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1.

図書
図書
1. Numerical recipes in C++ : the art of scientific computing. 2nd ed ([Text] : hardback - : complete CD-ROM (UNIX/Linux))
William H. Press ... [et al.]
出版情報: Cambridge [England] ; New York, NY, USA : Cambridge University Press, 2002  xxviii, 1002 p. ; 26 cm.
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2.

図書
図書
2. Geometric function theory and non-linear analysis
Tadeusz Iwaniec and Gaven Martin
出版情報: Oxford : Clarendon Press , New York : Oxford University Press, 2001  xv, 552 p. ; 25 cm
シリーズ名: Oxford mathematical monographs
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3.

図書
図書
3. Numerical mathematics
Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
出版情報: New York : Springer, c2000  xx, 654 p. ; 24 cm
シリーズ名: Texts in applied mathematics ; 37
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4.

図書
図書
4. Asymptotology : ideas, methods, and applications
by Igor V. Andrianov, Leonid I. Manevitch ; with help from Michiel Hazewinkel
出版情報: Dordrecht ; London : Kluwer Academic, c2002  xvii, 252 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 551
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Foreword
Preface
Acknowledgments
Synopsis
Introduction / 1.：
General Remarks
What does "Popular Science Book" Mean? / 2.：
Why "Asymptology"? / 3.：
What Are Asymptotic Methods?
Reduction of the System's Dimension
Regular Asymptotics and Boundary Layers
Asymptotic Series
Averaging and Homogenization / 4.：
Continuous limits / 5.：
Local and Nonlocal Linearization / 6.：
Estimation of Asymptotic Solution Errors / 7.：
Summation Procedures / 8.：
"Padeons" / 9.：
How to Make Both Ends Meet / 10.：
Renormalization / 11.：
Asymptotics and Computers / 12.：
Are Asymptotic Methods a Panacea? / 13.：
A Little Mathematics
Basic Formalism
A Simple Example
Regular and Singular Asymptotics
Asymptotic Decomposition
Supplementary Asymptotics
Continuous Approximation of a Chain of Masses
Search for Small Parameters
Newton Polyhedron
Catastrophe Theory
How Asymptotic Methods Work
Celestial Mechanics
Theory of Plates and Shells
Polymer Physics
Asymptotics and Engineering
Theory of Composite Materials
Biology
Et Cetera
Asymptotics and Art
Asymptotics in Pictures
Formation of New Concepts
Is Understanding an Asymptotic Process?
Asymptotic Methods and Physical Theories
Asymptotic Correspondence of Physical Theories
Mechanics by Aristotle and Galileo-Newton
Newton Mechanics and Special Relativity Theory
Geometrical and Wave Optics
Classical and Quantum Mechanics
"Simple Theories" in Physics
"The Cube of Theories"
Asymptotic Ways of Thinking for Beginners
Phenomenology and First Principles
Basic Relations of Shell Theory
How to Construct Consistent Phenomenological Theories
Some Conclusions
A Little History
Method of Averaging
Triumphs of Perturbation Methods
Galileo and the Principle of Idealization
Fathers of Asymptotic Methods
Leonhard Euler
Alexis-Claude Clairaut
Jean Le Rond d'Alembert
Joseph-Louis Lagrange
Pierre-Simon Laplace
Carl Friedrich Gauss
Jules-Henri Poincare
Alexander M. Lyapunov
Henri Eugene Pade
Ludwig Prandtl
Balthasar Van der Pol
Nickolay M. Krylov
Nickolay N. Bogoliubov
Conclusion
Appendices
Linear and Nonlinear Mathematical Physics: from Harmonic Waves to Solitons / A：
The Quasi-Linear World
On the Way to Nonlinear Physics
How Solitons Work
Certain Mathematical Notions of Catastrophe Theory / B：
Representation of Functions by Jets
Equivalency of a Function and its k-th Jet
Representation of Functions by Jets in Ordinary Points
Jets at Non-Degenerate Critical Points
Jets at Degenerate Critical Points
Control Parameters
Asymptotics and Scaling Transformations / C：
Estimation of Variables
Subsequent Approximations
Asymptotic Approaches: Attempt at a Definition / D：
Asymptotic Methods or a New Mathematics?
