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1.

図書
図書
1. Elementary differential equations and boundary value problems
William E. Boyce and Richard C. DiPrima
出版情報: New York : Wiley, c1965  xvi, 485 p. ill. ; 24 cm
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2.

図書
図書
2. Elementary differential equations and boundary value problems. 2nd ed
William E. Boyce and Richard C. Di Prima
出版情報: New York : Wiley, c1969  xiv, 533, A-43, I-8 p ; 24 cm
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3.

図書
図書
3. Green's functions. 2nd ed. (: pbk)
G.F. Roach
出版情報: Cambridge [Cambridgeshire] : Cambridge University Press, 1982  xiii, 325 p. ; 24 cm
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目次情報: 続きを見る
Preface to the First Edition
Preface to the Second Edition
The Concept of a Green's Function / Chapter 1：
Vector Spaces and Linear Transformations / Chapter 2：
Vector Spaces / 2.1：
Linearly Independent Vectors / 2.2：
Orthonormal Vectors / 2.3：
Linear Transformations / 2.4：
Systems of Finite Dimension / Chapter 3：
Matrices and Linear Transformations / 3.1：
Change of Basis / 3.2：
Eigenvalues and Eigenvectors / 3.3：
Symmetric Operators / 3.4：
Bounded Operators / 3.5：
Positive Definite Operators / 3.6：
Continuous Functions / Chapter 4：
Limiting Processes / 4.1：
Integral Operators / 4.2：
The Kernel of an Integral Operator / 5.1：
Symmetric Integral Transformations / 5.2：
Separable Kernels / 5.3：
Eigenvalues of a Symmetric Integral Operator / 5.4：
Expansion Theorems for Integral Transformations / 5.5：
Generalized Fourier Series and Complete Vector Spaces / Chapter 6：
Generalized Fourier Series / 6.1：
Approximation Theorem / 6.2：
Complete Vector Spaces / 6.3：
Differential Operators / Chapter 7：
Introduction / 7.1：
Inverse Operators and the [delta]-function / 7.2：
The Domain of a Linear Differential Operator / 7.3：
Adjoint Differential Operators / 7.4：
Self-Adjoint Second-Order Differential Operators / 7.5：
Non-Homogeneous Problems and Symbolic Operators / 7.6：
Green's Functions and Second-Order Differential Operators / 7.7：
The Problem of Eigenfunctions / 7.8：
Green's Functions and the Adjoint Operator / 7.9：
Spectral Representation and Green's Functions / 7.10：
Integral Equations / Chapter 8：
Classification of Integral Equations / 8.1：
Method of Successive Approximations / 8.2：
The Fredholm Alternative / 8.3：
Symmetric Integral Equations / 8.4：
Equivalence of Integral and Differential Equations / 8.5：
Green's Functions in Higher-Dimensional Spaces / Chapter 9：
Partial Differential Operators and [delta]-functions / 9.1：
Green's Identities / 9.3：
Fundamental Solutions / 9.4：
Self-Adjoint Elliptic Equations (The Dirichlet Problem) / 9.5：
Self-Adjoint Elliptic Equations (The Neumann Problem) / 9.6：
Parabolic Equations / 9.7：
Hyperbolic Equations / 9.8：
Worked Examples / 9.9：
Calculation of Particular Green's Functions / Chapter 10：
Method of Images / 10.1：
Generalized Green's Functions / 10.2：
Mixed Problems / 10.3：
Approximate Green's Functions / Chapter 11：
Generalized Potentials / 11.1：
A Representation Theorem / 11.4：
Choice of Approximate Kernal / 11.5：
Summary of the Green's Function Method / Appendix A：
Green's Function Method for Ordinary Differential Equations / A1：
Green's Function Method for Partial Differential Equations / A2：
Operators and Expressions / Appendix B：
The Lebesgue Integral / Appendix C：
Distributions / Appendix D：
Bibliography
Chapter References
Index
Preface to the First Edition
Preface to the Second Edition
The Concept of a Green's Function / Chapter 1：
4.

図書
図書
4. Elementary differential equations and boundary value problems. 6th ed (: cloth)
William E. Boyce, Richard C. DiPrima
出版情報: New York : Wiley, c1997  xvi, 749 p. ; 25 cm
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5.

