Boundary value problems and partial differential equations /
Powers, David L.
Boundary value problems and partial differential equations / David L. Powers. - 6th ed. - Amsterdam ; Boston : Elsevier Academic Press, c2011. - xi, 506 p: ill.; 24 cm.
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.
Boundary value problems--Problems, exercises, etc.
Differential equations, Partial--Problems, exercises, etc.
Electronic books.
515.353 / POW-B 2011 10601
Boundary value problems and partial differential equations / David L. Powers. - 6th ed. - Amsterdam ; Boston : Elsevier Academic Press, c2011. - xi, 506 p: ill.; 24 cm.
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.
Boundary value problems--Problems, exercises, etc.
Differential equations, Partial--Problems, exercises, etc.
Electronic books.
515.353 / POW-B 2011 10601