1.
図書
A.A. Andronov ・・・[et al.] ; translated from Russian by D. Louvish
出版情報:
Jerusalem : Israel Program for Scientific Translations; [distributed by Halstead Press, a division of] J. Wiley, New York , New York : Wiley, c1973 xxiii, 524 p. ; 25 cm
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2.
図書
F.V. Atkinson
3.
図書
Anatole Beck ; with the assistance of Jonathan and Mirit Lewin
4.
図書
by Ju. L. Daleckiĭ and M. G. Kreĭn
5.
図書
[by] Alice B. Dickinson
6.
図書
Harry Hochstadt
7.
図書
David G. Luenberger
出版情報:
New York : Wiley, c1979 xiv, 446 p. ; 24 cm
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目次情報:
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Difference and Differential Equations
Linear Algebra
Linear State Equations
Linear Systems with Constant Coefficients
Positive Linear Systems
Markov Chains
Concepts of Control
Analysis of Nonlinear Systems
Some Important Dynamic Systems
Optimal Control
References
Index
Difference and Differential Equations
Linear Algebra
Linear State Equations
8.
図書
R. Gabasov, F. Kirillova ; translated by John L. Casti
9.
図書
by Antonio Kumpera and Donald Spencer
10.
図書
John Heading
出版情報:
London : G. Allen and Unwin, 1971 iv, 92 p ; 23 cm
シリーズ名:
Problem solvers ; no. 1
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11.
図書
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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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：
12.
図書
[by] Richard E. Williamson [and] Hale F. Trotter
出版情報:
Englewood Cliffs, N.J. : Prentice-Hall, [1974] ix, 630 p. ; 25 cm
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目次情報:
04104-08 Trade Math One (20 Hours)
Builds on trainees' basic math skills to solve trade-reproblems
Covers calculations using denomiand volume calculations, English-metric system conversbasic geometry, and calculation of stretchouts
04104-08 Trade Math One (20 Hours)
Builds on trainees' basic math skills to solve trade-reproblems
Covers calculations using denomiand volume calculations, English-metric system conversbasic geometry, and calculation of stretchouts
13.
図書
by Earl D. Rainville and Phillip E. Bedient
出版情報:
New York : Macmillan, c1974 xiii, 511 p. ; 25 cm
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Definitions; Families of Curves / 1：
Equations of Order One / 2：
Numerical Methods / 3：
Elementary Applications / 4：
Additional Topics on Equations of Order One / 5：
Linear Differential Equations / 6：
Linear Equations with Constant Coefficients / 7：
Nonhomogeneous Equations: Undetermined Coefficients / 8：
Variation of Parameters / 9：
Applications / 10：
Linear Systems of Equations / 11：
Nonhomogeneous Systems of Equations / 12：
The Existence and Uniqueness of Solutions / 13：
The Laplace Transform / 14：
Inverse Transforms / 15：
Nonlinear Equations / 16：
Power Series Solutions / 17：
Solutions Near Regular Singular Points / 18：
Equations of Hypergeometric Type / 19：
Partial Differential Equations / 20：
Orthogonal Sets of Functions / 21：
Fourier Series / 22：
Boundary Value Problems / 23：
Additional Properties of the Laplace Transform / 24：
Partial Differential Equations Transform Methods / 25：
Answers to Odd-numbered Exercises
Index
Definitions; Families of Curves / 1：
Equations of Order One / 2：
Numerical Methods / 3：
14.
図書
Wolfgang Walter ; translated by Lisa Rosenblatt and Lawrence Shampine
15.
図書
Y. V. Venkatesh
16.
図書
by John Heading
出版情報:
London : Elek Science, c1975 [10], 342 p. ; 22 cm
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17.
図書
by Antonio Kumpera and Donald Spencer
18.
図書
Henri Cartan ; [translated from the French]
出版情報:
Paris : Hermann, c1971 [1],160 p. ; 23 cm
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19.
図書
George R. Sell
20.
図書
[by] Fred Brauer [and] John A. Nohel
21.
図書
[by] George F. Simmons
目次情報:
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The Nature of Differential Equations / 1：
First Order Equations / 2：
Second Order Linear Equations / 3：
Qualitative Properties of Solutions / 4：
Power Series Solutions and Special Functions / 5：
Fourier Series and Orthogonal Functions / 6：
Partial Differential Equations and Boundary Value Problems / 7：
Some Special Functions of Mathematical Physics / 8：
Laplace Transforms / 9：
Systems of First Order Equations / 10：
Nonlinear Equations / 11：
The Calculus of Variations / 12：
The Existence and Uniqueness of Solutions / 13：
Numerical Methods / 14：
The Nature of Differential Equations / 1：
First Order Equations / 2：
Second Order Linear Equations / 3：
22.
