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1.

図書
図書
1. Numerical solution of partial differential equations in science and engineering
Leon Lapidus, George F. Pinder
出版情報: New York : Wiley, c1982  677 p. ; 24 cm
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目次情報: 続きを見る
Fundamental Concepts / Chapter 1.：
Notation / 1.0.：
First-Order Partial Differential Equations / 1.1.：
First-Order Quasilinear Partial Differential Equations / 1.1.1.：
Initial Value or Cauchy Problem / 1.1.2.：
Application of Characteristic Curves / 1.1.3.：
Nonlinear First-Order Partial Differential Equations / 1.1.4.：
Second-Order Partial Differential Equations / 1.2.：
Linear Second-Order Partial Differential Equations / 1.2.1.：
Classification and Canonical Form of Selected Partial Differential Equations / 1.2.2.：
Quasilinear Partial Differential Equations and Other Ideas / 1.2.3.：
Systems of First-Order PDEs / 1.3.：
First-Order and Second-Order PDEs / 1.3.1.：
Characteristic Curves / 1.3.2.：
Applications of Characteristic Curves / 1.3.3.：
Initial and Boundary Conditions / 1.4.：
References
Basic Concepts in the Finite Difference and Finite Element Methods / Chapter 2.：
Introduction / 2.0.：
Finite Difference Approximations / 2.1.：
Taylor Series Expansions / 2.1.1.：
Operator Notation for u(x) / 2.1.3.：
Finite Difference Approximations in Two Dimensions / 2.1.4.：
Additional Concepts / 2.1.5.：
Introduction to Finite Element Approximations / 2.2.：
Method of Weighted Residuals / 2.2.1.：
Application of the Method of Weighted Residuals / 2.2.2.：
The Choice of Basis Functions / 2.2.3.：
Two-Dimensional Basis Functions / 2.2.4.：
Approximating Equations / 2.2.5.：
Relationship between Finite Element and Finite Difference Methods / 2.3.：
Finite Elements on Irregular Subspaces / Chapter 3.：
Triangular Elements / 3.0.：
The Linear Triangular Element / 3.1.1.：
Area Coordinates / 3.1.2.：
The Quadratic Triangular Element / 3.1.3.：
The Cubic Triangular Element / 3.1.4.：
Higher-Order Triangular Elements / 3.1.5.：
Isoparametric Finite Elements / 3.2.：
Transformation Functions / 3.2.1.：
Numerical Integration / 3.2.2.：
Isoparametric Serendipity Hermitian Elements / 3.2.3.：
Isoparametric Hermitian Elements in Normal and Tangential Coordinates / 3.2.4.：
Boundary Conditions / 3.3.：
Three-Dimensional Elements / 3.4.：
Parabolic Partial Differential Equations / Chapter 4.：
Partial Differential Equations / 4.0.：
Well-Posed Partial Differential Equations / 4.1.1.：
Model Difference Approximations / 4.2.：
Well-Posed Difference Forms / 4.2.1.：
Derivation of Finite Difference Approximations / 4.3.：
The Classic Explicit Approximation / 4.3.1.：
The Dufort-Frankel Explicit Approximation / 4.3.2.：
The Richardson Explicit Approximation / 4.3.3.：
The Backwards Implicit Approximation / 4.3.4.：
The Crank-Nicolson Implicit Approximation / 4.3.5.：
The Variable-Weighted Implicit Approximation / 4.3.6.：
Consistency and Convergence / 4.4.：
Stability / 4.5.：
Heuristic Stability / 4.5.1.：
Von Neumann Stability / 4.5.2.：
Matrix Stability / 4.5.3.：
Some Extensions / 4.6.：
Influence of Lower-Order Terms / 4.6.1.：
Higher-Order Forms / 4.6.2.：
Predictor-Corrector Methods / 4.6.3.：
Asymmetric Approximations / 4.6.4.：
Variable Coefficients / 4.6.5.：
Nonlinear Parabolic PDEs / 4.6.6.：
The Box Method / 4.6.7.：
Solution of Finite Difference Approximations / 4.7.：
Solution of Implicit Approximations / 4.7.1.：
Explicit versus Implicit Approximations / 4.7.2.：
Composite Solutions / 4.8.：
Global Extrapolation / 4.8.1.：
Some Numerical Results / 4.8.2.：
Local Combination / 4.8.3.：
Composites of Different Approximations / 4.8.4.：
Finite Difference Approximations in Two Space Dimensions / 4.9.：
Explicit Methods / 4.9.1.：
Irregular Boundaries / 4.9.2.：
Implicit Methods / 4.9.3.：
Alternating Direction Explicit (ADE) Methods / 4.9.4.：
Alternating Direction Implicit (ADI) Methods / 4.9.5.：
LOD and Fractional Splitting Methods / 4.9.6.：
Hopscotch Methods / 4.9.7.：
Mesh Refinement / 4.9.8.：
Three-Dimensional Problems / 4.10.：
ADI Methods / 4.10.1.：
Iterative Solutions / 4.10.2.：
Finite Element Solution of Parabolic Partial Differential Equations / 4.11.：
Galerkin Approximation to the Model Parabolic Partial Differential Equation / 4.11.1.：
Approximation of the Time Derivative / 4.11.2.：
Approximation of the Time Derivative for Weakly Nonlinear Equations / 4.11.3.：
Finite Element Approximations in One Space Dimension / 4.12.：
Formulation of the Galerkin Approximating Equations / 4.12.1.：
