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 -- 7.5 Two-Dimensional Problems -- 7.6 Comments and References -- Miscellaneous Exercises -- Bibliography -- Mathematical References -- Answers to Odd-Numbered Exercises -- Chapter 0 -- Chapter 1 -- Chapter 2 -- Chapter 3 -- Chapter 4 -- Chapter 5 -- Chapter 6 -- Chapter 7 -- Index.