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1.

図書

図書
Richard H. Enns, George C. McGuire
出版情報: Boston ; Basel : Birkhäuser, c2001  xiii, 691 p. ; 26 cm.
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Preface
Theory / Part I:
Introduction / 1:
Nonlinear Systems, Part I / 2:
Nonlinear Systems, Part II / 3:
Topological Analysis / 4:
Analytic Methods / 5:
The Numerical Approach / 6:
Limit Cycles / 7:
Forced Oscillators / 8:
Nonlinear Maps / 9:
Nonlinear PDE Phenomena / 10:
Numerical Simulation / 11:
Inverse Scattering Method / 12:
Experimental Activities / Part II:
Introduction to Nonlinear Experiments
Magnetic Force
Magnetic Tower
Spin Toy Pendulum
Driven Eardrum
Nonlinear Damping
Anaharmonic Potential
Iron Core Conductor
Nonlinear LRC Circuit
Tunnel Diode Negative Resistance Curve
Tunnel Diode Self-Excited Oscillator
Forced Duffing Equation
Focal Point Instability
Compound Pendulum / 13:
Damped Simple Pendulum / 14:
Stable Limit Cycle / 15:
Van der Pol Limit Cycle / 16:
Relaxation Oscillations: Neon Bulb / 17:
Relaxation Oscillations: Drinking Bird / 18:
Relaxation Oscillations: Tunnel Diode / 19:
Hard Spring / 20:
Nonlinear Resonance Curve: Mechanical / 21:
Nonlinear Resonance Curve: Electrical / 22:
Nonlinear Resonance Curve: Magnetic / 23:
Subharmonic Response: Period Doubling / 24:
Diode: Period Doubling / 25:
Five-Well Magnetic Potential / 26:
Power Spectrum / 27:
Entrainment and Quasiperiodicity / 28:
Quasiperiodicity / 29:
Chua's Butterfly / 30:
Route to Chaos / 31:
Driven Spin Toy / 32:
Mapping / 33:
Bibliography
Index
Preface
Theory / Part I:
Introduction / 1:
2.

図書

図書
Sergey P. Kiselev, Evgenii V. Vorozhtsov, Vasily M. Fomin
出版情報: Boston : Birkhäuser, c1999  xiv, 575 p. ; 25 cm
シリーズ名: Modeling and simulation in science, engineering & technology
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3.

図書

図書
Alfred Gray
出版情報: Boca Raton, Fla. : CRC Press, c1998  xxiv, 1053 p., [8] p. of plates ; 27 cm
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4.

図書

図書
Jerry Glynn, Theodore Gray
出版情報: Cambridge ; New York : Cambridge University Press, 1997  viii, 347 p. ; 24 cm
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5.

図書

図書
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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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.:
6.

図書

図書
Nicola Bellomo, Luigi Preziosi, Antonio Romano
出版情報: Boston : Birkhäuser, 2000  xii, 417 p. ; 25 cm
シリーズ名: Modeling and simulation in science, engineering & technology
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7.

図書

図書
Sadri Hassani
出版情報: New York : Springer, c2003  ix, 235 p. ; 24 cm
シリーズ名: Undergraduate texts in contemporary physics
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8.