図書
N.P. Bhatia, G.P. Szegö
23.
図書
[par] Jacqueline Lelong-Ferrand [et] Jean-Marie Arnaudiès
24.
図書
[by] Charles Conley
目次情報:
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Index
On stable properties of the solution set of an ordinary differential equation Elementary properties of flows
The Morse index Continuation
Bibliography
Index
On stable properties of the solution set of an ordinary differential equation Elementary properties of flows
The Morse index Continuation
25.
図書
W. A. Coppel
26.
図書
John J. Tyson
27.
図書
J.D. Murray
出版情報:
Oxford : Clarendon Press, 1974 vii, 140 p. ; 22 cm
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28.
図書
Thomas M. Creese, Robert M. Haralick
出版情報:
New York : McGraw-Hill, c1978 xvi, 552 p. ; 25 cm
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29.
図書
G.E. Ladas and V. Lakshmikantham
30.
図書
William T. Reid
31.
図書
T.T. Soong
32.
図書
S.D. Zaidman
33.
図書
C. Corduneanu
出版情報:
Bronx, N.Y. : Chelsea Pub. Co., c1977 xii, 205 p. ; 24 cm
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Introduction: Some Elementary Methods: The linear equation of the first order
The equation with separable variables Exact differential equations
The uniqueness problem: an example Some integral inequalities Problems
Existence Theory for Differential Equations: The first-order equation
First-order differential systems Equations and systems of higher order Peano existence theorem
A uniqueness theorem Problems Some Global Problems for Ordinary Differential
Equations: Statement of the problems Global uniqueness Global existence and the behavior of saturated solutions
Dependence of solutions on initial values Differential inequalities and the comparison method
A criterion of global existence Problems Some Special Classes of Differential
Systems and Equations: Linear systems: generalities Linear homogeneous systems Nonhomogeneous systems
Linear equations of higher order Autonomous systems Linear systems and equations with constant coefficients Problems
Stability Theory of Ordinary Differential Systems: Definitions and examples Stability of linear systems Stability in the first approximation
Stability theorems by comparison method Further stability results Stability of automatic control systems Problems
Volterra Integral Equations: Existence and uniqueness of solution An existence theorem
The linear equation The first-kind linear equation Some problems on the half-axis Problems
Fredholm Theory of Linear Integral Equations: The resolvent kernel
The entire functions of Fredholm and their applications
A glimpse of Hilbert space theory Eigenvalues, eigenfunctions and adjoint equations Problems
Theory of Self-Adjoint Integral Equations and Some Applications: Some properties of an integral operator
The existence of eigenvalues
The Hilbert-Schmidt expansion theorem Complete kernels and systems
The Sturm-Liouville problem Reduction to an integral equation: the first case Reduction to an integral equation: the second case Problems
Miscellanea (Nice Things): Maximum and minimum solutions of scalar differential equations
A theorem of Massera An oscillation theorem A formula of Picone and its consequences
Lienard's equation Differential systems without uniqueness Abel's integral equation
References
Index
Introduction: Some Elementary Methods: The linear equation of the first order
The equation with separable variables Exact differential equations
The uniqueness problem: an example Some integral inequalities Problems
34.
図書
John D. Dollard and Charles N. Friedman ; foreword by Felix E. Browder ; appendix by P. R. Masani
35.
図書
[by] William T. Reid
36.
図書
[by] J. Warga
出版情報:
New York : Academic Press, 1972 xiii, 531 p. ; 24 cm
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37.
図書
Klaus Deimling
38.
図書
N.J. Pullman
39.
図書
editor, Wiktor Eckhaus
出版情報:
Amsterdam : North Holland Pub. Co. , New York : sole distributors for the U.S.A. and Canada, American Elsevier Pub. Co., 1976 viii, 248 p. ; 24 cm
シリーズ名:
North-Holland mathematics studies ; 21
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40.
図書
Tyn Myint-U
出版情報:
New York : North-Holland, c1978 xii, 295 p. ; 24 cm
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41.
図書
Solomon Lefschetz
出版情報:
New York : Dover Publications, 1977 x, 390 p. ; 21 cm
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42.
