Adzievski / Siddiqi Introduction to Partial Differential Equations for Scientists and Engineers UsingMathematica

1. Auflage 2013
ISBN: 978-1-4665-1057-9
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 648 Seiten

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.

Autoren/Hrsg.

Adzievski, Kuzman

Siddiqi, Abul Hasan

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

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