Kurzweil Ordinary Differential Equations

Introduction to the Theory of Ordinary Differential Equations in the Real Domain
1. Auflage 2014
ISBN: 978-1-4832-9765-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 13, 440 Seiten, Web PDF

Reihe: Studies in Applied Mechanics

The author, Professor Kurzweil, is one of the world's top experts in the area of ordinary differential equations - a fact fully reflected in this book. Unlike many classical texts which concentrate primarily on methods of integration of differential equations, this book pursues a modern approach: the topic is discussed in full generality which, at the same time, permits us to gain a deep insight into the theory and to develop a fruitful intuition. The basic framework of the theory is expanded by considering further important topics like stability, dependence of a solution on a parameter, Carathéodory's theory and differential relations.The book is very well written, and the prerequisites needed are minimal - some basics of analysis and linear algebra. As such, it is accessible to a wide circle of readers, in particular to non-mathematicians.

Autoren/Hrsg.

Kurzweil, J.

Inhaltsverzeichnis

1;Front Cover;1
2;Ordinary Differential Equations: Introduction to the Theory of Ordinary Differential Equations in the Real Domain;4
3;Copyright Page;5
4;Table of Contents;8
5;PREFACE;6
6;REMARKS ON ENUMERATION OF FORMULAE;9
7;REMARKS ON THE ENGLISH EDITION;10
8;PRELIMINARIES;12
9;CHAPTER 1. INTRODUCTION;18
10;CHAPTER 2. ON ELEMENTARY METHODS OF INTEGRATION;31
11;CHAPTER 3. SYSTEMS OF DIFFERENTIAL EQUATIONS, VECTOR NOTATION;68
12;CHAPTER 4. LINEAR DIFFERENTIAL EQUATIONS;79
13;CHAPTER 5. AUTONOMOUS LINEAR DIFFERENTIAL EQUATIONS;105
14;CHAPTER 6. PERIODIC LINEAR DIFFERENTIAL EQUATIONS;135
15;CHAPTER 7. SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS;146
16;CHAPTER 8. ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS;164
17;CHAPTER 9. LINEAR BOUNDARY VALUE PROBLEMS;168
18;CHAPTER 10. LOCAL EXISTENCE OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS. KNESER THEOREM. FUKUHARA THEOREM;201
19;CHAPTER 11. UNIQUENESS;209
20;CHAPTER 12. GLOBAL PROPERTIES OF SOLUTIONS OF DIFFERENTIAL EQUATIONS;216
21;CHAPTER 13. DIFFERENTIABILITY OF THE SOLUTION WITH RESPECT TO INITIAL CONDITIONS;231
22;CHAPTER 14. DEPENDENCE OF THE SOLUTION ON A PARAMETER;242
23;CHAPTER 15. EXPONENTIAL STABILITY. HYPERBOLIC POINT, UNSTABLE AND STABLE MANIFOLD;268
24;CHAPTER 16. FIRST INTEGRALS. PARTIAL DIFFERENTIAL EQUATIONS;280
25;CHAPTER 17. AUTONOMOUS SYSTEMS OF TWO DIFFERENTIAL EQUATIONS;293
26;CHAPTER 18. CARATHÉODORY THEORY OF DIFFERENTIAL EQUATIONS DIFFERENTIAL RELATIONS;316
27;APPENDICES;355
28;REFERENCES;433
29;INDEX OF SYMBOLS;438
30;INDEX;439