図書
[by] P.G. Lowe
出版情報:
London : Cambridge University Press, 1971 xiii, 214 p. ; 24 cm
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43.
図書
R. Creighton Buck, in collaboration with Ellen F. Buck
出版情報:
Boston : Houghton Mifflin, c1976 x, 356, 62 p. ; 25 cm
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44.
図書
edited by Robert McKelvey
出版情報:
New York : Academic Press, 1970 x, 295 p ; 24 cm
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Oscillation theory of ordinary linear differential equations / by J. H. Barrett
Subfunctions and second-order ordinary differential inequalities / by L. K. Jackson
Topics in singular perturbations / by R. E. O'Malley
Classification of second order linear differential equations with respect to oscillation / by D. Willett
Oscillation theory of ordinary linear differential equations / by J. H. Barrett
Subfunctions and second-order ordinary differential inequalities / by L. K. Jackson
Topics in singular perturbations / by R. E. O'Malley
45.
図書
R.D. Driver
46.
図書
[By] E. A. Barbashin. Translated from Russian by Transcripta Service, London. Ed. by T. Lukes
出版情報:
Groningen : Wolters-Noordhoff, [1970] 223 p ; 23 cm
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47.
図書
[by] Jack L. Goldberg [and] Arthur J. Schwartz
48.
図書
V.I. Arnold ; translated and edited by Richard A. Silverman
出版情報:
Cambridge : MIT Press, c1973 viii, 280 p. ; 23 cm
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Preface
Frequently Used Notation
Basic Concepts / 1：
Phase Spaces and Phase Flows
Vector Fields on the Line / 2：
Phase Flows on the Line / 3：
Vector Fields and Phase Flows in the Plane / 4：
Nonautonomous Equations / 5：
The Tangent Space / 6：
Basic Theorems
The Vector Field near a Nonsingular Point / 7：
Applications to the Nonautonomous Case / 8：
Applications to Equations of Higher Order / 9：
Phase Curves of Autonomous Systems / 10：
The Directional Derivative. First Integrals / 11：
Conservative Systems with One Degree of Freedom / 12：
Linear Systems
Linear Problems / 13：
The Exponential of an Operator / 14：
Properties of the Exponential / 15：
The Determinant of the Exponential / 16：
The Case of Distinct Real Eigenvalues / 17：
Complexification and Decomplexification / 18：
Linear Equations with a Complex Phase Space / 19：
Complexification of a Real Linear Equation / 20：
Classification of Singular Points of Linear Systems / 21：
Topological Classification of Singular Points / 22：
Stability of Equilibrium Positions / 23：
The Case of Purely Imaginary Eigenvalues / 24：
The Case of Multiple Eigenvalues / 25：
More on Quasi-Polynomials / 26：
Nonautonomous Linear Equations / 27：
Linear Equations with Periodic Coefficients / 28：
Variation of Constants / 29：
Proofs of the Basic Theorems
Contraction Mappings / 30：
The Existence, Uniqueness, and Continuity Theorems / 31：
The Differentiable Manifolds / 33：
The Tangent Bundle. Vector Fields on a Manifold / 34：
The Phase Flow Determined by a Vector Field / 35：
The Index of a Singular Point of a Vector Field / 36：
Sample Examination Problems
Bibliography
Index
Preface
Frequently Used Notation
Basic Concepts / 1：
49.
図書
Robert H. Martin, Jr
50.
図書
Morris W. Hirsch and Stephen Smale
目次情報:
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Preface
First Examples
Newton's Equation and Kepler's Law
Linear Systems with Constant Coeffecients and Real Eigenvalues
Linear Systems with Constant Coefficients and Complex Eigenvalues
Linear Systems and Exponentials of Operators
Linear Systems and Canonical Forms of Operators
Contractions and Generic Properties of Operators
Fundamental Theory
Stability of Equilibria
Differential Equations for Electrical Circuits
The Poincare-Bendixson Theorem
Ecology
Periodic Attractors
Classical Mechanics
Nonautonomous Equations and Differentiability of Flows
Perturbation Theory and Structural Stability
Elementary Facts
Polynomials
On Canonical Forms
The Inverse Function Theorem
References
Answers to Selected Problems
Index
Preface
First Examples
Newton's Equation and Kepler's Law
51.
図書
S. Barnett, C. Storey
52.
図書
Einar Hille
図書
