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1.

図書
図書
1. Partial differential equations of mathematical physics and integral equations
Ronald B. Guenther and John W. Lee
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1988  xii, 544 p. ; 25 cm
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2.

図書
図書
2. 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.：
3.

図書
図書
3. Partial differential equations of mathematical physics
S.L. Sobolev ; translated from the third Russian edition by E.R. Dawson ; English translation edited by T.A.A. Broadbent
出版情報: Oxford : Pergamon Press, 1964  x, 430 p. ; 24 cm
シリーズ名: International series of monographs on pure and applied mathematics ; v. 56
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4.

図書
図書
4. Integral representations for spatial models of mathematical physics
Vladislav V. Kravchenko and Michael V. Shapiro
出版情報: Harlow : Longman, 1996  247 p. ; 25 cm
シリーズ名: Pitman research notes in mathematics series ; 351
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5.

図書
図書
5. Continuous symmetries, Lie algebras, differential equations and computer algebra
Willi-Hans Steeb
出版情報: Singapore : World Scientific, c1996  xi, 360 p. ; 23 cm
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6.

図書
図書
6. Soliton equations and Hamiltonian systems (: pbk)
L.A. Dickey
出版情報: Singapore : World Scientific, c1991  ix, 310 p. ; 23 cm
シリーズ名: Advanced series in mathematical physics / editor-in-charge, D.H. Phong, S.-T. Yan ; v. 12
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7.

図書
図書
7. Partielle Differentialgleichungen in der mathematischen Physik. Erstveröffentlichung
S.G. Michlin ; in dt. Sprache hrsg. von S. Prössdorf ; [dt. Übers. Bernd Silbermann]
出版情報: Berlin : Akademie-Verlag, 1978  xiv, 519 p. ; 24 cm
シリーズ名: Mathematische Lehrbücher und Monographien ; 1 Abt. ; Mathematische Lehrbücher ; Bd. 30
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8.

図書
図書
8. Bäcklund transformations and their applications
C. Rogers and W.F. Shadwick
出版情報: New York : Academic Press, 1982  xiii, 334 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 161
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9.

図書
図書
9. Complex analysis in partial differential equations and mathematical physics (: gw ; : us ; : softcover)
G.M. Khenkin (ed.)
出版情報: Berlin ; New York : Springer-Verlag, c1993  286 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 54 . Several complex variables ; 5
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10.

