Textbook in PDF format

The first edition of this book was published in 2021, just prior to the time when Antonio passed away. Perhaps the publication was somewhat rushed due to the surge of the pandemic. Antonio and I agreed that we would revise it as soon as possible. Unfortunately, Antonio passed away quite suddenly and unexpectedly, at about the same time as the book was being printed. The revision has mostly addressed correcting some misprints and errors that are fairly common in the first edition of a book. Many new examples and exercises have been added or substituted. Also, a lot of effort has been made to make the presentation, especially of the first half, as lucid as possible. The first half should be quite suitable for a one-semester undergraduate course in differential equations, taught at most universities in the US. It is suitable for a well-motivated student with a minimal knowledge of Algebra and Calculus. Complete solutions to all the even number problems are given in the back of the book.
Memorial Dedicated to Professor Antonio Ambrosetti.
Preface.
A brief survey of some topics in calculus.
First order linear differential equations.
Analytical study of first order differential equations.
Solving and analyzing some nonlinear first order equations.
Exact differential equations.
Second order linear differential equations.
Higher order linear equations.
Systems of first order equations.
Phase plane analysis.
Introduction to stability.
Series solutions for linear differential equations.
Laplace transform.
A primer on equations of Sturm–Liouville type.
A primer on linear PDE in 2D. I: first order equations.
A primer on linear PDE in 2D. II: second order equations.
The Euler–Lagrange equations in the Calculus of Variations: an introduction.
Solutions.
Bibliography.
Index