Introduction to Partial Differential Equations for Scientists and Engineers Using Mathematica
Fourier Series The Fourier Series of a Periodic Function Convergence of Fourier Series Integration and Differentiation of Fourier Series Fourier Sine and Fourier Cosine Series Mathematica Projects Integral Transforms The Fourier Transform and Elementary Properties Inversion Formula of the Fourier Transform Convolution Property of the Fourier Transform The Laplace Transform and Elementary Properties Differentiation and Integration of the Laplace Transform Heaviside and Dirac Delta Functions Convolution Property of the Laplace Transform Solution of Differential Equations by the Integral Transforms The Sturm Liouville Problems Regular Sturm Liouville Problem Eigenvalues and Eigenfunctions Eigenfunction Expansion Singular Sturm Liouville Problem: Legendre's Equation Singular Sturm Liouville Problem: Bessel's Equation Partial Differential Equations Basic Concepts and Definitions Formulation of Initial and Boundary Problems Classification of Partial Differential Equations Some Important Classical Linear Partial Differential Equations The Principle of Superposition First Order Partial Differential Equations Linear Equations with Constant Coefficients Linear Equations with Variable Coefficients First Order Non Linear Equations Cauchy's Method of Characteristics Mathematica Projects Hyperbolic Partial Differential Equations The Vibrating String and Derivation of the Wave Equation Separation of Variables for the Homogeneous Wave Equation D'Alambert's Solution of the Wave Equation Inhomogeneous Wave Equations Solution of the Wave Equation by Integral Transforms Two Dimensional Wave Equation: Vibrating Membrane The Wave Equation in Polar and Spherical Coordinates Numerical Solutions of the Wave Equation Mathematica Projects Parabolic Partial Differential Equations Heat Flow and Derivation of the Heat Equation Separation of Variables for the One Dimensional Heat Equation Inhomogeneous Heat Equations Solution of the Heat Equation by Integral Transforms Two Dimensional Heat Equation The Heat Equation in Polar and Spherical Coordinates Numerical Solutions of the Heat Equation Mathematica Projects Elliptic Partial Differential Equations The Laplace and Poisson Equations Separation of Variables for the Laplace Equation The Laplace Equation in Polar and Spherical Coordinates Poisson Integral Formula Numerical Solutions of the Laplace Equation Mathematica Projects Appendix A. Special Functions Appendix B. Table of the Fourier Transform of Some Functions Appendix C. Table of the Laplace Transform of Some Functions