Ordinary Differential Equations

Introduction to the Theory of Ordinary Differential Equations in the Real Domain

J. Kurzweil

• Publisher: North Holland
• Year: 2014
• ISBN:
  9781483297651
• Topic: Mathematics
• Subtopic: Differential Equations
• Index: Mathematics

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.

Table of contents

• Front Cover
• Ordinary Differential Equations: Introduction to the Theory of Ordinary Differential Equations in the Real Domain
• Copyright Page
• Table of Contents
• PREFACE
• REMARKS ON ENUMERATION OF FORMULAE
• REMARKS ON THE ENGLISH EDITION
• PRELIMINARIES
• CHAPTER 1. INTRODUCTION
• CHAPTER 2. ON ELEMENTARY METHODS OF INTEGRATION
• CHAPTER 3. SYSTEMS OF DIFFERENTIAL EQUATIONS, VECTOR NOTATION
• CHAPTER 4. LINEAR DIFFERENTIAL EQUATIONS
• CHAPTER 5. AUTONOMOUS LINEAR DIFFERENTIAL EQUATIONS
• CHAPTER 6. PERIODIC LINEAR DIFFERENTIAL EQUATIONS
• CHAPTER 7. SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS
• CHAPTER 8. ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS
• CHAPTER 9. LINEAR BOUNDARY VALUE PROBLEMS
• CHAPTER 10. LOCAL EXISTENCE OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS. KNESER THEOREM. FUKUHARA THEOREM
• CHAPTER 11. UNIQUENESS
• CHAPTER 12. GLOBAL PROPERTIES OF SOLUTIONS OF DIFFERENTIAL EQUATIONS
• CHAPTER 13. DIFFERENTIABILITY OF THE SOLUTION WITH RESPECT TO INITIAL CONDITIONS
• CHAPTER 14. DEPENDENCE OF THE SOLUTION ON A PARAMETER
• CHAPTER 15. EXPONENTIAL STABILITY. HYPERBOLIC POINT, UNSTABLE AND STABLE MANIFOLD
• CHAPTER 16. FIRST INTEGRALS. PARTIAL DIFFERENTIAL EQUATIONS
• CHAPTER 17. AUTONOMOUS SYSTEMS OF TWO DIFFERENTIAL EQUATIONS
• CHAPTER 18. CARATHÉODORY THEORY OF DIFFERENTIAL EQUATIONS DIFFERENTIAL RELATIONS
• APPENDICES
• REFERENCES
• INDEX OF SYMBOLS
• INDEX