. Laplace Equation -- 7.4. Other Equations -- Exercises -- ch. 8 Fourier Transformations -- 8.1. Full Fourier Transformation -- 8.2. Fourier Sine and Cosine Transformations -- 8.3. Other Applications -- Exercises -- ch. 9 Laplace Transformation -- 9.1. Definition and Properties -- 9.2. Applications -- Exercises -- ch. 10 Method of Green's Functions -- 10.1. Heat Equation -- 10.2. Laplace Equation -- 10.3. Wave Equation -- Exercises -- ch. 11^ General Second-Order Linear Partial Differential Equations with Two Independent Variables -- 11.1. Canonical Form
• Note continued: 11.2. Hyperbolic Equations -- 11.3. Parabolic Equations -- 11.4. Elliptic Equations -- Exercises -- ch. 12 Method of Characteristics -- 12.1. First-Order Linear Equations -- 12.2. First-Order Quasilinear Equations -- 12.3. One-Dimensional Wave Equation -- 12.4. Other Hyperbolic Equations -- Exercises -- ch. 13 Perturbation and Asymptotic Methods -- 13.1. Asymptotic Series -- 13.2. Regular Perturbation Problems -- 13.3. Singular Perturbation Problems -- Exercises -- ch. 14 Complex Variable Methods -- 14.1. Elliptic Equations -- 14.2. Systems of Equations -- Exercises.

ISBN

• 9781439811399
• 1439811393

LCCN

2010014608

OCLC

• ocn540161487
• 540161487
• SCSB-1561717

Owning Institutions

Princeton University Library