Differential Equations in 24 Hours, Scott Imhoff, Outskirts Press, 2016

This is in some ways a new edition of Imhoff's Shortcut to Differential Equations.  The book presents the basic methods used to solve ordinary differential equations.  The title is not meant to be taken literally, the book is divided into 24 lectures which could be delivered - hence 24 hours.  The book contains many examples, and it includes the answers to the exercises.  The author focuses on methods that you will actually use - he doesn't include all the typical methods found in today bloated text books - this is good as you would never encounter many of these methods again.  A few biographical sketches have been included - these add nothing to the book, but at a list price of $12.95, there is no reason to complain.  If you are highly motivated, or if you need a refresher this book is a good resource.  I have added it to my collection and I will use it to bring the undergraduate researchers up to speed quickly.

Partial differential equation are only mentioned.  When ever I encounter a new book on differential equations, I think of the retired University of Mississippi theoretical physicist Gordon Baird.  When I was a beginning graduate student, he said to me one day how surprised he was that courses in differential equations only covered ordinary differential equations in the course of a semester.  He went on to say that if they were to use something like Francis Hildebrand's Advanced Calculus for Engineers that you could cover ODEs and PDEs in one semester.  This book was later to become Advanced Calculus for Applications - though, I note that Amazon has a nice reprint of the original 1949 edition in paperback.  The situation hasn't improved in the 38 years since Gordon told me this - today's books are even more bloated than those of 1978.  So if you want to learn ODEs, Imhoff is a good start, then spend another $16.95 and over the course of 6 months you can become an expert solver of (linear) differential equations.

Hildebrand was an MIT Professor, the course at MIT still uses Hildebrand's book and is available on MIT open courseware.  The course is from 2004, but I think Hildebrand retired in 1984.  You can download a nice set of lecture notes.  I will pull out my copy of Advanced Calculus for Engineers and write an appreciation in the next few days.