Introduction to partial differential equations for scientists and engineers using Mathematica [Book] / Kuzman Adzievski, Abul Hasan Siddiqi.

"A Chapman & Hall book."

Includes bibliographical references (p. 574) and indexes.

Machine generated contents note: 1.1.Fourier Series of Periodic Functions -- 1.2.Convergence of Fourier Series -- 1.3.Integration and Differentiation of Fourier Series -- 1.4.Fourier Sine and Cosine Series -- 1.5.Projects Using Mathematica -- 2.1.The Laplace Transform -- 2.1.1.Definition and Properties of the Laplace Transform -- 2.1.2.Step and Impulse Functions -- 2.1.3.Initial-Value Problems and the Laplace Transform -- 2.1.4.The Convolution Theorem -- 2.2.Fourier Transforms -- 2.2.1.Definition of Fourier Transforms -- 2.2.2.Properties of Fourier Transforms -- 2.3.Projects Using Mathematica -- 3.1.Regular Sturm-Liouville Problems -- 3.2.Eigenfunction Expansions -- 3.3.Singular Sturm-Liouville Problems -- 3.3.1.Definition of Singular Sturm-Liouville Problems -- 3.3.2.Legendre's Differential Equation -- 3.3.3.Bessel's Differential Equation -- 3.4.Projects Using Mathematica -- 4.1.Basic Concepts and Terminology -- 4.2.Partial Differential Equations of the First Order -- 4.3.Linear Partial Differential Equations of the Second Order -- 4.3.1.Important Equations of Mathematical Physics -- 4.3.2.Classification of Linear PDEs of the Second Order -- 4.4.Boundary and Initial Conditions -- 4.5.Projects Using Mathematica -- 5.1.d'Alembert's Method -- 5.2.Separation of Variables Method for the Wave Equation -- 5.3.The Wave Equation on Rectangular Domains -- 5.3.1.Homogeneous Wave Equation on a Rectangle -- 5.3.2.Nonhomogeneous Wave Equation on a Rectangle -- 5.3.3.The Wave Equation on a Rectangular Solid -- 5.4.The Wave Equation on Circular Domains -- 5.4.1.The Wave Equation in Polar Coordinates -- 5.4.2.The Wave Equation in Spherical Coordinates -- 5.5.Integral Transform Methods for the Wave Equation -- 5.5.1.The Laplace Transform Method for the Wave Equation -- 5.5.2.The Fourier Transform Method for the Wave Equation -- 5.6.Projects Using Mathematica -- 6.1.The Fundamental Solution of the Heat Equation -- 6.2.Separation of Variables Method for the Heat Equation -- 6.3.The Heat Equation in Higher Dimensions -- 6.3.1.Green Function of the Higher Dimensional Heat Equation -- 6.3.2.The Heat Equation on a Rectangle -- 6.3.3.The Heat Equation in Polar Coordinates -- 6.3.4.The Heat Equation in Cylindrical Coordinates -- 6.3.5.The Heat Equation in Spherical Coordinates -- 6.4.Integral Transform Methods for the Heat Equation -- 6.4.1.The Laplace Transform Method for the Heat Equation -- 6.4.2.The Fourier Transform Method for the Heat Equation -- 6.5.Projects Using Mathematica -- 7.1.The Fundamental Solution of the Laplace Equation -- 7.2.Laplace and Poisson Equations on Rectangular Domains -- 7.3.Laplace and Poisson Equations on Circular Domains -- 7.3.1.Laplace Equation in Polar Coordinates -- 7.3.2.Poisson Equation in Polar Coordinates -- 7.3.3.Laplace Equation in Cylindrical Coordinates -- 7.3.4.Laplace Equation in Spherical Coordinates -- 7.4.Integral Transform Methods for the Laplace Equation -- 7.4.1.The Fourier Transform Method for the Laplace Equation -- 7.4.2.The Hankel Transform Method -- 7.5.Projects Using Mathematica -- 8.1.Basics of Linear Algebra and Iterative Methods -- 8.2.Finite Differences -- 8.3.Finite Difference Methods for Laplace & Poisson Equations -- 8.4.Finite Difference Methods for the Heat Equation -- 8.5.Finite Difference Methods for the Wave Equation -- A.Table of Laplace Transforms -- B.Table of Fourier Transforms -- C.Series and Uniform Convergence Facts -- D.Basic Facts of Ordinary Differential Equations -- E.Vector Calculus Facts -- F.A Summary of Analytic Function Theory -- G.Euler Gamma and Beta Functions -- H.Basics of Mathematica.

With a special emphasis on engineering and science applications, this textbook provides a mathematical introduction to PDEs at the undergraduate level. It takes a new approach to PDEs by presenting computation as an integral part of the study of differential equations. The authors use Mathematica® along with graphics to improve understanding and interpretation of concepts. They also present exercises in each chapter and solutions to selected examples. Topics discussed include Laplace and Fourier transforms as well as Sturm-Liouville boundary value problems.