# Dynamical Systems

## An Introduction with Applications in Economics and Biology

• Pierre N. V. Tu
Textbook

1. Front Matter
Pages i-xi
2. Pierre N. V. Tu
Pages 1-3
3. Pierre N. V. Tu
Pages 5-38
4. Pierre N. V. Tu
Pages 39-57
5. Pierre N. V. Tu
Pages 59-77
6. Pierre N. V. Tu
Pages 79-105
7. Pierre N. V. Tu
Pages 107-123
8. Pierre N. V. Tu
Pages 125-148
9. Pierre N. V. Tu
Pages 149-164
10. Pierre N. V. Tu
Pages 165-198
11. Pierre N. V. Tu
Pages 199-213
12. Pierre N. V. Tu
Pages 215-238
13. Back Matter
Pages 239-252

### Introduction

Dynamic tools of analysis and modelling are increasingly used in Economics and Biology and have become more and more sophisticated in recent years, to the point where the general students without training in Dynamic Systems (DS) would be at a loss. No doubt they are referred to the original sources of mathematical theorems used in the various proofs, but the level of mathematics is generally beyond them. Students are thus left with the burden of somehow understanding advanced mathematics by themselves, with· very little help. It is to these general students, equipped only with a modest background of Calculus and Matrix Algebra that this book is dedicated. It aims at providing them with a fairly comprehensive box of dynamical tools they are expected to have at their disposal. The first three Chapters start with the most elementary notions of first and second order Differential and Difference Equations. For these, no matrix theory and hardly any calculus are needed. Then, before embarking on linear and nonlinear DS, a review of some Linear Algebra in Chapter 4 provides the bulk of matrix theory required for the study of later Chapters. Systems of Linear Differ­ ential Equations (Ch. 5) and Difference Equations (Ch. 6) then follow to provide students with a good background in linear DS, necessary for the subsequent study of nonlinear systems. Linear Algebra, reviewed in Ch. 4, is used freely in these and subsequent chapters to save space and time.

### Keywords

Differentialgleichungen differential equation differential equations dynamical systems dynamische Systeme

#### Authors and affiliations

• Pierre N. V. Tu
• 1
1. 1.Department of EconomicsThe University of CalgaryCalgaryCanada

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-662-02779-0
• Copyright Information Springer-Verlag Berlin Heidelberg 1992
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-540-55780-7
• Online ISBN 978-3-662-02779-0
• Buy this book on publisher's site