図書
図書
5. Elementary differential equations and boundary value problems. 3rd ed (: pbk)
William E. Boyce and Richard C. DiPrima
出版情報: New York : Wiley, c1977  xiv, 582, [56] p. ; 24 cm
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目次情報: 続きを見る
Preface
Introduction / Chapter 1：
Some Basic Mathematical Models; Direction Fields / 1.1：
Solutions of Some Differential Equations / 1.2：
Classification of Differential Equations / 1.3：
Historical Remarks / 1.4：
First Order Differential Equations / Chapter 2：
Linear Equations with Variable Coefficients / 2.1：
Separable Equations / 2.2：
Modeling with First Order Equations / 2.3：
Differences Between Linear and Nonlinear Equations / 2.4：
Autonomous Equations and Population Dynamics / 2.5：
Exact Equations and Integrating Factors / 2.6：
Numerical Approximations: Euler's Method / 2.7：
The Existence and Uniqueness Theorem / 2.8：
First Order Difference Equations / 2.9：
Second Order Linear Equations / Chapter 3：
Homogeneous Equations with Constant Coefficients / 3.1：
Fundamental Solutions of Linear Homogeneous Equations / 3.2：
Linear Independence and the Wronskian / 3.3：
Complex Roots of the Characteristic Equation / 3.4：
Repeated Roots; Reduction of Order / 3.5：
Nonhomogeneous Equations; Method of Undetermined Coefficients / 3.6：
Variation of Parameters / 3.7：
Mechanical and Electrical Vibrations / 3.8：
Forced Vibrations / 3.9：
Higher Order Linear Equations / Chapter 4：
General Theory of nth Order Linear Equations / 4.1：
Homogeneous Equations with Constant Coeffients / 4.2：
The Method of Undetermined Coefficients / 4.3：
The Method of Variation of Parameters / 4.4：
Series Solutions of Second Order Linear Equations / Chapter 5：
Review of Power Series / 5.1：
Series Solutions near an Ordinary Point, Part I / 5.2：
Series Solutions near an Ordinary Point, Part II / 5.3：
Regular Singular Points / 5.4：
Euler Equations / 5.5：
Series Solutions near a Regular Singular Point, Part I / 5.6：
Series Solutions near a Regular Singular Point, Part II / 5.7：
Bessel's Equation / 5.8：
The Laplace Transform / Chapter 6：
Definition of the Laplace Transform / 6.1：
Solution of Initial Value Problems / 6.2：
Step Functions / 6.3：
Differential Equations with Discontinuous Forcing Functions / 6.4：
Impulse Functions / 6.5：
The Convolution Integral / 6.6：
Systems of First Order Linear Equations / Chapter 7：
Review of Matrices / 7.1：
Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors / 7.3：
Basic Theory of Systems of First Order Linear Equations / 7.4：
Homogeneous Linear Systems with Constant Coefficients / 7.5：
Complex Eigenvalues / 7.6：
Fundamental Matrices / 7.7：
Repeated Eigenvalues / 7.8：
Nonhomogeneous Linear Systems / 7.9：
Numerical Methods / Chapter 8：
The Euler or Tangent Line Method / 8.1：
Improvements on the Euler Method / 8.2：
The Runge-Kutta Method / 8.3：
Multistep Methods / 8.4：
More on Errors; Stability / 8.5：
Systems of First Order Equations / 8.6：
Nonlinear Differential Equations and Stability / Chapter 9：
The Phase Plane; Linear Systems / 9.1：
Autonomous Systems and Stability / 9.2：
Almost Linear Systems / 9.3：
Competing Species / 9.4：
Predator-Prey Equations / 9.5：
Liapunov's Second Method / 9.6：
Periodic Solutions and Limit Cycles / 9.7：
Chaos and Strange Attractors; the Lorenz Equations / 9.8：
Partial Differential Equations and Fourier Series / Chapter 10：
Two-Point Boundary Valve Problems / 10.1：
Fourier Series / 10.2：
The Fourier Convergence Theorem / 10.3：
Even and Odd Functions / 10.4：
Separation of Variables; Heat Conduction in a Rod / 10.5：
Other Heat Conduction Problems / 10.6：
The Wave Equation; Vibrations of an Elastic String / 10.7：
Laplace's Equation / 10.8：
Derivation of the Heat Conduction Equation / Appendix A.：
Derivation of the Wave Equation / Appendix B.：
Boundary Value Problems and Sturm-Liouville Theory / Chapter 11：
The Occurrence of Two Point Boundary Value Problems / 11.1：
Sturm-Liouville Boundary Value Problems / 11.2：
Nonhomogeneous Boundary Value Problems / 11.3：
Singular Sturm-Liouville Problems / 11.4：
Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion / 11.5：
Series of Orthogonal Functions: Mean Convergence / 11.6：
Answers to Problems
Index
Preface
Introduction / Chapter 1：
Some Basic Mathematical Models; Direction Fields / 1.1：
6.

