Ordinary Differential Equations And Dynamical Systems

Gives a self contained introduction to the field of ordinary differential equations with emphasis on the dynamical systems point of view. Requires some basic knowledge from calculus, complex functions, and linear algebra.

**Tag(s):**
Mathematics

**Publication date**: 31 Dec 2007

**ISBN-10**:
n/a

**ISBN-13**:
n/a

**Paperback**:
n/a

**Views**: 11,183

**Type**: N/A

**Publisher**:
n/a

**License**:
n/a

**Post time**: 12 Dec 2007 05:30:35

Ordinary Differential Equations And Dynamical Systems

Gives a self contained introduction to the field of ordinary differential equations with emphasis on the dynamical systems point of view. Requires some basic knowledge from calculus, complex functions, and linear algebra.

Excerpts from the Abstract:

This book provides an introduction to ordinary differential equations and dynamical systems. We start with some simple examples of explicitly solvable equations. Then we prove the fundamental results concerning the initial value problem: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore we consider linear equations, the Floquet theorem, and the autonomous linear flow.

Then we establish the Frobenius method for linear equations in the complex domain and investigate Sturm-Liouville type boundary value problems including oscillation theory.

Next we introduce the concept of a dynamical system and discuss stability including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems.

We prove the Poincare-Bendixson theorem and investigate several examples of planar systems from classical mechanics, ecology, and electrical engineering. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed as well.

Finally, there is an introduction to chaos. Beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits.

Prerequisites:

This book only requires some basic knowledge from calculus, complex functions, and linear algebra which should be covered in the usual courses.

This book provides an introduction to ordinary differential equations and dynamical systems. We start with some simple examples of explicitly solvable equations. Then we prove the fundamental results concerning the initial value problem: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore we consider linear equations, the Floquet theorem, and the autonomous linear flow.

Then we establish the Frobenius method for linear equations in the complex domain and investigate Sturm-Liouville type boundary value problems including oscillation theory.

Next we introduce the concept of a dynamical system and discuss stability including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems.

We prove the Poincare-Bendixson theorem and investigate several examples of planar systems from classical mechanics, ecology, and electrical engineering. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed as well.

Finally, there is an introduction to chaos. Beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits.

Prerequisites:

This book only requires some basic knowledge from calculus, complex functions, and linear algebra which should be covered in the usual courses.

Tweet

About The Author(s)

No information is available for this author.

Book Categories

Computer Science
Introduction to Computer Science
Introduction to Computer Programming
Algorithms and Data Structures
Artificial Intelligence
Computer Vision
Machine Learning
Neural Networks
Game Development and Multimedia
Data Communication and Networks
Coding Theory
Computer Security
Information Security
Cryptography
Information Theory
Computer Organization and Architecture
Operating Systems
Image Processing
Parallel Computing
Concurrent Programming
Relational Database
Document-oriented Database
Data Mining
Big Data
Data Science
Digital Libraries
Compiler Design and Construction
Functional Programming
Logic Programming
Object Oriented Programming
Formal Methods
Software Engineering
Agile Software Development
Information Systems
Geographic Information System (GIS)

Mathematics
Mathematics
Algebra
Abstract Algebra
Linear Algebra
Number Theory
Numerical Methods
Precalculus
Calculus
Differential Equations
Category Theory
Proofs
Discrete Mathematics
Theory of Computation
Graph Theory
Real Analysis
Complex Analysis
Probability
Statistics
Game Theory
Queueing Theory
Operations Research
Computer Aided Mathematics

Supporting Fields
Web Design and Development
Mobile App Design and Development
System Administration
Cloud Computing
Electric Circuits
Embedded System
Signal Processing
Integration and Automation
Network Science
Project Management

Operating System
Programming/Scripting
Ada
Assembly
C / C++
Common Lisp
Forth
Java
JavaScript
Lua
Microsoft .NET
Rexx
Perl
PHP
Python
R
Rebol
Ruby
Scheme
Tcl/Tk

Miscellaneous
Sponsors