Uncertainty-Complementarity-Compatibility
Some Web-Pages / E：
References
About the Authors
Author Index
Topic Index
Foreword
Preface
Acknowledgments
5.

図書
図書
5. Stability and transition : theory and application : efficient numerical methods with computer programs (:us ; :gw)
Tuncer Cebeci
出版情報: Long Beach, Calif. : Horizons , Berlin : Springer, c2004  xii, 262 p. ; 25 cm
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Introduction / 1：
Transition Process / 1.1：
Prediction of Transition / 1.2：
Empirical Correlations / 1.2.1：
Michel's Method / 1.2.2：
Granville's Method / 1.2.3：
H-R[subscript x] Method / 1.2.4：
Factors that Influence Transition / 1.3：
Effects of Freestream Turbulence and Noise / 1.3.1：
Effects of Pressure Gradient / 1.3.2：
Effects of Heat Transfer / 1.3.3：
Effects of Surface Roughness / 1.3.4：
Effects of Suction / 1.3.5：
Effects of Surface Curvature / 1.3.6：
References
Stability-Transition Theory / 2：
Underlying Mathematical Arguments for e[superscript n]-Method / 2.1：
Linear Stability Equations / 2.3：
Orr-Sommerfeld Equation / 2.3.1：
Properties of the Orr-Sommerfeld Equation for Two-Dimensional Flows / 2.3.2：
e[superscript n]-Method for Two-Dimensional Flows / 2.4：
e[superscript n]-Method for Three-Dimensional Flows / 2.5：
Eigenvalue Formulations / 2.5.1：
The Zarf / 2.5.2：
Numerical Method / 3：
Numerical Solution of the Orr-Sommerfeld Equation for Two-Dimensional Flows / 3.1：
Eigenvalue Procedure for Stability Diagrams / 3.2.1：
Eigenvalue Procedure for Transition / 3.2.2：
Numerical Solution of the Orr-Sommerfeld Equation for Three-Dimensional Flows: Mack/Arnal Eigenvalue Formulation / 3.3：
Numerical Solution of the Orr-Sommerfeld Equation for Three-Dimensional Flows: Cebeci-Stewartson Eigenvalue Formulation / 3.4：
Eigenvalue Procedure for Zarf / 3.4.1：
Estimation of Eigenvalues / 3.4.2：
Appendix 3A
Stability Transition Program for Two-Dimensional Incompressible Flows / 4：
Description of the Computer Program STP / 4.1：
MAIN / 4.2.1：
Subroutine VELPRO / 4.2.2：
Subroutine CSAVE / 4.2.3：
Subroutine NEWTON / 4.2.4：
Subroutine NEWTONI / 4.2.5：
Stability Diagrams for Falkner-Skan Flows / 4.3：
Falkner-Skan Flows / 4.3.1：
Sample Calculations for Constructing Stability Diagrams for Blasius Flow / 4.3.2：
Sample Calculations for Constructing Stability Diagrams for Lower-Branch Solutions of the Falkner-Skan Equation / 4.3.3：
Sample Calculations for Predicting Transition / 4.4：
Flat-Plate Flow / 4.4.1：
Airfoil Flow / 4.4.2：
Description of the Computer Program STPW / 4.5：
Input to STPW / 4.5.1：
Sample Calculations / 4.5.2：
Shooting Method / Appendix 4A：
Description of the Method for f"[subscript w greater than or equal] 0 / 4A.1：
Description of the Method for f"[subscript w less than sign] 0 / 4A.2：
Computer Program / 4A.3：
An Interactive Boundary-Layer and Stability-Transition Program for Two-Dimensional Flows / 5：
Interactive Boundary-Layer Method / 5.1：
Turbulence Model / 5.2.1：
Inviscid Method / 5.2.2：
Extension of the Interactive Boundary-Layer and Stability-Transition Approach to Multielement Airfoils / 5.2.4：
Airfoils at High Reynolds Numbers / 5.4：
Accuracy of the e[superscript n]-Method for Flows with Separation / 5.5：
Airfoils at Low Reynolds Numbers / 5.6：
Multielement Airfoils / 5.7：
Stability-Transition Program for Three-Dimensional Incompressible Flows / 6：
Description of the Computer Program 3DSTP and Sample Calculations / 6.1：
Description of the Computer Program / 6.2.1：
Applications of 3DSTP / 6.2.2：
ONERA-D Infinite Swept Wing / 6.3.1：
Prolate Spheroid / 6.3.2：
Prediction of Transition with Curvature Effect / 6.4：
Stability Equations with Curvature Terms / 6.4.1：
Calculation of the Curvature Terms / 6.4.2：
Effects of Sweep Angle and Reynolds Number on Transition with Curvature Effect Included in the Stability Equations / 6.4.3：
