Differential Equations

Name: Differential Equations | Classical to Controlled
Brand: Academic Press
Price: 80.95 EUR
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Classical to Controlled

Lukes(Autor*in)

Lukes(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

337 Seiten

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978-0-08-095668-8 (ISBN)

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Front Cover
Differential Equations: Classical to Controlled
Copyright Page
Contents
Preface
Chapter 1. Introduction
1.1 Origin and Evolution
1.2 Sources of First-Order Equations
1.3 Classical Questions
1.4 Control Questions
Chapter 2. Matrix Algebra-The Natural Language of Linear Systems
2.1 Terminology
2.2 Addition, Multiplication, and Scalar Multiplication
2.3 The n-Vector Spaces fn
2.4 Systems of Linear Algebraic Equations
2.5 Matrix Inversion
2.6 Large-Scale Matrix Computations Using Computers
2.7 Determinant Functions
2.8 Eigenvalues, Eigenspaces, Characteristic and Minimal Polynomials
2.9 The Jordan Form of a Matrix
Chapter 3. Linear Constant-Coefficient Equations: Computation
3.1 The Initial-Value Problem
3.2 The ABC Algorithm
3.3 A Vector Method for Computing the Matrix C
3.4 Explicit Formulas for C(c) and F(t)
3.5 Additional Comments about Computing and Changing Variables
Chapter 4. Linear Constant-Coefficient Equations: Theory
4.1 Preliminary Remarks
4.2 Some Elementary Matrix Analysis
4.3 Existence, Uniqueness, and Solution Representations Using etA
4.4 The Structure of etA
4.5 The Theoretical Foundation of the ABC Algorithm for Computing etA
4.6 Explicit Formulas for C(c) and etA
Chapter 5. Linear Constant-Coefficient Equations: Qualitative Behavior
5.1 Stability and Periodic Oscillation
5.2 The Lyapunov Approach to Asymptotic Stability
Chapter 6. General Linear Equations with Time-Varying Coefficients
6.1 Widening the Scope
6.2 Preliminaries
6.3 The Fundamental Matrix Series Defining F
6.4 Existence and Uniqueness of Solutions to Vector Differential Equations and Their Duals
6.5 Variation-of-Parameters Formulas for Vector and Matrix Differential Equations
6.6 Estimates of Solution Norms
6.7 Fundamental Matrices of Equations with Time-Varying Coefficients
6.8 Continuous Time, Discrete State Markov Processes
Chapter 7. Commutative Linear Differential Equations
7.1 Introductory Comments
7.2 The Definition and an Example of Commutative Equations
7.3 Computation of Closed-Form Solutions to Linear Commutative Equations
7.4 Some Sufficient Conditions for Commutivity
7.5 Matrix Functions and Operations Preserving Commutivity
7.6 The Special Case n = 2
7.7 A Criterion for Exponential Decay of Solutions
Chapter 8. Periodic Linear Equations
8.1 Periodic Homogeneous Equations
8.2 Qualitative Behavior
8.3 Nonhomogeneous Equations
8.4 Periodic Commutative Equations
Chapter 9. Local Existence and Uniqueness Theory of Nonlinear Equations
9.1 Complications That Can Occur
9.2 Local Existence and Uniqueness
Chapter 10. Global Solutions
10.1 Introduction
10.2 Maximal Solutions and Extensions of Local Solutions
10.3 The Behavior of Solutions on Maximal Intervals
Chapter 11. The General Solution-Dependence of Solutions on Parameters
11.1 Mathematical Preliminaries
11.2 A Space of Curves
11.3 The General Solution (D, ?) to the Cauchy Problem (D, f) and Continuous Dependence on Parameters
11.4 Differential Dependence of the General Solution (D, ?) on Parameters and Related Variational Equations
Chapter 12. Limit Properties of Solutions
12.1 Limit Sets and Invariance
12.2 Stability of Nonlinear Equations
12.3 Partial Stability
12.4 Local Behavior and Linearization about Rest Points
12.5 Planar Systems
Chapter 13. Applications in Control Theory
13.1 The Controlled and Uncontrolled Equations
13.2 Transient and Steady-State Parts of the Solution
13.3 The Frequency Response Function
13.4 The ABC Approach to Computing Frequency Response Matrices
13.5 Controllability
13.6 Altering System Dynamics by Linear Feedback
13.7 Decoupling and Recoupling-Nonintertive Design
13.8 Controllability of Nonlinear Equations
13.9 The Domain C of Null Controllability
References
Index

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