Elementary Differential Equations by William E. Boyce
My rating: 4 of 5 stars

Yet another review of academic textbook that I have been using for a long time. William E. Boyce and Richard C. DiPrima's Elementary Differential Equations and Boundary value Problems may be one of the most enduring textbooks on the academic market. I believe its first edition dates back to 1971 and the book that I am reviewing here is Edition 10, published in 2012. I have been using this text for almost 20 years, beginning with the sixth edition.

Ordinary Differential Equations is an upper-division mathematics course that I have taught most frequently of all math courses - 20 times. In the 1980s and 1990s I used a variety of textbooks, none of which satisfied my needs and - more importantly - the needs of my students. They were either too superficial, where the authors attempted to avoid the mathematical rigor in order to, presumably, make the texts more "readable" by the students, or they focused too much on rigorous formalisms at the expense of readability. In my view, Boyce and DiPrima's text achieves a perfect balance between rigor and accessibility. For instance, Section 2.4, Differences Between Linear and Nonlinear Equations contains treatment of subtle issues that aren't usually discussed in "easier" texts yet the writing is not prohibitively technical for a student, not even necessarily an A student. I love Chapter 5 that deals with series solutions, where the authors were able to cleanly separate more elementary material on solutions near an ordinary point from the more advanced topics of solutions near regular singular points. I also like the coverage of Laplace transform method and particularly the topic of handling discontinuous forcing functions.

Being an applied - rather than "pure" - mathematician I emphasize applications when teaching differential equations. Boyce and DiPrima's text does quite a good job in presenting to the reader the applications not only from the traditional fields like population dynamics or mechanical and electrical vibrations. True, there are textbooks that better deal with applications, say Borelli's book Differential Equations: A Modeling Perspective, but then I have found these more "applied" texts lacking in the theoretical aspect.

In addition to the nice balance between the formal and the readable and between theory an applications, I like the problems that the authors provide for the students' individual work. Each section has a large and varied set of problems that allow me to customize homework assignments to the level of the particular set of students in my class.

I normally use only the first eight chapters of the textbook and omit the material on nonlinear differential equations, stability, partial differential equations, and Fourier series (the last two topics are the subject of another course in which I use Boundary value Problems which I have also reviewed here on Goodreads.

Other than the fact that mathematical modeling sections of the textbook, particularly Section 2.3, Modeling with First Order Equations, could be improved, I would definitely prefer an edition of the textbook that focuses solely on ordinary differential equations. Students have to pay exorbitant prices (up to $200) for a textbook whose substantial portions they do not need.

Four stars.


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