Computer Program 3DSTPWC and Sample Calculations / 6.5：
Description of Input / 6.5.1：
A Stability-Transition Program for Three-Dimensional Compressible Flows on Wings / 6.5.2：
Boundary-Layer Equations / 7.1：
Initial Conditions / 7.3：
Quasi-Three-Dimensional Boundary-Layer Equations / 7.3.1：
Attachment Line Equations / 7.3.2：
Interface Program / 7.4：
Choice of the Surface Coordinate System / 7.5.1：
Geometric Parameters of the Coordinate System / 7.5.2：
Calculation of Inviscid Velocity Components for Boundary-Layer Grid / 7.5.3：
Solution of the Boundary-Layer Equations / 7.5.4：
Transformed Equations / 7.6.1：
Solution of the Stability Equations for Compressible Flows / 7.6.2：
AS409 Infinite Swept Wing / 7.8：
Experimental Data / 7.8.1：
Calculations with the Mack-Arnal Formulation / 7.8.2：
Calculations with the Cebeci-Stewartson Formulation / 7.8.3：
Software for Calculating Transition in Incompressible and Compressible Flows on Wings with and without Suction / 7.9：
Boundary Layer Program / 7.9.1：
Calculation of Zarf / 7.9.2：
Amplification Calculations / 7.9.3：
Summary of Transition Calculations / 7.9.4：
Calculation of the Lower Branch of the Zarf / 7.9.5：
Amplification Calculations for Disturbances from the Lower Branch / 7.9.6：
Amplification Calculations for Disturbances from the Upper Branch / 7.9.7：
Transition Prediction by Parabolized Stability Equations / 8：
Parabolized Stability Equations / 8.1：
Subroutine START / 8.3：
Subroutine COEF / 8.4.2：
Subroutine GETNA / 8.4.3：
Solution Algorithm: Subroutines MATRIX6, GAUSS, USOLV, GAMSV / 8.4.4：
Sample Calculations with PSE / 8.5：
Computer Programs in the CD-ROM Accompanying the Book / Appendix A：
Shooting Method: For f"(0) [greater than or equal] 0 / A.1：
Shooting Method: For f"(0) [less than sign] 0 / A.2：
2D Stability Transition Program (STP2D) / A.3：
Interactive Boundary-layer (IBL) Program / A.4：
Panel Method (HSPM), 2D Interface Program (IPRPM2D), Inverse Boundary-Layer Program (INBLP) and STP2D / A.5：
HSPM, IPRPM2D, Boundary-Layer Infinite Swept Wing (BLISW) Program and 3D Stability-Transition Program (3DSTP) / A.6：
Stability-Transition Program Based on Parabolized Stability Equations (PSE) / A.7：
Cross-Flow Dominated Flows / A.7.1：
Flows in Which Tollmien-Schlichting (T-S) Waves Dominate / A.7.2：
Computer Programs in the CD-ROM Available from the Author / Appendix B：
Boundary Layer and Stability-Transition Program for Air, Water and Sea (STPW) / B.1：
Panel Method (HSPM), 2D Interface Program (IPRPM), Infinite Swept Wing Boundary-Layer Program (BLISW) and 3D Stability Transition Program with Curvature Effects (3DSTPWC) / B.2：
HSPM, IPRPM, BLISW, 3DSTPWC, Parabolized Stability Equations (PSE) / B.3：
Flows in Which Tollmien-Schlichting (T-S) Instability Dominates / B.3.1：
Interactive Boundary-Layer Method for Single and Multielement Airfoils (MEIBL) / Appendix C：
Application of MEIBL to Three-Dimensional Flows / C.1：
Inviscid Flow / C.1.1：
Viscous Flow / C.1.2：
Interaction / C.1.3：
Coordinate Systems for Viscous and Inviscid Flow Calculations / C.2：
User's Manual / C.3：
Input Data / C.3.1：
Output Data / C.3.2：
Detailed Flow at [alpha] = 4[degree] and [alpha] = 20[degree] / C.4：
Force and Moment Coefficient Calculations / C.4.2：
Software for Calculating Transition in Three-Dimensional Compressible Flows / Appendix D：
Description of the Boundary Layer Program / D.1：
Input Data Description / D.1.1：
Output Data Description / D.1.2：
Description of the Transition Calculation Procedure / D.2：
Zarf Calculation / D.2.1：
Amplification Calculation / D.2.2：
Summary of the Procedure / D.2.3：
Sample Calculation: Input and Output Data Description / D.3：
Input File Description / D.3.1：
Zarf Upper Branch Calculation / D.3.2：
Quick Reference Manual / D.3.5：
Subject Index
Introduction / 1：
Transition Process / 1.1：
Prediction of Transition / 1.2：
6.