Linear Basis Function Approximation / 4.12.2.：
Higher-Degree Polynomial Basis Function Approximation / 4.12.3.：
Formulation Using the Dirac Delta Function / 4.12.4.：
Orthogonal Collocation Formulation / 4.12.5.：
Asymmetric Weighting Functions / 4.12.6.：
Finite Element Approximations in Two Space Dimensions / 4.13.：
Galerkin Approximation in Space and Time / 4.13.1.：
Galerkin Approximation in Space Finite Difference in Time / 4.13.2.：
Asymmetric Weighting Functions in Two Space Dimensions / 4.13.3.：
Lumped and Consistent Time Matrices / 4.13.4.：
Collocation Finite Element Formulation / 4.13.5.：
Treatment of Sources and Sinks / 4.13.6.：
Alternating Direction Formulation / 4.13.7.：
Finite Element Approximations in Three Space Dimensions / 4.14.：
Example Problem / 4.14.1.：
Summary / 4.15.：
Elliptic Partial Differential Equations / Chapter 5.：
Model Elliptic PDEs / 5.0.：
Specific Elliptic PDEs / 5.1.1.：
Further Items / 5.1.2.：
Finite Difference Solutions in Two Space Dimensions / 5.2.：
Five-Point Approximations and Truncation Error / 5.2.1.：
Nine-Point Approximations and Truncation Error / 5.2.2.：
Approximations to the Biharmonic Equation / 5.2.3.：
Boundary Condition Approximations / 5.2.4.：
Matrix Form of Finite Difference Equations / 5.2.5.：
Direct Methods of Solution / 5.2.6.：
Iterative Concepts / 5.2.7.：
Formulation of Point Iterative Methods / 5.2.8.：
Convergence of Point Iterative Methods / 5.2.9.：
Line and Block Iteration Methods / 5.2.10.：
Acceleration and Semi-Iterative Overlays / 5.2.11.：
Finite Difference Solutions in Three Space Dimensions / 5.3.：
Iteration Concepts / 5.3.1.：
Finite Element Methods for Two Space Dimensions / 5.3.3.：
Galerkin Approximation / 5.4.1.：
Collocation Approximation / 5.4.2.：
Mixed Finite Element Approximation / 5.4.4.：
Approximation of the Biharmonic Equation / 5.4.5.：
Boundary Integral Equation Methods / 5.5.：
Fundamental Theory / 5.5.1.：
Boundary Element Formulation / 5.5.2.：
Linear Interpolation Functions / 5.5.3.：
Poisson's Equation / 5.5.5.：
Nonhomogeneous Materials / 5.5.6.：
Combination of Finite Element and Boundary Integral Equation Methods / 5.5.7.：
Three-Dimensional Finite Element Simulation / 5.6.：
Hyperbolic Partial Differential Equations / 5.7.：
Equations of Hyperbolic Type / 6.0.：
Finite Difference Solution of First-Order Scalar Hyperbolic Partial Differential Equations / 6.2.：
Stability, Truncation Error, and Other Features / 6.2.1.：
Other Approximations / 6.2.2.：
Dissipation and Dispersion / 6.2.3.：
Hopscotch Methods and Mesh Refinement / 6.2.4.：
Finite Difference Solution of First-Order Vector Hyperbolic Partial Differential Equations / 6.3.：
Finite Difference Solution of First-Order Vector Conservative Hyperbolic Partial Differential Equations / 6.4.：
Finite Difference Solutions to Two- and Three-Dimensional Hyperbolic Partial Differential Equations / 6.5.：
Finite Difference Schemes / 6.5.1.：
Two-Step, ADI, and Strang-Type Algorithms / 6.5.2.：
Conservative Hyperbolic Partial Differential Equations / 6.5.3.：
Finite Difference Solution of Second-Order Model Hyperbolic Partial Differential Equations / 6.6.：
One-Space-Dimension Hyperbolic Partial Differential Equation / 6.6.1.：
Explicit Algorithms / 6.6.2.：
Implicit Algorithms / 6.6.3.：
Simultaneous First-Order Partial Differential Equations / 6.6.4.：
Mixed Systems / 6.6.5.：
Two- and Three-Space-Dimensional Hyperbolic Partial Differential Equations / 6.6.6.：
Implicit ADI and LOD Methods / 6.6.7.：
Finite Element Solution of First-Order Model Hyperbolic Partial Differential Equations / 6.7.：
Asymmetric Weighting Function Approximation / 6.7.1.：
An H[superscript -1] Galerkin Approximation / 6.7.3.：
Orthogonal Collocation with Asymmetric Bases / 6.7.4.：
Finite Element Solution of Two- and Three-Space-Dimensional First-Order Hyperbolic Partial Differential Equations / 6.7.6.：
Galerkin Finite Element Formulation / 6.8.1.：
Finite Element Solution of First-Order Vector Hyperbolic Partial Differential Equations / 6.8.2.：
Finite Element Solution of Two- and Three-Space-Dimensional First-Order Vector Hyperbolic Partial Differential Equations / 6.9.1.：
Finite Element Solution of One-Space-Dimensional Second-Order Hyperbolic Partial Differential Equations / 6.10.1.：
Time Approximations / 6.11.1.：
Finite Element Solution of Two- and Three-Space-Dimensional Second-Order Hyperbolic Partial Differential Equations / 6.11.3.：
Index / 6.12.1.：
Fundamental Concepts / Chapter 1.：
Notation / 1.0.：
First-Order Partial Differential Equations / 1.1.：
2.

