Includes illustrations.

Contents:
Preface
About the Author
Acknowledgments
The Notation and Preliminary Results
Introduction
Basic Concepts
The Cauchy Problem: Local Analysis
Uniqueness
The Cauchy Problem: Global Analysis
Cauchy Problems and Linear Systems
Boundary-Value Problems for Linear Systems
Some Regularity Results
Stability Results
The Method of Characteristics for First-Order Linear and Quasi-Linear Partial Differential Equations
Basic Ideas in Control Theory
Additional Notes
References
Index

Readership: Undergraduate and graduate students, especially those interested by the role played by differential equations in mathematics and science in general.

Differential equations can bring mathematics to life, describing phenomena originating in physics, chemistry, biology, economics, and more. Used by scientists and engineers alike, differential equations are also the starting point of much purely mathematical activity. They also play a role in the formulation and resolution of problems in harmonic analysis, differential geometry, and probability calculus. A large part of functional analysis has therefore been motivated by the need to solve questions in the analysis of differential systems, as with numerical analysis.

Differential equations are doubly relevant, then: as significant in many areas of mathematics, and as important machinery for applying mathematics to real-world problems. This book therefore aims to provide a rigorous introduction to the theoretical study of differential equations, and to demonstrate their utility with applications in many fields.

Ordinary Differential Equations and Applications originates from several courses given by the author for decades at the University of Seville. It aims to bring together rigorous mathematical theory and the rich variety of applications for differential equations. The book examines many aspects of differential equations: their existence, uniqueness, and regularity, alongside their continuous dependence on data and parameters. Delving into permanent interpretation of the laws of differential equations, we also look at the role of data and how their solutions behave. Each chapter finishes with a collection of exercises, many of which also contain useful hints.