図書
図書
6. Metal forming analysis
R.H. Wagoner, J.-L. Chenot
出版情報: Cambridge : Cambridge University Press, 2001  xiii, 376 p. ; 27 cm
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7.

図書
図書
7. Introduction to numerical analysis (: pbk)
Arnold Neumaier
出版情報: Cambridge ; New York : Cambridge University Press, 2001  viii, 356 p. ; 24 cm
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Preface
The Numerical Evaluation of Expressions / 1.：
Arithmetic Expressions and Automatic Differentiation / 1.1：
Numbers, Operations, and Elementary Functions / 1.2：
Numerical Stability / 1.3：
Error Propagation and Condition / 1.4：
Interval Arithmetic / 1.5：
Exercises / 1.6：
Linear Systems of Equations / 2.：
Gaussian Elimination / 2.1：
Variations on a Theme / 2.2：
Rounding Errors, Equilibration, and Pivot Search / 2.3：
Vector and Matrix Norms / 2.4：
Condition Numbers and Data Perturbations / 2.5：
Iterative Refinement / 2.6：
Error Bounds for Solutions of Linear Systems / 2.7：
Interpolation and Numerical Differentiation / 2.8：
Interpolation by Polynomials / 3.1：
Extrapolation and Numerical Differentiation / 3.2：
Cubic Splines / 3.3：
Approximation by Splines / 3.4：
Radial Basis Functions / 3.5：
Numerical Integration / 3.6：
The Accuracy of Quadrature Formulas / 4.1：
Gaussian Quadrature Formulas / 4.2：
The Trapezoidal Rule / 4.3：
Adaptive Integration / 4.4：
Solving Ordinary Differential Equations / 4.5：
Step Size and Order Control / 4.6：
Univariate Nonlinear Equations / 4.7：
The Secant Method / 5.1：
Bisection Methods / 5.2：
Spectral Bisection Methods for Eigenvalues / 5.3：
Convergence Order / 5.4：
Error Analysis / 5.5：
Complex Zeros / 5.6：
Methods Using Derivative Information / 5.7：
Systems of Nonlinear Equations / 5.8：
Preliminaries / 6.1：
Newton's Method and Its Variants / 6.2：
Further Techniques for Nonlinear Systems / 6.3：
References / 6.5：
Index
Preface
The Numerical Evaluation of Expressions / 1.：
Arithmetic Expressions and Automatic Differentiation / 1.1：
8.

