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Viser: The Qualitative Theory of Ordinary Differential Equations - An Introduction
The Qualitative Theory of Ordinary Differential Equations Vital Source e-bog
Fred Brauer
(2012)
The Qualitative Theory of Ordinary Differential Equations
An Introduction
Fred Brauer og John A. Nohel
(1990)
Sprog: Engelsk
om ca. 10 hverdage
Detaljer om varen
- Vital Source searchable e-book (Reflowable pages): 320 sider
- Udgiver: Dover Publications (December 2012)
- ISBN: 9780486151519
Bookshelf online: 5 år fra købsdato.
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Detaljer om varen
- Paperback: 320 sider
- Udgiver: Dover Publications, Incorporated (Marts 1990)
- Forfattere: Fred Brauer og John A. Nohel
- ISBN: 9780486658469
1.1 A Simple Mass-Spring System
1.2 Coupled Mass-Spring Systems
1.3 Systems of First-Order Equations
1.4 Vector-Matrix Notation for Systems
1.5 The Need for a Theory
1.6 Existence, Uniqueness, and Continuity
1.7 The Gronwall InequalityChapter 2. Linear Systems, with an Introduction to Phase Space Analysis
2.1 Introduction
2.2 Existence and Uniqueness for Linear Systems
2.3 Linear Homogeneous Systems
2.4 Linear Nonhomogeneous Systems
2.5 Linear Systems with Constant Coefficients
2.6 Similarity of Matrices and the Jordan Canonical Form
2.7 Asymptotic Behavior of Solutions of Linear Systems with Constant Coefficients
2.8 Autonomous Systems--Phase Space--Two-Dimensional Systems
2.9 Linear Systems with Periodic Coefficients; Miscellaneous ExercisesChapter 3. Existence Theory
3.1 Existence in the Scalar Case
3.2 Existence Theory for Systems of First-Order Equations
3.3 Uniqueness of Solutions
3.4 Continuation of Solutions
3.5 Dependence on Initial Conditions and Parameters; Miscellaneous ExercisesChapter 4. Stability of Linear and Almost Linear Systems
4.1 Introduction
4.2 Definitions of Stability
4.3 Linear Systems
4.4 Almost Linear Systems
4.5 Conditional Stability
4.6 Asymptotic Equivalence
4.7 Stability of Periodic SolutionsChapter 5. Lyapunov's Second Method
5.1 Introductory Remarks
5.2 Lyapunov's Theorems
5.3 Proofs of Lyapunov's Theorems
5.4 Invariant Sets and Stability
5.5 The Extent of Asymptotic Stability--Global Asymptotic Stability
5.6 Nonautonomous SystemsChapter 6. Some Applications
6.1 Introduction
6.2 The Undamped Oscillator
6.3 The Pendulum
6.4 Self-Excited Oscillations--Periodic Solutions of the Liénard Equation
6.5 The Regulator Problem
6.6 Absolute Stability of the Regulator SystemAppendix
1. Generalized Eigenvectors, Invariant Subspaces, and Canonical Forms of MatricesAppendix
2. Canonical Forms of 2 x 2 MatricesAppendix
3. The Logarithm of a MatrixAppendix
4. Some Results from Matrix Theory Bibliography; Index