Author: Terrell, Robert
Date of Publication: 2014.
Title: Notes on Differential Equations (Version 5: 2014)
Accessed 16 August 2016.
The author offers Octave code for this text. In the Preface the author says, “I may point out that the title is not Solving Differential Equations; we derive them, discuss them, review calculus background for them, apply them, sketch and compute them, and also solve them and interpret the solutions. This breadth is new to many students.” To which we might add, “and to faculty.”
There is a nice feature the author describes at the start of the text, “Some of the exercises have the format, `What’s rong with this?’ These are either questions asked by students or errors taken from test papers of students in this class, so it could be quite beneficial to study them.”
There is a very readable mix of theory, application, computer algebra system which is very refreshing.
The material does discuss the usual suspects, heat and wave partial differential equations as well as the vibration of a drum head, but does cover Laplace Transform. The path to Fourier series is historical and very interesting. The last chapter is a “tribute” to chaos with attempts to model weather, well, futile attempts!
The author says in the preface,
“These Notes on Differential Equations are an introduction and invitation. The focus is on
- important models
- calculus (review?) in applied contexts
“I may point out that the title is not Solving Differential Equations; we derive them, discuss them, review calculus background for them, apply them, sketch and compute them, and also solve them and interpret the solutions. This breadth is new to many students.
"The notes, available for many years on my web page, have evolved from lectures I have given while teaching the Engineering Mathematics courses at Cornell University. They could be used for an introductory unified course on ordinary and partial differential equations. There is minimal manipulation and a lot of emphasis on the teaching of concepts by example.”
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