図書
図書
8. Computational physics : an introduction. 2nd ed
Franz J. Vesely
出版情報: New York : Kluwer Academic/Plenum Publishers, c2001  xvi, 259 p. ; 26 cm
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The Three Pillars of Computational Physics / I：
Finite Differences / 1：
Interpolation Formulae / 1.1：
NGF Interpolation / 1.1.1：
NGB Interpolation / 1.1.2：
ST Interpolation / 1.1.3：
Difference Quotients / 1.2：
DNGF Formulae / 1.2.1：
DNGB Formulae / 1.2.2：
DST Formulae / 1.2.3：
Finite Differences in Two Dimensions / 1.3：
Sample Applications / 1.4：
Classical Point Mechanics / 1.4.1：
Diffusion and Thermal Conduction / 1.4.2：
Linear Algebra / 2：
Exact Methods / 2.1：
Gauss Elimination and Back Substitution / 2.1.1：
Simplifying Matrices: The Householder Transformation / 2.1.2：
LU Decomposition / 2.1.3：
Tridiagonal Matrices: Recursion Method / 2.1.4：
Iterative Methods / 2.2：
Jacobi Relaxation / 2.2.1：
Gauss-Seidel Relaxation (GSR) / 2.2.2：
Successive Over-Relaxation (SOR) / 2.2.3：
Alternating Direction Implicit Method (ADI) / 2.2.4：
Conjugate Gradient Method (CG) / 2.2.5：
Eigenvalues and Eigenvectors / 2.3：
Largest Eigenvalue and Related Eigenvector / 2.3.1：
Arbitrary Eigenvalue/-vector: Inverse Iteration / 2.3.2：
Potential Equation / 2.4：
Electronic Orbitals / 2.4.3：
Stochastics / 3：
Equidistributed Random Variates / 3.1：
Linear Congruential Generators / 3.1.1：
Shift Register Generators / 3.1.2：
Other Distributions / 3.2：
Fundamentals / 3.2.1：
Transformation Method / 3.2.2：
Generalized Transformation Method / 3.2.3：
Rejection Method / 3.2.4：
Multivariate Gaussian Distribution / 3.2.5：
Equidistribution in Orientation Space / 3.2.6：
Random Sequences / 3.3：
Markov Processes / 3.3.1：
Autoregressive Processes / 3.3.3：
Wiener-Levy Process / 3.3.4：
Markov Chains and the Monte Carlo method / 3.3.5：
Stochastic Optimization / 3.4：
Simulated Annealing / 3.4.1：
Genetic Algorithms / 3.4.2：
Everything Flows / II：
Ordinary Differential Equations / 4：
Initial Value Problems of First Order / 4.1：
Euler-Cauchy Algorithm / 4.1.1：
Stability and Accuracy of Difference Schemes / 4.1.2：
Explicit Methods / 4.1.3：
Implicit Methods / 4.1.4：
Predictor-Corrector Method / 4.1.5：
Runge-Kutta Method / 4.1.6：
Extrapolation Method / 4.1.7：
Initial Value Problems of Second Order / 4.2：
Verlet Method / 4.2.1：
Nordsieck Formulation of the PC Method / 4.2.2：
Symplectic Algorithms / 4.2.4：
Numerov's Method / 4.2.6：
Boundary Value Problems / 4.3：
Shooting Method / 4.3.1：
Relaxation Method / 4.3.2：
Partial Differential Equations / 5：
Initial Value Problems I (Hyperbolic) / 5.1：
FTCS Scheme; Stability Analysis / 5.1.1：
Lax Scheme / 5.1.2：
Leapfrog Scheme (LF) / 5.1.3：
Lax-Wendroff Scheme (LW) / 5.1.4：
Lax and Lax-Wendroff in Two Dimensions / 5.1.5：
Initial Value Problems II (Parabolic) / 5.2：
FTCS Scheme / 5.2.1：
Implicit Scheme of First Order / 5.2.2：
Crank-Nicholson Scheme (CN) / 5.2.3：
Dufort-Frankel Scheme (DF) / 5.2.4：
Boundary Value Problems: Elliptic DE / 5.3：
Relaxation and Multigrid Techniques / 5.3.1：
ADI Method for the Potential Equation / 5.3.2：
Fourier Transform Method (FT) / 5.3.3：
Cyclic Reduction (CR) / 5.3.4：
Anchors Aweigh / III：
Simulation and Statistical Mechanics / 6：
Model Systems of Statistical Mechanics / 6.1：
A Nutshellfull of Fluids and Solids / 6.1.1：
Tricks of the Trade / 6.1.2：
Monte Carlo Method / 6.2：
Molecular Dynamics Simulation / 6.3：
Hard Spheres / 6.3.1：
Continuous Potentials / 6.3.2：
Beyond Basic Molecular Dynamics / 6.3.3：
Evaluation of Simulation Experiments / 6.4：
Pair Correlation Function / 6.4.1：
Autocorrelation Functions / 6.4.2：
Particles and Fields / 6.5：
Ewald summation / 6.5.1：
Particle-Mesh Methods (PM and P3M) / 6.5.2：
Stochastic Dynamics / 6.6：
Quantum Mechanical Simulation / 7：
Diffusion Monte Carlo (DMC) / 7.1：
Path Integral Monte Carlo (PIMC) / 7.2：
Wave Packet Dynamics (WPD) / 7.3：
Density Functional Molecular Dynamics (DFMD) / 7.4：
Hydrodynamics / 8：
Compressible Flow without Viscosity / 8.1：
Explicit Eulerian Methods / 8.1.1：
Particle-in-Cell Method (PIC) / 8.1.2：
Smoothed Particle Hydrodynamics (SPH) / 8.1.3：
Incompressible Flow with Viscosity / 8.2：
Vorticity Method / 8.2.1：
Pressure Method / 8.2.2：
Free Surfaces: Marker-and-Cell Method (MAC) / 8.2.3：
Lattice Gas Models for Hydrodynamics / 8.3：
Lattice Gas Cellular Automata / 8.3.1：
The Lattice Boltzmann Method / 8.3.2：
Direct Simulation Monte Carlo / Bird method / 8.4：
Appendixes
Machine Errors / A：
Discrete Fourier Transformation / B：
Fast Fourier Transform (FFT) / B.1：
Bibliography
Index
The Three Pillars of Computational Physics / I：
Finite Differences / 1：
Interpolation Formulae / 1.1：
9.

