Partial differential equations : an introduction with Mathematica and MAPLE

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Partial differential equations : an introduction with Mathematica and MAPLE / Ioannis P. Stavroulakis, Stepan A. Tersian

資料種別:

図書

出版情報:

Singapore ; River Edge, N.J. : World Scientific, c1999

形態:

x, 297 p. ; 23 cm

著者名:

ISBN:

9789810238919 [9810238916] (: alk. paper)

書誌ID:

BA45041638

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references and index

主題:

Differential equations, Partial; Maple (Computer file); Mathematica (Computer file); Mathematical physics

言語:

英語

目次情報:

First-order Partial Differential Equations / 1.：

Introduction

Linear First-order Equations / 2.：

The Cauchy Problem for First-order Quasi-linear Equations / 3.：

General Solutions of Quasi-linear Equations / 4.：

Fully-nonlinear First-order Equations / 5.：

Second-order Partial Differential Equations

Linear equations / 6.：

Classification and Canonical Forms of Equations in Two Independent Variables / 7.：

Classification of Almost-linear Equations in R[superscript n] / 8.：

One-Dimensional Wave Equation

The Wave Equation on the Whole Line. D'Alembert Formula / 9.：

The Wave Equation on the Half-line. Reflection Method / 10.：

Mixed Problem for the Wave Equation / 11.：

Inhomogeneous Wave Equation / 12.：

Conservation of the Energy / 13.：

Weak Derivatives and Weak Solutions / 14.：

One-Dimensional Diffusion Equation

Maximum-minimum Principle for the Diffusion Equation / 15.：

The Diffusion Equation on the Whole Line / 16.：

Diffusion on the Half-line / 17.：

Inhomogeneous Diffusion Equation on the Whole Line / 18.：

Shock Waves and Conservation Laws

Conservation laws / 19.：

Burgers' Equation / 20.：

Weak Solutions. Riemann Problem / 21.：

Discontinuous Solutions of Conservation Laws. Rankine-Hugoniot Condition / 22.：

The Laplace Equation

Harmonic functions. Maximum-minimum Principle / 23.：

Green's Identities / 24.：

Green's Functions / 25.：

Green's Functions for a Half-space and Sphere / 26.：

Harnack's Inequalities and Theorems / 27.：

Fourier Series and Fourier Method for PDEs

Fourier Series / 28.：

Orthonormal Systems. General Fourier series / 29.：

Fourier Method for the Diffusion Equation / 30.：

Fourier Method for the Wave Equation / 31.：

Fourier Method for the Laplace Equation / 32.：

Diffusion and Wave Equations in Higher Dimensions

Diffusion Equation in Three Dimensional Space / 33.：

Fourier Method for the Diffusion Equation in Higher Dimensions / 34.：

Kirchoff's Formula for the Wave Equation. Huygens' Principle / 35.：

Fourier Method for the Wave Equation on the Plane. Nodal Sets / 36.：

References

Answers and Hints to Selected Exercises

Index

First-order Partial Differential Equations / 1.：

Introduction

Linear First-order Equations / 2.：

The Cauchy Problem for First-order Quasi-linear Equations / 3.：

General Solutions of Quasi-linear Equations / 4.：

Fully-nonlinear First-order Equations / 5.：

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