Differential Equations: Theory and Applications : with Maple®
David Betounes (Author)
This book provides a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as important applications of the theory. The text is written to be used in the traditional way (emphasis on the theory with the computer component as optional) or in a more applied way (emphasis on the applications and the computer material). The accompanying CD contains Maple worksheets to use in working the exercises and extending the examples. The disk also contains special Maple code for performing various tasks. In addition to its use in a traditional one- or two- (there is enough material for two) semester graduate course in mathematics, the book is organized to be used for interdisciplinary courses in applied mathematics, physics, and engineering. Researchers and professionals may also find the supplementary material on the disk on discrete dynamical systems, theory of iterated maps, and code for performing specific tasks on the disks particularly useful
eBook, English, 2001
Springer New York : Imprint : Springer, New York, NY, 2001
1 online resource
9781475749717, 9781475749731, 1475749716, 1475749732
864568980
Printed edition:
1 Introduction
2 Techniques, Concepts, and Examples
3 Existence and Uniqueness: The Flow Map
4 One-Dimensional Systems
5 Linear Systems
6 Linearization and Transformation
7 Stability Theory
8 Integrable Systems
9 Newtonian Mechanics
10 Motion on a Submanifold
11 Hamiltonian Systems
A Elementary Analysis
A.1 Multivariable Calculus
A.2 The Chain Rule
A.3 The Inverse and Implicit Function Theorems
A.4 Taylor's Theorem and The Hessian
A.5 The Change of Variables Formula
B Lipschitz Maps and Linearization
B.1 Norms
B.2 Lipschitz Functions
B.3 The Contraction Mapping Principle
B.4 The Linearization Theorem
C Linear Algebra
C.1 Vector Spaces and Direct Sums
C.2 Bilinear Forms
C.3 Inner Product Spaces
C.4 The Principal Axes Theorem
C.5 Generalized Eigenspaces
C.6 Matrix Analysis
C.6.1 Power Series with Matrix Coefficients
D CD-ROM Contents
English