図書
図書
9. Fundamentals of engineering numerical analysis (: pbk ; : hbk)
Parviz Moin
出版情報: Cambridge : Cambridge University Press, 2001  xiv, 209 p. ; 26 cm
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Preface
Interpolation / 1：
Lagrange Polynomial Interpolation / 1.1：
Cubic Spline Interpolation / 1.2：
Exercises
Further Reading
Numerical Differentiation--Finite Differences / 2：
Construction of Difference Formulas Using Taylor Series / 2.1：
A General Technique for Construction of Finite Difference Schemes / 2.2：
An Alternative Measure for the Accuracy of Finite Differences / 2.3：
Pade Approximations / 2.4：
Non-Uniform Grids / 2.5：
Numerical Integration / 3：
Trapezoidal and Simpson's Rules / 3.1：
Error Analysis / 3.2：
Trapezoidal Rule with End-Correction / 3.3：
Romberg Integration and Richardson Extrapolation / 3.4：
Adaptive Quadrature / 3.5：
Gauss Quadrature / 3.6：
Numerical Solution of Ordinary Differential Equations / 4：
Initial Value Problems / 4.1：
Numerical Stability / 4.2：
Stability Analysis for the Euler Method / 4.3：
Implicit or Backward Euler / 4.4：
Numerical Accuracy Revisited / 4.5：
Trapezoidal Method / 4.6：
Linearization for Implicit Methods / 4.7：
Runge--Kutta Methods / 4.8：
Multi-Step Methods / 4.9：
System of First-Order Ordinary Differential Equations / 4.10：
Boundary Value Problems / 4.11：
Shooting Method / 4.11.1：
Direct Methods / 4.11.2：
Numerical Solution of Partial Differential Equations / 5：
Semi-Discretization / 5.1：
von Neumann Stability Analysis / 5.2：
Modified Wavenumber Analysis / 5.3：
Implicit Time Advancement / 5.4：
Accuracy via Modified Equation / 5.5：
Du Fort--Frankel Method: An Inconsistent Scheme / 5.6：
Multi-Dimensions / 5.7：
Implicit Methods in Higher Dimensions / 5.8：
Approximate Factorization / 5.9：
Stability of the Factored Scheme / 5.9.1：
Alternating Direction Implicit Methods / 5.9.2：
Mixed and Fractional Step Methods / 5.9.3：
Elliptic Partial Differential Equations / 5.10：
Iterative Solution Methods / 5.10.1：
The Point Jacobi Method / 5.10.2：
Gauss--Seidel Method / 5.10.3：
Successive Over Relaxation Scheme / 5.10.4：
Multigrid Acceleration / 5.10.5：
Discrete Transform Methods / 6：
Fourier Series / 6.1：
Discrete Fourier Series / 6.1.1：
Fast Fourier Transform / 6.1.2：
Fourier Transform of a Real Function / 6.1.3：
Discrete Fourier Series in Higher Dimensions / 6.1.4：
Discrete Fourier Transform of a Product of Two Functions / 6.1.5：
Discrete Sine and Cosine Transforms / 6.1.6：
Applications of Discrete Fourier Series / 6.2：
Direct Solution of Finite Differenced Elliptic Equations / 6.2.1：
Differentiation of a Periodic Function Using Fourier Spectral Method / 6.2.2：
Numerical Solution of Linear, Constant Coefficient Differential Equations with Periodic Boundary Conditions / 6.2.3：
Matrix Operator for Fourier Spectral Numerical Differentiation / 6.3：
Discrete Chebyshev Transform and Applications / 6.4：
Numerical Differentiation Using Chebyshev Polynomials / 6.4.1：
Quadrature Using Chebyshev Polynomials / 6.4.2：
Matrix Form of Chebyshev Collocation Derivative / 6.4.3：
A Review of Linear Algebra / A：
Vectors, Matrices and Elementary Operations / A.1：
System of Linear Algebraic Equations / A.2：
Effects of Round-off Error / A.2.1：
Operations Counts / A.3：
Eigenvalues and Eigenvectors / A.4：
Index
Preface
Interpolation / 1：
Lagrange Polynomial Interpolation / 1.1：
10.

