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Differential Equations: A Modeling Perspective
This effective and practical new edition continues to focus on differential equations as a powerful tool in constructing mathematical models for the physical world. It emphasizes modeling and visualization of solutions throughout. Each chapter introduces a model and then goes on to look at solutions of the differential equations involved using an integrated analytical, numerical, and qualitative approach. The authors present the material in a way that's clear and understandable to students at all levels. Throughout the text the authors convey their enthusiasm and excitement for the study of ODEs.
736 pages, Hardcover
First published January 12, 1996
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Displaying 1 - 2 of 2 reviews
May 17, 2024
I’m going to be clutching this on my deathbed. Approachable yet rigorous, good exercises with selected solutions, focus on intuition building and modeling approach. Very well organized.
June 21, 2021
1.0 out of 5 stars
Don't Bother
August 2, 2005
I can't come up with anyone who should bother reading this book. First, the authors don't really state who their audience is. The closest they come is on the first page of the Preface where they say:
"...with the powerful and inexpensive computing tools currently available, we think that now is the right time to reconnect differential equations to its roots via an introductory course from a modeling perspective. That is the goal of this text."
Then, on page ix, they give a Chapter Dependency Chart which includes breakouts for Engineering students, Math/Physics students, Biology/Pre-Med students, and "A Course Emphasizing Systems." Regardless of the "Math/Physics" entry, above, the preponderance of evidence from the text itself leads to me believe that the intended audience is those who will apply differential equations (DEQs) in their jobs (i.e., non-Math-types) using computer models. Of course, the fact that I have to synthesize (i.e., guess) the intended audience from various parts of the book instead of the authors just telling me is a strike against the book right there.
My guess as to the audience is supported, to some extent, by the way this book is written. It seems to assume knowledge of various areas of physics, chemistry, engineering, and biology. The point of the book doesn't seem to be to teach the understanding of the math underlying how to work with and solve DEQs. Instead, it seems to be to teach some cookie-cutter steps to follow, perhaps using the "Lucky Guess Approach to Finding a Particular Solution" (I'm not kidding), or if that fails, how to get the problem to a point where it can be entered into a "solver" and graphed. I guess that's the "modeling perspective." The bigger problem is that the book doesn't even do a very good job of that. First, the book seems to assume a pretty detailed knowledge of DEQs themselves. Second, the authors skip huge swaths of how they solve their examples (I won't even talk about missing steps in the few "proofs" they give). One particular case keeps popping into my mind. The authors spend a couple of lines translating the verbal problem into the DEQ, wave their hands and says "after some algebra," and present a very-non-obvious solution equation which stretches across the entire page. My guess is that the "some algebra" they skipped would take several pages of calculus and algebraic manipulation. If non-math-types are the audience, I don't see how skipping ALL the math in examples will help them get to the answers. And, finally, the authors also skip steps in telling the reader how to translate situations into the DEQs themselves. For instance, when they introduce the Predator-Prey model, they give verbal descriptions of the "Laws" involved and present the reader with the DEQs. After the fact, they generically talk about why the equations look this way, but they don't try to walk the readers through the process they used to come up with the DEQs.
So, in a nutshell, math-types should stay away from this book since it doesn't really seem to be a math book, and non-math-types should stay away from it because it skips too many steps and assumes too much. I really can't even see the point of this book. Perhaps if it were used as a companion to a manual in some kind of course in DEQ modeling (solver) SOFTWARE. But, as is, I rate this book as just 1 star out of 5: useless.
Don't Bother
August 2, 2005
I can't come up with anyone who should bother reading this book. First, the authors don't really state who their audience is. The closest they come is on the first page of the Preface where they say:
"...with the powerful and inexpensive computing tools currently available, we think that now is the right time to reconnect differential equations to its roots via an introductory course from a modeling perspective. That is the goal of this text."
Then, on page ix, they give a Chapter Dependency Chart which includes breakouts for Engineering students, Math/Physics students, Biology/Pre-Med students, and "A Course Emphasizing Systems." Regardless of the "Math/Physics" entry, above, the preponderance of evidence from the text itself leads to me believe that the intended audience is those who will apply differential equations (DEQs) in their jobs (i.e., non-Math-types) using computer models. Of course, the fact that I have to synthesize (i.e., guess) the intended audience from various parts of the book instead of the authors just telling me is a strike against the book right there.
My guess as to the audience is supported, to some extent, by the way this book is written. It seems to assume knowledge of various areas of physics, chemistry, engineering, and biology. The point of the book doesn't seem to be to teach the understanding of the math underlying how to work with and solve DEQs. Instead, it seems to be to teach some cookie-cutter steps to follow, perhaps using the "Lucky Guess Approach to Finding a Particular Solution" (I'm not kidding), or if that fails, how to get the problem to a point where it can be entered into a "solver" and graphed. I guess that's the "modeling perspective." The bigger problem is that the book doesn't even do a very good job of that. First, the book seems to assume a pretty detailed knowledge of DEQs themselves. Second, the authors skip huge swaths of how they solve their examples (I won't even talk about missing steps in the few "proofs" they give). One particular case keeps popping into my mind. The authors spend a couple of lines translating the verbal problem into the DEQ, wave their hands and says "after some algebra," and present a very-non-obvious solution equation which stretches across the entire page. My guess is that the "some algebra" they skipped would take several pages of calculus and algebraic manipulation. If non-math-types are the audience, I don't see how skipping ALL the math in examples will help them get to the answers. And, finally, the authors also skip steps in telling the reader how to translate situations into the DEQs themselves. For instance, when they introduce the Predator-Prey model, they give verbal descriptions of the "Laws" involved and present the reader with the DEQs. After the fact, they generically talk about why the equations look this way, but they don't try to walk the readers through the process they used to come up with the DEQs.
So, in a nutshell, math-types should stay away from this book since it doesn't really seem to be a math book, and non-math-types should stay away from it because it skips too many steps and assumes too much. I really can't even see the point of this book. Perhaps if it were used as a companion to a manual in some kind of course in DEQ modeling (solver) SOFTWARE. But, as is, I rate this book as just 1 star out of 5: useless.
Displaying 1 - 2 of 2 reviews