Mickens R. Introduction to Qualitative Methods for Differential Equations 2025

Textbook in PDF format

Introduction to Qualitative Methods for Differential Equations provides an alternative approach to teaching and understanding differential equations. The basic methodology of the book is centred on finding reformulations of differential equations in such a manner that they become (partially, at least) problems in geometry. Through this approach, the book distils the critical aspects of the qualitative theory of differential equations and illustrates their application to a number of nontrivial problems.
Features
Self-contained with suggestions for further reading.
Concise and approachable exposition with only minimal pre-requisites.
Ideal for self-study.
Appropriate for undergraduate mathematicians, engineers, and other quantitative science students.
Preface.
Preliminaries.
What Is a Solution?
One-Dimensional Systems.
Two-Dimensional Dynamical Systems.
Sturm–Liouville Problems.
Partial Differential Equations.
Introduction to Bifurcations.
Applications.
Appendix A.
Bibliography.
Index