図書
図書
10. Computational science and engineering
Gilbert Strang
出版情報: Wellesley, Mass. : Wellesley-Cambridge Press, c2007  xi, 716 p. ; 27 cm
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目次情報: 続きを見る
Applied Linear Algebra / 1：
Four special matrices / 1.1：
Differences, derivatives, and boundary conditions / 1.2：
Elimination leads to K = LDL^T / 1.3：
Inverses and delta functions / 1.4：
Eigenvalues and eigenvectors / 1.5：
Positive definite matrices / 1.6：
Numerical linear algebra: LU, QR, SVD / 1.7：
Best basis from the SVD / 1.8：
A Framework for Applied Mathematics / 2：
Equilibrium and the stiffness matrix / 2.1：
Oscillation by Newton's law / 2.2：
Least squares for rectangular matrices / 2.3：
Graph models and Kirchhoff's laws / 2.4：
Networks and transfer functions / 2.5：
Nonlinear problems / 2.6：
Structures in equilibrium / 2.7：
Covariances and recursive least squares / 2.8：
Graph cuts and gene clustering / 2.9：
Boundary Value Problems / 3：
Differential equations of equilibrium / 3.1：
Cubic splines and fourth order equations / 3.2：
Gradient and divergence / 3.3：
Laplace's equation / 3.4：
Finite differences and fast Poisson solvers / 3.5：
The finite element method / 3.6：
Elasticity and solid mechanics / 3.7：
Fourier Series and Integrals / 4：
Fourier series for periodic functions / 4.1：
Chebyshev, Legendre, and Bessel / 4.2：
The discrete Fourier transform and the FFT / 4.3：
Convolution and signal processing / 4.4：
Fourier integrals / 4.5：
Deconvolution and integral equations / 4.6：
Wavelets and signal processing / 4.7：
Analytic Functions / 5：
Taylor series and complex integration / 5.1：
Famous functions and great theorems / 5.2：
The Laplace transform and z-transform / 5.3：
Spectral methods of exponential accuracy / 5.4：
Initial Value Problems / 6：
Introduction / 6.1：
Finite difference methods for ODEs / 6.2：
Accuracy and stability for u_t = c u_x / 6.3：
The wave equation and staggered leapfrog / 6.4：
Diffusion, convection, and finance / 6.5：
Nonlinear flow and conservation laws / 6.6：
Fluid mechanics and Navier-Stokes / 6.7：
Level sets and fast marching / 6.8：
Solving Large Systems / 7：
Elimination with reordering / 7.1：
Iterative methods / 7.2：
Multigrid methods / 7.3：
Conjugate gradients and Krylov subspaces / 7.4：
Optimization and Minimum Principles / 8：
Two fundamental examples / 8.1：
Regularized least squares / 8.2：
Calculus of variations / 8.3：
Errors in projections and eigenvalues / 8.4：
The Saddle Point Stokes problem / 8.5：
Linear programming and duality / 8.6：
Adjoint methods in design / 8.7：
Applied Linear Algebra / 1：
Four special matrices / 1.1：
Differences, derivatives, and boundary conditions / 1.2：
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