図書
図書
6. Non-classical equations of mixed type and their applications in gas dynamics (: sz ; : us)
A.G. Kuz'min
出版情報: Basel ; Boston : Birkhäuser, 1992  ix, 288 p. ; 24 cm
シリーズ名: International series of numerical mathematics ; v. 109
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7.

図書
図書
7. Differentialgleichungen und Randwertprobleme : Lehrbuch für Naturwissenschaftler und Ingenieure
A. Kneschke
出版情報: Leipzig : B.G. Teubner  v. ; 21 cm
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8.

図書
図書
8. Ordinary and partial differential equations : with special functions, Fourier series, and boundary value problems (: pbk)
Ravi P. Agarwal, Donal O'Regan
出版情報: New York ; London : Springer, c2009  xiv, 410 p. ; 24 cm
シリーズ名: Universitext
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目次情報: 続きを見る
Preface
Solvable Differential Equations / 1：
Second-Order Differential Equations / 2：
Preliminaries to Series Solutions / 3：
Solution at an Ordinary Point / 4：
Solution at a Singular Point / 5：
Solution at a Singular Point (Cont'd.) / 6：
Legendre Polynomials and Functions / 7：
Chebyshev, Hermite and Laguerre Polynomials / 8：
Bessel Functions / 9：
Hypergeometric Functions / 10：
Piecewise Continuous and Periodic Functions / 11：
Orthogonal Functions and Polynomials / 12：
Orthogonal Functions and Polynomials (Cont'd.) / 13：
Boundary Value Problems / 14：
Boundary Value Problems (Cont'd.) / 15：
Green's Functions / 16：
Regular Perturbations / 17：
Singular Perturbations / 18：
Sturm-Liouville Problems / 19：
Eigenfunction Expansions / 20：
Eigenfunction Expansions (Cont'd.) / 21：
Convergence of the Fourier Series / 22：
Convergence of the Fourier Series (Cont'd.) / 23：
Fourier Series Solutions of Ordinary Differential Equations / 24：
Partial Differential Equations / 25：
First-Order Partial Differential Equations / 26：
Solvable Partial Differential Equations / 27：
The Canonical Forms / 28：
The Method of Separation of Variables / 29：
The One-Dimensional Heat Equation / 30：
The One-Dimensional Heat Equation (Cont'd.) / 31：
The One-Dimensional Wave Equation / 32：
The One-Dimensional Wave Equation (Cont'd.) / 33：
Laplace Equation in Two Dimensions / 34：
Laplace Equation in Polar Coordinates / 35：
Two-Dimensional Heat Equation / 36：
Two-Dimensional Wave Equation / 37：
Laplace Equation in Three Dimensions / 38：
Laplace Equation in Three Dimensions (Cont'd.) / 39：
Nonhomogeneous Equations / 40：
Fourier Integral and Transforms / 41：
Fourier Integral and Transforms (Cont'd.) / 42：
Fourier Transform Method for Partial DEs / 43：
Fourier Transform Method for Partial DEs (Cont'd.) / 44：
Laplace Transforms / 45：
Laplace Transforms (Cont'd.) / 46：
Laplace Transform Method for Ordinary DEs / 47：
Laplace Transform Method for Partial DEs / 48：
Well-Posed Problems / 49：
Verification of Solutions / 50：
References for Further Reading
Index
Preface
Solvable Differential Equations / 1：
Second-Order Differential Equations / 2：
9.

図書
図書
9. Differentialgleichungen und Randwertprobleme : Lehrbuch für Naturwissenschaftler und Ingenieure. 2., überarbeitete Aufl (Bd. 1)
A. Kneschke
出版情報: Berlin : Verlag Technik, 1960, c1957  540 p. ; 21 cm
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目次情報:
Bd. 1. Gewöhnliche Differentialgleichungen
Bd. 1. Gewöhnliche Differentialgleichungen
10.

図書
図書
10. Elementary differential equations and boundary value problems. 10th ed (: [hardcover])
William E. Boyce, Richard C. DiPrima
出版情報: Hoboken, N.J. : Wiley, c2012  xix, 809 p. ; 27 cm
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