I will be leading a discussion class on differential equations for engineers this coming semester and I am wondering if anyone has a book that they could recommend. The book that will be used in the course is the book by Boyce and DiPrima. I am looking for a supplementary book from which to take problems to solve in class. Is there a book that has conceptual but not overly theoretical problems for differential equations? problems which are insightful but not too complicated? These problems are not the sort of problems which test skills in algebraic manipulation (I know it's ironic given that this is an engineering class) but problems which reinforce understanding of the concept?
Suggestions greatly appreciated. Thanks!
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$\begingroup$"Ordinary Differential Equations" by Morris Tenenbaum and Harry Pollard contains a comprehensive and well-written treatment of all topics concerning ODEs.
$\endgroup$ $\begingroup$You might take a look at M. Braun, "Differential Equations and Their Applications". It has lots of good problems and examples.
$\endgroup$ $\begingroup$Math 18-03at MIT has a lovely book on ODEs for engineers by Prof. Haynes R. Miller, hidden undersupplementary notes. Miller's style is conversational, clear, lively:
Every good formula deserves a particularly illuminating example.
The chapter titles:
- Notation and language 3
- Modeling by first order linear ODEs 6
- Solutions of first order linear ODEs 10
- Sinusoidal solutions 16
- The algebra of complex numbers 23
- The complex exponential 27
- Beats 34
- RLC circuits 38
- Normalization of solutions 41
- Operators and the exponential response formula 45
- Undetermined coefficients 53
- Resonance and the exponential shift law 55
- Natural frequency and damping ratio 60
- Frequency response 62
- The Wronskian 72
- More on Fourier series 75
- Impulses and generalized functions 86
- Impulse and step responses 93
- Convolution 98
- Laplace transform technique: coverup 101
- The Laplace transform and generalized functions 106
- The pole diagram and the Laplace transform 112
- Amplitude response and the pole diagram 119
- The Laplace transform and more general systems 121
- First order systems and second order equations 123
- Phase portraits in two dimensions 127
Many chapters have Mathlets, interactive applets on the web, to learn by doing. For example, Mathlet damping ratio:
(This is just a screenshot — if anyone knows how to make mathlets run live on SE, please edit.)
$\endgroup$ $\begingroup$For ODEs, I would recommend A First Course in Differential Equations with Modeling Applications by Dennis Zill.
A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS, 10th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible book speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. Written in a straightforward, readable, and helpful style, the book provides a thorough treatment of boundary-value problems and partial differential equations.
Then for a first course in PDEs, I would recommend Applied Partial Differential Equations with Fourier Series and Boundary Value Problems by Richard Haberman.
$\endgroup$ $\begingroup$This book emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations. Coverage includes Fourier series, orthogonal functions, boundary value problems, Green’s functions, and transform methods. This text is ideal for readers interested in science, engineering, and applied mathematics.
I've taught DE out of Boyce and DiPrima about 20 times (mostly engineering majors.) I have suggested on my syllabus the Schaum's Outline for Differential Equations as a supplement. Besides being cheap, it has tons of worked out problems and tons of supplementary problems with answers. The explanations are very clean and terse (this is a good thing.) Each chapter gets right to the problem solving, which is what DE is about.
Most importantly: I've gotten a whopping lot of good feedback from the students who have used the book.
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