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Ordinary differential equations/ (Record no. 151171)

MARC details
000 -LEADER
fixed length control field	00364nam a2200145Ia 4500
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number	9812530029
040 ## - CATALOGING SOURCE
Transcribing agency	CUS
082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number	515.35
Item number	BIR/O
100 ## - MAIN ENTRY--PERSONAL NAME
Personal name	Birkhoff, Garrett.
245 #0 - TITLE STATEMENT
Title	Ordinary differential equations/
Statement of responsibility, etc.	Garrett Birkhoff, Gian-Carlo Rota.
250 ## - EDITION STATEMENT
Edition statement	4th ed.
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc.	New York:
Name of publisher, distributor, etc.	John Wiley & Sons,
Date of publication, distribution, etc.	2003.
300 ## - PHYSICAL DESCRIPTION
Extent	399 p. :
Other physical details	ill. ;
Dimensions	24 cm.
505 ## - FORMATTED CONTENTS NOTE
Formatted contents note	1 FIRST-ORDER OF DIFFERENTIAL EQUATIONS 1<br/>1. Introduction <br/>2. Fundamental Theorem of the Calculus <br/>3. First-order Linear Equations <br/>4. Separable Equations <br/>5. Quasilinear Equations; Implicit Solutions <br/>6. Exact Differentials; Integrating Factors <br/>7. Linear Fractional Equations <br/>8. Graphical and Numerical Integration <br/>9. The Initial Value Problem <br/>10. Uniqueness and Continuity <br/>11. A Comparison Theorem <br/>12. Regular and Normal Curve Families <br/>2 SECOND-ORDER LINEAR EQUATIONS <br/>1. Bases of Solutions <br/>2. Initial Value Problems <br/>3. Qualitative Behavior; Stability <br/>4. Uniqueness Theorem <br/>5. The Wronskian <br/>6. Separation and Comparison Theorems <br/>7. The Phase Plane <br/>8. Adjoint Operators; Lagrange Identity <br/>9. Green's Functions <br/>10. Two-endpoint Problems <br/>11. Green's Functions, <br/>3 LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS <br/>1. The Characteristic Polynomial <br/>2. Complex Exponential Functions <br/>3. The Operational Calculus <br/>4. Solution Bases <br/>5. Inhomogeneous Equations <br/>Contents<br/>6. Stability <br/>7. The Transfer Function <br/>8. The Nyquist Diagram <br/>9. The Greenes Function<br/>4 POWER SERIES SOLUTIONS <br/>1. Introduction <br/>2. Method of Undetermined Coefficients <br/>3. More Examples <br/>4. Three First-order DEs <br/>5. Analytic Functions <br/>6. Method of Majorants <br/>7. Sine and Cosine Functions <br/>8. Bessel Functions <br/>9. First-order Nonlinear DEs <br/>10. Radius of Convergence <br/>11. Method of Majorants, <br/>12. Complex Solutions <br/>5 PLANE AUTONOMOUS SYSTEMS <br/>1. Autonomous Systems <br/>2. Plane Autonomous Systems <br/>3. The Phase Plane, <br/>4. Linear Autonomous Systems <br/>5. Linear Equivalence <br/>6. Equivalence Under Diffeomorphisms <br/>7. Stability <br/>8. Method of Liapunov <br/>9. Undamped Nonlinear Oscillations <br/>10. Soft and Hard Springs <br/>11. Damped Nonlinear Oscillations <br/>12. Limit Cycles <br/>6 EXISTENCE AND UNIQUENESS THEOREMS <br/>1. Introduction <br/>2. Lipschitz conditions <br/>3. Well-posed Problems <br/>4. Continuity <br/>5. Normal Systems <br/>6. Equivalent Integral Equation <br/>7. Successive Approximation <br/>8. Linear Systems <br/>9. Local Existence Theorem <br/>Contents<br/>10. The Peano Existence Theorem <br/>11. Analytic Equations <br/>12. Continuation of Solutions <br/>13. The Perturbation Equation <br/>7 APPROXIMATE SOLUTIONS <br/>1. Introduction <br/>2. Error Bounds <br/>3. Deviation and Error <br/>4. Mesh-halving; Richardson Extrapolation <br/>5. Midpoint Quadrature <br/>6. Trapezoidal Quadrature <br/>7. Trapezoidal Integration <br/>8. The Improved Euler Method <br/>9. The Modified Euler Method <br/>10. Cumulative Error Bound 226<br/>8 EFFICIENT NUMERICAL INTEGRATION <br/>1. Difference Operators <br/>2. Polynomial Interpolation <br/>3. Interpolation Errors <br/>4. Stability <br/>5. Numerical Differentiation; Roundoff <br/>6. Higher Order Quadrature <br/>7. Gaussian Quadrature <br/>8. Fourth-order Runge-Kutta <br/>9. Millie's Method <br/>10. Multistep Methods <br/>9 REGULAR SINGULAR POINTS <br/>1. Introduction <br/>2. Movable Singular Points <br/>3. First-order Linear Equations <br/>4. Continuation Principle; Circuit Matrix <br/>5. Canonical Bases <br/>6. RegularSingular Points <br/>7. Bessel Equation <br/>8. The Fundamental Theorem <br/>9. Alternative Proof of the Fundamental Theorem <br/>10. Hypergeometric Functions <br/>11. The Jacobi Polynomials <br/>12. Singular Points at Infinity <br/>13. Fuchsian Equations <br/>10 STURM-LIOUVILLE SYSTEMS <br/>1. Sturm-Liouvilie Systems <br/>2. Sturm-Liouville Series <br/>3. Physical Interpretations <br/>4. Singular Systems <br/>5. Prufer Substitution <br/>6. Sturm Comparison Theorem <br/>7. Sturm Oscillation Theorem <br/>8. The Sequence of Eigenfunctions <br/>9. The Liouville Normal Form <br/>10. Modified Priifer Substitution <br/>11. The Asymptotic Behavior of Bessel Functions <br/>12. Distribution of Eigenvalues <br/>13. Normalized Eigenfunctions <br/>14. Inhomogeneous Equations <br/>15. Green's Functions <br/>16. The Schroedinger Equation <br/>17. The Square-well Potential <br/>18. Mixed Spectrum <br/>11 EXPANSIONS IN EIGENFUNCTIONS <br/>1. Fourier Series <br/>2. Orthogonal Expansions <br/>3. Mean-square Approximation <br/>4. Completeness <br/>5. Orthogonal Polynomials<br/>6. Properties of Orthogonal Polynomials <br/>7. Chebyshev Polynomials <br/>8. Euclidean Vector Spaces <br/>9. Completeness of Eigenfunctions <br/>10. Hilbert Space <br/>11. Proof of Completeness <br/>APPENDIX A: LINEAR SYSTEMS <br/>1. Matrix Norm <br/>2. Constant-coefficient Systems <br/>3. The Matrizant <br/>4. Floquet Theorem; Canonical Bases <br/>APPENDIX B: BIFURCATION THEORY <br/>1. What Is Bifurcation? <br/>2. Poincare Index Theorem <br/>3. Hamiltonian Systems <br/>4. Hamiltonian Bifurcations <br/>5. Poincare Maps <br/>6. Periodically Forced Systems <br/>BIBLIOGRAPHY <br/>INDEX
650 ## - SUBJECT
Keyword	Differential equations
700 ## - ADDED ENTRY--PERSONAL NAME
Personal name	Rota, Gian-Carlo.
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type	General Books

Holdings
Withdrawn status	Lost status	Damaged status	Not for loan	Home library	Current library	Shelving location	Date acquired	Full call number	Accession number	Date last seen	Date last checked out	Koha item type
				Central Library, Sikkim University	Central Library, Sikkim University	General Book Section	28/08/2016	515.35 BIR/O	P05843	09/09/2019	09/09/2019	General Books