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図書
図書
1. Partial differential equations : an introduction with Mathematica and MAPLE (: alk. paper)
Ioannis P. Stavroulakis, Stepan A. Tersian
出版情報: Singapore ; River Edge, N.J. : World Scientific, c1999  x, 297 p. ; 23 cm
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目次情報: 続きを見る
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.：
2.

図書
図書
2. Partial differential equations and Mathematica
Prem K. Kythe, Pratap Puri, Michael R. Schäferkotter
出版情報: Boca Raton, Fla. ; Tokyo : CRC Press, c1997  xx, 378 p. ; 24 cm
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