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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Adzievski, Kuzman. Introduction to Partial Differential Equations for Scientists and Engineers UsingMathematica. Hoboken : CRC Press, ©2013 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Kuzman Adzievski; Abul Hasan Siddiqi |

ISBN: | 9781466510579 1466510579 |

OCLC Number: | 908077949 |

Description: | 1 online resource (645 pages) |

Contents: | Front Cover; Contents; Chapter 1 Fourier Series; Chapter 2 Integral Transforms; Chapter 3 Sturm{liouville Problems; Chapter 4 Partial Differential Equations; Chapter 5 The Wave Equation; Chapter 6 The Heat Equation; Chapter 7 Laplace And Poisson Equations; Chapter 8 Finite Difference Numerical Methods; Appendices; A. Table Of Laplace Transforms; B. Table Of Fourier Transforms; C. Series And Uniform Convergence Facts; D. Basic Facts Of Ordinary Dierential Equations; E. Vector Calculus Facts; F.A Summary Of Analytic Function Theory; G. Euler Gamma And Beta Functions; H. Basics Of Mathematica. |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

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 MathematicaÂ® 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. 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 "The presentation is simple and clear, with no sacrifice of rigor. Throughout the text, the illustrations, numerous solved examples and the use of Mathematica to visualize computations have been chosen to make the exposition as clear as possible. The book represents a good tool for facilitating the proper understanding of basic concepts and applications of PDEs."-Zentralblatt MATH 1282 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 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(R) 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. Read more...

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