Boundary value problems and partial differential equations / David L. Powers.

By: Powers, David LContributor(s): ebrary, IncMaterial type: TextTextPublication details: Amsterdam ; Boston : Elsevier Academic Press, c2011Edition: 6th edDescription: xi, 506 p: ill.; 24 cmSubject(s): Boundary value problems -- Problems, exercises, etc | Differential equations, Partial -- Problems, exercises, etcGenre/Form: Electronic books.DDC classification: 515.353 Online resources: Full text available from Ebook Central - Academic Complete
Contents:
Cover -- Contents -- Preface -- Chapter 0. Ordinary Differential Equations -- 0.1 Homogeneous Linear Equations -- 0.2 Nonhomogeneous Linear Equations -- 0.3 Boundary Value Problems -- 0.4 Singular Boundary Value Problems -- 0.5 Green's Functions -- Chapter Review -- Miscellaneous Exercises -- Chapter 1. Fourier Series and Integrals -- 1.1 Periodic Functions and Fourier Series -- 1.2 Arbitrary Period and Half-Range Expansions -- 1.3 Convergence of Fourier Series -- 1.4 Uniform Convergence -- 1.5 Operations on Fourier Series -- 1.6 Mean Error and Convergence in Mean -- 1.7 Proof of Convergence -- 1.8 Numerical Determination of Fourier Coefficients -- 1.9 Fourier Integral -- 1.10 Complex Methods -- 1.11 Applications of Fourier Series and Integrals -- 1.12 Comments and References -- Chapter Review -- Miscellaneous Exercises -- Chapter 2. The Heat Equation -- 2.1 Derivation and Boundary Conditions -- 2.2 Steady-State Temperatures -- 2.3 Example: Fixed End Temperatures -- 2.4 Example: Insulated Bar -- 2.5 Example: Different Boundary Conditions -- 2.6 Example: Convection -- 2.7 Sturm-Liouville Problems -- 2.8 Expansion in Series of Eigenfunctions -- 2.9 Generalities on the Heat Conduction Problem -- 2.10 Semi-Infinite Rod -- 2.11 Infinite Rod -- 2.12 The Error Function -- 2.13 Comments and References -- Chapter Review -- Miscellaneous Exercises -- Chapter 3. The Wave Equation -- 3.1 The Vibrating String -- 3.2 Solution of the Vibrating String Problem -- 3.3 d'Alembert's Solution -- 3.4 One-Dimensional Wave Equation: Generalities -- 3.5 Estimation of Eigenvalues -- 3.6 Wave Equation in Unbounded Regions -- 3.7 Comments and References -- Chapter Review -- Miscellaneous Exercises -- Chapter 4. The Potential Equation -- 4.1 Potential Equation -- 4.2 Potential in a Rectangle -- 4.3 Further Examples for a Rectangle -- 4.4 Potential in Unbounded Regions -- 4.5 Potential in a Disk -- 4.6 Classification and Limitations -- 4.7 Comments and References -- Chapter Review -- Miscellaneous Exercises -- Chapter 5. Higher Dimensions and Other Coordinates -- 5.1 Two-Dimensional Wave Equation: Derivation -- 5.2 Three-Dimensional Heat Equation -- 5.3 Two-Dimensional Heat Equation: Solution -- 5.4 Problems in Polar Coordinates -- 5.5 Bessel's Equation -- 5.6 Temperature in a Cylinder -- 5.7 Vibrations of a Circular Membrane -- 5.8 Some Applications of Bessel Functions -- 5.9 Spherical Coordinates; Legendre Polynomials -- 5.10 Some Applications of Legendre Polynomials -- 5.11 Comments and References -- Chapter Review -- Miscellaneous Exercises -- Chapter 6. Laplace Transform -- 6.1 Definition and Elementary Properties -- 6.2 Partial Fractions and Convolutions -- 6.3 Partial Differential Equations -- 6.4 More Difficult Examples -- 6.5 Comments and References -- Miscellaneous Exercises -- Chapter 7. Numerical Methods -- 7.1 Boundary Value Problems -- 7.2 Heat Problems -- 7.3 Wave Equation -- 7.4 Potential Equation --
Summary: Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, (Clarkson) has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering.* CD with animations and graphics of solutions, additional exercises and chapter review questions.
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Holdings
Item type Current library Call number Copy number Status Date due Barcode Item holds
Books Books Namal Library
Mathematics 		515.353 POW-B 2011 10601 (Browse shelf (Opens below)) 1 Available 0010601
Total holds: 0

