Introduction to Partial Differential Equations for Scientists and Engineers Using Mathematica USING MATHEMATICA

With special emphasis on engineering and science applications, this textbook provides a mathematical introduction to the field of partial differential equations (PDEs). The text represents a new approach to PDEs at the undergraduate level by presenting computation as an integral part of the study of differential equations. The authors use the computer software Mathematica® along with graphics to improve understanding and interpretation of concepts. The book also presents solutions to selected examples as well as exercises in each chapter. Topics include Laplace and Fourier transforms as well as Sturm-Liuville Boundary Value Problems.

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 TransformsThe Fourier Transform and Elementary Properties Inversion Formula of the Fourier Transform Convolution Property of the Fourier TransformThe 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 ExpansionSingular 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 EquationsSome Important Classical Linear Partial Differential Equations The Principle of SuperpositionFirst 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 ProjectsHyperbolic 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 EquationInhomogeneous 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 EquationsHeat Flow and Derivation of the Heat Equation Separation of Variables for the One Dimensional Heat Equation Inhomogeneous Heat EquationsSolution of the Heat Equation by Integral Transforms Two Dimensional Heat Equation The Heat Equation in Polar and Spherical Coordinates Numerical Solutions of the Heat EquationMathematica ProjectsElliptic Partial Differential EquationsThe Laplace and Poisson EquationsSeparation of Variables for the Laplace EquationThe Laplace Equation in Polar and Spherical Coordinates Poisson Integral FormulaNumerical Solutions of the Laplace EquationMathematica Projects Appendix A. Special FunctionsAppendix B. Table of the Fourier Transform of Some FunctionsAppendix C. Table of the Laplace Transform of Some Functions

Adzievski, Kuzman; Siddiqi, Abul Hasan