Boundary value problems : and partial differential equations

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.
7.