Author: Robinson, James C.
Date of Publication: 2015
Title: An Introduction to Ordinary Differential Equations. Cambridge University Press.
Accessed 16 August 2016.
We quote from the introduction by the author,
“This refreshing, introductory textbook covers standard techniques for solving ordinary differential equations, as well as introducing students to qualitative methods such as phase-plane analysis. The presentation is concise, informal yet rigorous; it can be used for either one-term or one-semester courses.
“Topics such as Euler’s method, difference equations, the dynamics of the logistic map and the Lorenz equations, demonstrate the vitality of the subject, and provide pointers to further study. The author also encourages a graphical approach to the equations and their solutions, and to that end the book is profusely illustrated. The MATLAB files used to produce many of the figures are provided in an accompanying website.
“Numerous worked examples provide motivation for, and illustration of, key ideas and show how to make the transition from theory to practice. Exercises are also provided to test and extend understanding; full solutions for these are available for teachers.”
This 415 page work proceeds with a nice mixture of theory and application with lots of graphical illustrations to depict both. There is much attention to the qualitative approach to the study as well.
The solution strategies are offered in the usual order with illustrations from physical models mostly. Although, there are some interesting twists introduced right in the text early in each strategy, e.g.. Newton’s Law of Cooling in an unheated building with a varying ambient temperature is studied as an example of integrating factor strategy.
There are digressions to help the reader, e.g., combining two oscillating terms is addressed as a two page aside in a just in time manner.
An entire chapter is devoted to oscillations and the exercises here begin to get rich, e.g., buoyancy problems are offered. An interesting exercise about the undue oscillations in the London Millennium Bride is offered as well. And when it comes to forcing functions there is nice materials e.g., washing machine motion. Resonance is richly discussed with some historical material presented for motivation.
Both series and numerical methods solution strategies are offered in good manner. And there is a nice section on difference equations as well.
The study of linear systems is rich in qualitative analyses, but no real applications. Ecological systems are given a chapter, but again, no application exercises, just a setting for qualitative analyses.
Partial differential equations are not discussed in the text. As such there is no attention to Fourier series either.
The style of the book is almost conversational in places which makes for a good read for students.
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