Cover --
Contents --
Preface --
Chapter 0. Ordinary Differential Equations --
0.1 Homogeneous Linear Equations --
0.2 Nonhomogeneous Linear Equations --
0.3 Boundary Value Problems --
0.4 Singular Boundary Value Problems --
0.5 Green's Functions --
Chapter Review --
Miscellaneous Exercises --
Chapter 1. Fourier Series and Integrals --
1.1 Periodic Functions and Fourier Series --
1.2 Arbitrary Period and Half-Range Expansions --
1.3 Convergence of Fourier Series --
1.4 Uniform Convergence --
1.5 Operations on Fourier Series --
1.6 Mean Error and Convergence in Mean --
1.7 Proof of Convergence --
1.8 Numerical Determination of Fourier Coefficients --
1.9 Fourier Integral --
1.10 Complex Methods --
1.11 Applications of Fourier Series and Integrals --
1.12 Comments and References --
Chapter Review --
Miscellaneous Exercises --
Chapter 2. The Heat Equation --
2.1 Derivation and Boundary Conditions --
2.2 Steady-State Temperatures --
2.3 Example: Fixed End Temperatures --
2.4 Example: Insulated Bar --
2.5 Example: Different Boundary Conditions --
2.6 Example: Convection --
2.7 Sturm-Liouville Problems --
2.8 Expansion in Series of Eigenfunctions --
2.9 Generalities on the Heat Conduction Problem --
2.10 Semi-Infinite Rod --
2.11 Infinite Rod --
2.12 The Error Function --
2.13 Comments and References --
Chapter Review --
Miscellaneous Exercises --
Chapter 3. The Wave Equation --
3.1 The Vibrating String --
3.2 Solution of the Vibrating String Problem --
3.3 d'Alembert's Solution --
3.4 One-Dimensional Wave Equation: Generalities --
3.5 Estimation of Eigenvalues --
3.6 Wave Equation in Unbounded Regions --
3.7 Comments and References --
Chapter Review --
Miscellaneous Exercises --
Chapter 4. The Potential Equation --
4.1 Potential Equation --
4.2 Potential in a Rectangle --
4.3 Further Examples for a Rectangle --
4.4 Potential in Unbounded Regions --
4.5 Potential in a Disk --
4.6 Classification and Limitations --
4.7 Comments and References --
Chapter Review --
Miscellaneous Exercises --
Chapter 5. Higher Dimensions and Other Coordinates --
5.1 Two-Dimensional Wave Equation: Derivation --
5.2 Three-Dimensional Heat Equation --
5.3 Two-Dimensional Heat Equation: Solution --
5.4 Problems in Polar Coordinates --
5.5 Bessel's Equation --
5.6 Temperature in a Cylinder --
5.7 Vibrations of a Circular Membrane --
5.8 Some Applications of Bessel Functions --
5.9 Spherical Coordinates; Legendre Polynomials --
5.10 Some Applications of Legendre Polynomials --
5.11 Comments and References --
Chapter Review --
Miscellaneous Exercises --
Chapter 6. Laplace Transform --
6.1 Definition and Elementary Properties --
6.2 Partial Fractions and Convolutions --
6.3 Partial Differential Equations --
6.4 More Difficult Examples --
6.5 Comments and References --
Miscellaneous Exercises --
Chapter 7. Numerical Methods --
7.1 Boundary Value Problems --
7.2 Heat Problems --
7.3 Wave Equation --
7.4 Potential Equation --


Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, (Clarkson) has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering.* CD with animations and graphics of solutions, additional exercises and chapter review questions.

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