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Ordinary Differential Equations: Brief RevisionFirst-Order Equations Homogeneous Linear Equations with Constant Coefficients Nonhomogeneous Linear Equations with Constant Coefficients Cauchy–Euler Equations Functions and Operators Fourier SeriesThe Full Fourier Series Fourier Sine Series Fourier Cosine Series Convergence and Differentiation Sturm–Liouville ProblemsRegular Sturm–Liouville Problems Other Problems Bessel Functions Legendre Polynomials Spherical Harmonics Some Fundamental Equations of Mathematical PhysicsThe Heat Equation The Laplace Equation The Wave EquationOther Equations The Method of Separation of VariablesThe Heat Equation The Wave Equation The Laplace EquationOther Equations Equations with More than Two Variables Linear Nonhomogeneous ProblemsEquilibrium Solutions Nonhomogeneous Problems The Method of Eigenfunction ExpansionThe Heat Equation The Wave Equation The Laplace Equation Other Equations The Fourier TransformationsThe Full Fourier Transformation The Fourier Sine and Cosine TransformationsOther Applications The Laplace TransformationDefinition and Properties Applications The Method of Green’s FunctionsThe Heat Equation The Laplace Equation The Wave Equation General Second-Order Linear Partial Differential Equations with Two Independent VariablesThe Canonical Form Hyperbolic Equations Parabolic Equations Elliptic Equations The Method of CharacteristicsFirst-Order Linear Equations First-Order Quasilinear Equations The One-Dimensional Wave Equation Other Hyperbolic Equations Perturbation and Asymptotic MethodsAsymptotic Series Regular Perturbation Problems Singular Perturbation Problems Complex Variable Methods Elliptic Equations Systems of Equations Answers to Odd-Numbered Exercises Appendix Bibliography Index Exercises appear at the end of each chapter.