図書
図書
2. The mathematics of Paul Erdös (1 : hardcover : acid-free paper ; 2 : hardcover : acid-free paper)
Ronald L. Graham, Jaroslav Nešetřil (eds.)
出版情報: Berlin : Springer, c1997  2 v. ; 25 cm
シリーズ名: Algorithms and combinatorics ; 13-14
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3.

図書
図書
3. Probability theory. 4th ed (v. 1 : us - v. 2 : gw)
M. Loève
出版情報: New York ; Berlin : Springer-Verlag, c1977-1978  2 v. ; 24 cm
シリーズ名: Graduate texts in mathematics ; 45-46
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4.

図書
図書
4. Differential thermal analysis (v. 1 ; v. 2)
edited by R.C. Mackenzie
出版情報: London ; New York : Academic Press, 1970-1972  2 v. ; 24 cm
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5.

図書
図書
5. The theory of groups. 2nd English ed (v. 1 ; v. 2)
by A.G. Kurosh ; translated from the Russian and edited by K.A. Hirsch
出版情報: New York : Chelsea Pub. Co., c1960  v. ; 23 cm
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6.

図書
図書
6. Spectral analysis and time series (v. 1 ; v. 2)
M.B. Priestley
出版情報: London : New York : Academic Press, c1981  2 v. (xvii, [45], 890 p.) ; 24 cm
シリーズ名: Probability and mathematical statistics : a series of monographs and textbooks
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目次情報:
v. 1. Univariate series
v. 2. Multivariate series, prediction and control
v. 1. Univariate series
v. 2. Multivariate series, prediction and control
7.

図書
図書
7. Dynamical systems : an international symposium (v. 1 ; v. 2)
edited by Lamberto Cesari, Jack K. Hale, Joseph P. LaSalle
出版情報: New York : Academic Press, 1976  2 v. ; 24 cm
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8.

図書
図書
8. Quantum mechanics (v. 1 : hard - v. 2 : pbk)
Albert Messiah ; [translated from the French by G.M. Temmer]
出版情報: Amsterdam : North-Holland , New York : Sole dostributors for U.S.A., Intersicence Publishers, 1961-1962  2 v. (xv, 1136 p.) ; 22 cm
シリーズ名: Series in physics
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9.

図書
図書
9. 高等数学教程 (1 : 1巻第1分冊 - 12 : 5巻第2分冊)
スミルノフ [著] ; 彌永昌吉 [ほか] 飜訳監修 ; 福原満洲雄訳者代表
出版情報: 東京 : 共立出版, 1958.5-1962.10  12冊 ; 22cm
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10.

図書
図書
10. 数論 (1 ; 2 ; 3)
河田敬義著
出版情報: 東京 : 岩波書店, 1978.2-1979.2  3冊 (432p) ; 21cm
シリーズ名: 岩波講座基礎数学 / 小平邦彦監修 ; 岩堀長慶 [ほか] 編 ; 7 . 代数学||ダイスウガク ; 6
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