Christian Constanda

Solution Techniques for Elementary Partial Differential Equations

• Gebundenes Buch

Produktbeschreibung

Table of contents:
Ordinary Differential Equations: A Brief Overview. Fourier Series. The Heat, Laplace and Wave Equations. The Method of Separation of Variables. The Method of Eigenfunction Expansion. The Fourier Transformations. The Laplace Transformation. Green's Functions. The General Second Order Linear Equation in Two Independent Variables. The Method of Characteristics. Perturbation and Asymptotic Methods.

Many texts on partial differential equations (PDEs) are too detailed and voluminous, making them daunting to the average student. This undergraduate treatment is designed as a no-frills text that explains completely but succinctly the major methods used in elementary PDEs. This text stands apart by providing full but concise explanations of the essence of the topics and many worked examples and exercises, which should facilitate a quick understanding of the material. Solution Techniques for Elementary Partial Differential Equations has been class tested with great success, and postscript files will be available to instructors for producing overhead projector transparencies for class instruction.

Produktdetails

• Verlag: Chapman & Hall/CRC
• Englisch
• ISBN-13: 9781584882572
• ISBN-10: 1584882573
• Artikelnr.: 21034422

Inhaltsangabe

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. 2. Fourier Series.
2.1. The Full Fourier Series. 2.2. Fourier Sine and Cosine Series. 2.3.
Convergence and Differentiation. 2.4. Series Expansion of More General
Functions. 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. 4. Some Fundamental Equations of
Mathematical Physics. 4.1. The Heat Equation. 4.2 The Laplace Equation.
4.3. The Wave Equation. 4.4. Other Equations. 5. The Method of Separation
of Variables. 5.1. The Heat Equation. 5.2. The Wave Equation. 5.3. The
Laplace Equation. 5.4. Other Equations. 5.5. Equations with More than Two
Variables. 6. Linear Nonhomogeneous Problems. 6.1. Equilibrium Solutions.
6.2. Nonhomogeneous Problems. 7. The Method of Eigenfunction Expansion.
7.1. The Nonhomogeneous Heat Equation. 7.2. The Nonhomogeneous Wave
Equation. 7.3. The Nonhomogeneous Laplace Equation. 7.4. Other
Nonhomogeneous Equations. 8. The Fourier Transformations. 8.1. The Full
Fourier Transformation. 8.2. The Fourier Sine and Cosine Transformations.
8.3. Other Applications. 9. The Laplace Transformation. 9.1. Definition and
Properties. 9.2. Applications. 10. The Method of Green's Functions. 10.1.
The Heat Equation. 10.2. The Laplace Equation. 10.3. The Wave Equation.
11. General Second-Order Linear Equations. 11.1. The Canonical Form. 11.2.
Hyperbolic Equations. 11.3. Parabolic Equations. 11.4. Elliptic Equations.
11.5. Other Problems. 12. The Method of Characteristics. 12.1. First-Order
Linear Equations. 12.2. First-Order Quasilinear Equations. 12.3. The
One-Dimensional Wave Equation. 12.4. Other Hyperbolic Equations. 13.
Perturbation and Asymptotic Methods. 13.1. Asymptotic Series. 13.2. Regular
Perturbation Problems. 13.3. Singular Perturbation Problems. 14. Complex
Variable Methods. 14.1. Elliptic Equations. 14.2. Systems of Equations.
Appendices.

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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. 2. Fourier Series. 2.1. The Full Fourier Series. 2.2. Fourier Sine and Cosine Series. 2.3. Convergence and Differentiation. 2.4. Series Expansion of More General Functions. 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. 4. Some Fundamental Equations of Mathematical Physics. 4.1. The Heat Equation. 4.2 The Laplace Equation. 4.3. The Wave Equation. 4.4. Other Equations. 5. The Method of Separation of Variables. 5.1. The Heat Equation. 5.2. The Wave Equation. 5.3. The Laplace Equation. 5.4. Other Equations. 5.5. Equations with More than Two Variables. 6. Linear Nonhomogeneous Problems. 6.1. Equilibrium Solutions. 6.2. Nonhomogeneous Problems. 7. The Method of Eigenfunction Expansion. 7.1. The Nonhomogeneous Heat Equation. 7.2. The Nonhomogeneous Wave Equation. 7.3. The Nonhomogeneous Laplace Equation. 7.4. Other Nonhomogeneous Equations. 8. The Fourier Transformations. 8.1. The Full Fourier Transformation. 8.2. The Fourier Sine and Cosine Transformations. 8.3. Other Applications. 9. The Laplace Transformation. 9.1. Definition and Properties. 9.2. Applications. 10. The Method of Green's Functions. 10.1. The Heat Equation. 10.2. The Laplace Equation. 10.3. The Wave Equation. 11. General Second-Order Linear Equations. 11.1. The Canonical Form. 11.2. Hyperbolic Equations. 11.3. Parabolic Equations. 11.4. Elliptic Equations. 11.5. Other Problems. 12. The Method of Characteristics. 12.1. First-Order Linear Equations. 12.2. First-Order Quasilinear Equations. 12.3. The One-Dimensional Wave Equation. 12.4. Other Hyperbolic Equations. 13. Perturbation and Asymptotic Methods. 13.1. Asymptotic Series. 13.2. Regular Perturbation Problems. 13.3. Singular Perturbation Problems. 14. Complex Variable Methods. 14.1. Elliptic Equations. 14.2. Systems of Equations. Appendices.

Rezensionen

"In my opinion, this is quite simply the best book of its kind that I have seen thus far."
-Professor Peter Schiavone, University of Alberta, from the Foreword to the Fourth Edition

Praise for the previous editions

An ideal tool for students taking a first course in PDEs, as well as for the lecturers who teach such courses."
-Marian Aron, Plymouth University, UK

"This is one of the best books on elementary PDEs this reviewer has read so far. Highly recommended."
-CHOICE