図書
図書
10. Mathematical physics with partial differential equations
James R. Kirkwood
出版情報: Amsterdam : Academic Press, c2013  xii, 418 p. ; 24 cm
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目次情報: 続きを見る
Preface
Preliminaries / 1：
Self-Adjoint Operators / 1-1：
Fourier Coefficients
Exercises
Curvilinear Coordinates / 1-2：
Scaling Factors
Volume Integrals
The Gradient
The Laplacian
Spherical Coordinates
Other Curvilinear Systems
Applications
An Alternate Approach (Optional)
Approximate Identities and the Dirac-δ Function / 1-3：
Approximate Identities
The Dirac-δ Function in Physics
Some Calculus for the Dirac-δ Function
The Dirac-δ Function in Curvilinear Coordinates
The Issue of Convergence / 1-4：
Series of Real Numbers
Convergence versus Absolute Convergence
Series of Functions
Power Series
Taylor Series
Some Important Integration Formulas / 1-5：
Other Facts We Will Use Later
Another Important Integral
Vector Calculus / 2：
Vector Integration / 2-1：
Path Integrals
Line Integrals
Surfaces
Parameterized Surfaces
Integrals of Scalar Functions Over Surfaces
Surface Integrals of Vector Functions
Divergence and Curl / 2-2：
Cartesian Coordinate Case
Cylindrical Coordinate Case
Spherical Coordinate Case
The Curl
The Curl in Cartesian Coordinates
The Curl in Cylindrical Coordinates
The Curl in Spherical Coordinates
Green's Theorem, the Divergence Theorem, and Stokes' Theorem / 2-3：
The Divergence (Gauss') Theorem
Stokes' Theorem
An Application of Stokes' Theorem
An Application of the Divergence Theorem
Conservative Fields
Green's Functions / 3：
Introduction
Construction of Green's Function Using the Dirac-δ Function / 3-1：
Construction of Green's Function Using Variation of Parameters / 3-2：
Construction of Green's Function from Eigenfunctions / 3-3：
More General Boundary Conditions / 3-4：
The Fredholm Alternative (or, What If 0 Is an Eigenvalue?) / 3-5：
Green's Function for the Laplacian in Higher Dimensions / 3-6：
Fourier Series / 4：
Basic Definitions / 4-1：
Methods of Convergence of Fourier Series / 4-2：
Fourier Series on Arbitrary Intervals
The Exponential Form of Fourier Series / 4-3：
Fourier Sine and Cosine Series / 4-4：
Double Fourier Series / 4-5：
Exercise
Three Important Equations / 5：
Laplace's Equation / 5-1：
Derivation of the Heat Equation in One Dimension / 5-2：
Derivation of the Wave Equation in One Dimension / 5-3：
An Explicit Solution of the Wave Equation / 5-4：
Converting Second-Order PDEs to Standard Form / 5-5：
Sturm-Liouville Theory / 6：
The Self-Adjoint Property of a Sturm-Liouville Equation / 6-1：
Completeness of Eigenfunctions for Sturm-Liouville Equations / 6-2：
Uniform Convergence of Fourier Series / 6-3：
Separation of Variables in Cartesian Coordinates / 7：
Solving Laplace's Equation on a Rectangle / 7-1：
Laplace's Equation on a Cube / 7-2：
Solving the Wave Equation in One Dimension by Separation of Variables / 7-3：
Solving the Wave Equation in Two Dimensions in Cartesian Coordinates by Separation of Variables / 7-4：
Solving the Heat Equation in One Dimension Using Separation of Variables / 7-5：
The Initial Condition Is the Dirac-δ Function
Steady State of the Heat Equation / 7-6：
Checking the Validity of the Solution / 7-7：
Solving Partial Differential Equations in Cylindrical Coordinates Using Separation of Variables / 8：
An Example Where Bessel Functions Arise
The Solution to Bessel's Equation in Cylindrical Coordinates / 8-1：
Solving Laplace's Equation in Cylindrical Coordinates Using Separation of Variables / 8-2：
The Wave Equation on a Disk (Drum Head Problem) / 8-3：
The Heat Equation on a Disk / 8-4：
Solving Partial Differential Equations in Spherical Coordinates Using Separation of Variables / 9：
An Example Where Legendre Equations Arise / 9-1：
The Solution to Bessel's Equation in Spherical Coordinates / 9-2：
Legendre's Equation and Its Solutions / 9-3：
Associated Legendre Functions / 9-4：
Laplace's Equation in Spherical Coordinates / 9-5：
The Fourier Transform / 10：
The Fourier Transform as a Decomposition / 10-1：
The Fourier Transform from the Fourier Series / 10-2：
Some Properties of the Fourier Transform / 10-3：
Solving Partial Differential Equations Using the Fourier Transform / 10-4：
The Spectrum of the Negative Laplacian in One Dimension / 10-5：
The Fourier Transform in Three Dimensions / 10-6：
The Laplace Transform / 11：
Properties of the Laplace Transform / 11-1：
Solving Differential Equations Using the Laplace Transform / 11-2：
Solving the Heat Equation Using the Laplace Transform / 11-3：
The Wave Equation and the Laplace Transform / 11-4：
Solving PDEs with Green's Functions / 12：
Solving the Heat Equation Using Green's Function / 12-1：
Green's Function for the Nonhomogeneous Heat Equation
The Method of Images / 12-2：
Method of Images for a Semi-infinite Interval
Method of Images for a Bounded Interval
Green's Function for the Wave Equation / 12-3：
Green's Function and Poisson's Equation / 12-4：
Appendix: Computing the Laplacian with the Chain Rule
References
Index
Preface
Preliminaries / 1：
Self-Adjoint Operators / 1-1：
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