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Elementary Differential Equations 9th Edition
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If you are a student reading my review and your instructor has assigned Boyce and DiPrima, I encourage you to ask your instructor why they have chosen Boyce and DiPrima. I would ask them seriously to consider using Hirsch, Smale and Devaney (if it is a more theoretical course), or George F. Simmons' book. If it is their first time teaching the course then fine, they don't know the ODE book selection, but if they have taught it several times I am confused why they would choose Boyce and DiPrima. (By the way, I think that the default book for calculus, Stewart, is actually quite good for many audiences, while I cannot imagine any audience, applied or theoretical, brilliant or below average, for whom Boyce and DiPrima is the best book choice.)
The presentation of phase portraits doesn't adequately explain how to draw them (for example, where does the book explain how to find the axes of an elliptical orbit?), and is split between chapters 7 and 9. Perhaps here Boyce and DiPrima decided that they didn't need to give a really good explanation of something as long as they say it twice. Their practice of drawing a phase portrait and then showing an x/t graph beside it mystifies phase portraits to students: students aren't used to drawing parametrized curves and this mixes the notion of a parametrized curve up with a curve (t,x(t)); perhaps the authors thought they were in fact clarifying this distinction, but their pedagogical abilities are so poor that they did the reverse of what they planned.
The examples in the text are poorly chosen and do not sufficiently prepare students for some of the techniques needed to solve the exercises. For example, in section 5.2 the two examples calculating power series solutions both have y'' and y in the equation, with no y' term, while questions involving ODEs with y' terms appear in the exercises. Also, the tediously long explanations are just that: tedious. They are chatty in an unhelpful way. What would be helpful are solutions that spell out every single step of an argument, instead of the qualitative descriptions that the authors inject into their writing, which are not especially perceptive and that make the text seem overwhelming.
I can't think of a satisfying reason why there are separate chapters for higher orders equations and systems of first order equations. Doing this makes it seem like there are two separate notions of Wronskian while in fact they are exactly the same. And the chapter on higher order equations comes between the chapter on linear (mostly constant coefficient) second order equations and power series solutions of linear second order differential equations, which fit well together: first we do the constant coefficient case, and then we show a method that works more generally. And the authors have stuck a chapter on numerical methods between the chapters on systems of linear equations and nonlinear systems, which are a natural couple.
I expect many people could write a better book than this, but to make a really good ODE textbook would take many years work by a writer, not a "me too" job that an ambitious mathematician would dash off in a summer, perhaps lecturing a few times. I think the ideal setting for an author of such an ideal text would be to teach ODE at several different institutions, teaching students with different backgrounds and interests over several years. An author should have the confidence to excise topics like undetermined coefficients: if we teach students two methods for solving inhomogeneous linear equations, they will learn both worse and become confused about when to use them. And a chapter on basic calculus of variations has a much tighter connection with ODE than a single chapter on PDE, which I don't think belongs in a book on ODE.
For an advanced course, an instructor could either use Hirsch, Smale and Devaney, or for a very advanced course, Arnold. For a less intense course that is approachable by both well prepared and less well prepared students, I strongly suggest trying George F. Simmons' "Differential equations with applications and historical notes". Unlike Boyce and DiPrima, who give nearly contextless biographies that feel like they were talentlessly cut and pasted from an encyclopedia by someone with no historical learning, Simmons gives page long descriptions of the history of some of the authors and concepts he discusses and one can see from his writing that he has taken the time to get a connected and detailed understanding of the history of the subject.
For example, this book makes understanding the techniques of variation of parameters and undetermined coefficients ridiculously painful to understand. And don't even get me started on the chapter on Laplace transforms -- I could barely understand a single thing there!
However, it's not all bad. *most* of the earlier chapters' contents are pretty good. Still, there are some murky bits and random theoretical topics addressed only half-heartedly, but for the most part, they're okay.
Also, as I said before, the problems in this book aren't bad! My professor usually assigned suggested problems from the text and doing them really helped me memorize the techniques that I learned from Paul's Online Notes...erm, I mean from the chapter!
So yeah, it's an average, run of the mill, hard-to-understand textbook. If you're required to use it for a class, make sure you pay attention and not skip class thinking that you can learn from the book! If you're looking for a book for self study...well, I guess you can use it for the problems, but for the actual material, don't bother with it, just use Paul's Online Notes or ask for help on math forums or something.
Who ever the editor was, needs to be fired. 10 editions! 10 published copies of this book. And it seems like it just can't be done right. The examples in this book appears to be erratic in organization and is even confusing on the approach.
The book clearly wasn't constructed for students whom are just entering the field for differential equations as it appears to be more of a "handy-dandy" reminder if you can get past some unnecessary contributions to some solutions, or certain solutions just randomly going from start to done.
What's more annoying, was that in the first chapter, section 1.3, there was no explination that could have remotely helped for some of the problems you would see for that section. Are you serious? These people could seriously learn from Pearson McGraw. They might do some BS religious edits, but at least they know how to make a good math book. Full of examples (not just the easy case), clear explinations.
The problems in the book have been pretty helpful... mind you that is after going to a website that has done a good job at working through the entire problem step by step in a clear and unpolluted format. That website is slader.com for those looking for help with this thing, and are too cheap to pay for chegg (like me).
I'm only on chapter 2 in my university class right now, and I'm already loathing this book.