図書

図書
Kenneth Shiskowski, Karl Frinkle
出版情報: Hoboken, N.J. : Wiley, c2011  xiv, 598 p. ; 25 cm
シリーズ名: Pure and applied mathematics
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Preface
Conventions and Notations
An Introduction to Mathematica" / 1:
The Very Basics / 1.1:
Basic Arithmetic / 1.2:
Lists and Matrices / 1.3:
Expressions versus Functions / 1.4:
Plotting and Animations / 1.5:
Solving Systems of Equations / 1.6:
Basic Programming / 1.7:
Linear Systems of Equations and Matrices / 2:
Linear Systems of Equations / 2.1:
Augmented Matrix of a Linear System and Row Operations / 2.2:
Some Matrix Arithmetic / 2.3:
Gauss-Jordan Elimination and Reduced Row Echelon Form / 3:
Gauss-Jordan Enmination and rref / 3.1:
Elementary Matrices / 3.2:
Sensitivity of Solutions to Error in the Linear System / 3.3:
Applications of Linear Systems and Matrices / 4:
Applications of Linear Systems to Geometry / 4.1:
Applications of Linear Systems to Curve Fitting / 4.2:
Applications of Linear Systems to Economics / 4.3:
Applications of Matrix Multiplication to Geometry / 4.4:
An Application of Matrix Multiplication to Economics / 4.5:
Determinants, Inverses, and Cramer's Rule / 5:
Determinants and Inverses from the Adjoint Formula / 5.1:
Finding Determinants by Expanding along Any Row or Column / 5.2:
Determinants Found by Triangularizing Matrices / 5.3:
LU Factorization / 5.4:
Inverses from rref / 5.5:
Gramer's Rule / 5.6:
Basic Vector Algebra Topics / 6:
Vectors / 6.1:
Dot Product / 6.2:
Cross Product / 6.3:
Vector Projection / 6.4:
A Few Advanced Vector Algebra Topics / 7:
Rotations in Space / 7.1:
"Rolling" a Circle along a Curve / 7.2:
The TNB Frame / 7.3:
Independence, Basis, and Dimension for Subspaces of Rn / 8:
Subspaces of Rn / 8.1:
Independent and Dependent Sets of Vectors in Rn / 8.2:
Basis and Dimension for Subspaces of Rn / 8.3:
Vector Projection onto a Subspace of Rn / 8.4:
The Gram-Schmidt Orthonormalization Process / 8.5:
Linear Maps from Rn to Rm / 9:
Basics about Linear Maps / 9.1:
The Kernel and Image Subspaces of a Linear Map / 9.2:
Composites of Two Linear Maps and Inverses / 9.3:
Change of Bases for the Matrix Representation of a Linear Map / 9.4:
383 / 10:
The Effect of a Linear Map on Area and Arclength in Two Dimensions / 10.1:
The Decomposition of Linear Maps into Rotations, Reflections, and Rescalings in R2 / 10.2:
The Effect of Linear Maps on Volume, Area, arid Arclength in R3 / 10.3:
Rotations, Reflections, and Rescalings in Three Dimensions / 10.4:
Affine Maps / 10.5:
Least-Squares Fits and Pseudo inverses / 11:
Pseudoinverse to a Nonsquare Matrix and Almost Solving an Overdetermined Linear System / 11.1:
Fits and Pseudoinverses / 11.2:
Least-Squares Fits and Pseudoinverses / 11.3:
Eigenvalues and Eigenvectors / 12:
What Are Eigenvalues and Eigenvectors, and Why Do We Need Them? / 12.1:
Summary of Definitions and Methods for Computing Eigenvalues and Eigenvectors as Well as the Exponential of a Matrix / 12.2:
Applications of the Diagonalizability of Square Matrices / 12.3:
Solving a Square First-Order Linear System of Differential Equations / 12.4:
Basic Facts about Eigenvalues, Eigenvectors, and Diagonalizability / 12.5:
The Geometry of the Ellipse Using Eigenvalues and Eigenvectors / 12.6:
A Mathematica Eigen-Function / 12.7:
Bibliographic Material
Indexes
Keyword Index
Index of Mathematica Commands
Preface
Conventions and Notations
An Introduction to Mathematica" / 1:
9.

図書

図書
John R. Wicks
出版情報: Reading, Mass. : Addison-Wesley, c1996  xxiii, 368, [16] p. ; 24 cm.
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Introductory Material
Introduction to Mathematica
Introduction to Linear Systems and Row Operations
Linear Systems and Applications
Linear Systems and Gaussian Elimination
Gaussian Elimination by Example
A Summary of Gaussian Elimination
Backsubstitution and Backaddition
Gaussian Elimination with Mathematica
The General Solution to Linear Systems
Matrix Algebra
Matrix Multiplication from a Geometric Viewpoint
Matrix Arithmetic
Matrix Arithmetic with Mathematica
Properties of Matrix Algebra
Matrix Algebra and Block Matrices
Matrix Inverses: Definitions and Basic Properties
Computing Matrix Inverses
Matrix Inverses and Systems of Equations
Systems From Two Advanced Viewpoints
Elementary Matrices and the PTLU Decomposition
Applications of the PTLU Decomposition
Discovering Determinants
Systems of Equations from a Geometric Viewpoint
Abstract Vector Spaces and Bases
Vectors and Vector Spaces
Coordinate Systems and Bases
Independent and Spanning Sets
Constructing Bases
The Theory of Bases
Subspaces and Linear Transformations
Inner Product Spaces
Inner Products
Orthonormal Bases and Projections
Gram-Schmidt Orthonormalization
Change of Basis and Eigensystems
Linear Transformations and Matrices
The Effects of Changing Coordinates
Discrete Dynamical Systems and Eigensystems
Eigenvectors and Eigenvalues
Appendix of Mathematica Commands
Introductory Material
Introduction to Mathematica
Introduction to Linear Systems and Row Operations
10.

図書

図書
Victor G. Ganzha and Evgenii V. Vorozhtsov
出版情報: Boca Raton, Fla : CRC Press, c1996  347 p. ; 25 cm.
シリーズ名: Symbolic and numeric computation series
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