Differential Equations 004 Edition by Paul Blanchard (PDF)

Description

Incorporating an innovative modeling approach, this book for a one-semester differential equations course emphasizes conceptual understanding to help users relate information taught in the classroom to real-world experiences. Certain models reappear throughout the book as running themes to synthesize different concepts from multiple angles, and a dynamical systems focus emphasizes predicting the long-term behavior of these recurring models. Users will discover how to identify and harness the mathematics they will use in their careers, and apply it effectively outside the classroom.Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I had to get this for a course next semester, and have started to go through it. It seems quite good, but I’ll update this review in May with my final conclusions when I’ve read and done it all.The reviewers who don’t like it should read the first two paragraphs of the preface, which explain clearly why the authors tried something different. If anyone wants a classic ODE textbook or reference book, there’s hardly a lack of them; in particular Dover has some very good and inexpensive textbooks. My personal opinion, coming back to math after 30+ years, is that it’s rather hidebound, and given the poor record math departments have of attracting and retaining students, a change would do it good. There could well be people who study ODEs for their intrinsic interest, from a pure math perspective, but they have got to be a tiny minority. Most students will benefit most from learning to understand how to use ODEs, what they tell you, and how to get solutions, for science and engineering applications. That’s what this book appears to be focused on. In particular, since it seeks to explain modeling with differential equations, the hardest step of which is how to map from reality to model (just as with junior high school word problems). That part of modeling is not primarily mathematical, so the language of discourse has to be natural language, not math itself. This is the first book I’ve used that makes any serious (if introductory) effort to explain that step, and I appreciate it.As for the price, agreed, it’s ridiculous. The American textbook industry deserves a revolt by the masses, and over time will get one, just as the recording industry got one. One problem is that many teachers are oblivious to the price of the books they choose–some literally do not know the price and do not make the trivial effort required nowadays to find out. Of course the education industry deserves a revolt by the masses too…

⭐I used this text to teach differential equations to advanced high school seniors and it worked extremely well. After considering several other texts, I was sold on this book for three reasons:1. Rather than older-style differential equations books that focus on analytic methods, this book has a consistent approach of using a combination of analytic, qualitative, and numerical methods. As an industrial mathematician, most differential equations that I worked with could not be solved analytically and thus numerical and qualitative techniques became key tools.2. The friendly expository style of the authors motivates the material and is easier for students to understand than more formal textbooks. New material is always introduced by concrete examples before getting into theory.3. The book is written from a dynamical systems point of view and the authors tap into many interesting results from the past 40-50 years, e.g., the Lorenz equations, modeling epidemics, adaptive shock absorbers, etc.Perhaps my most pleasant surprise teaching the course was how much the students liked and learned from DETools, the differential equation software that comes with the textbook. We regularly used DETools in class (there’s essentially no learning curve) and its use energized the students and made much more clear to them the nature of solutions.I also found the exploratory projects at the end of each chapter very valuable. My students liked the challenge of these more general and open-ended problems, and the projects solidified their understanding.As far as the nuts and bolts of teaching the course, I typically covered one section per day, and we did most of the sections in Chapters 1-6. Regrettably we didn’t get to the last two chapters of the book, but they are quite good. Chapter 7 gets into the nitty gritty of numerical methods (e.g., effects of finite arithmetic) and Chapter 8 is a nice introduction to discrete dynamical methods. (A one-semester course in differential equations can only cover so much, so the text leaves to a later course many special techniques for analytically solving ODEs and it does not cover boundary value problems or the Fourier method.)In summary, I am in very much in agreement with August 7, 2013 review by “G Cantor” that “it would be difficult to find a better introductory text for ordinary differential equations.” This text is a great intro that makes the subject come alive and does an excellent job preparing students to work with differential equations both in later college colleges and in the real world.

⭐This is an excellent text. Sadly, DE Tools are not included in this edition. The authors have an excellent video course on Great Courses which I highly recommend as an accessory.

⭐This book was a nightmare to work with. Much of the mathematics was made painfully difficult because of the insistence on using what the book refers to as “qualitative” methods. This means graphs, and a lot of them. This may sound like a good way to give a visual interpretation of a differential equation; however, the graphs tend to obscure the logic behind much of the more complex topics making many problems difficult to understand, let alone solve. My other problem with using graphs is that they were imprecise and so drawing them in the first place seemed to be irrelevant if you could understand the tail behavior of a differential equation using analytic methods. This book was also written in a colloquial style (which has become the norm for science and mathematics textbooks unfortunately) which made many ideas difficult to understand quantitatively. Using words like “very big” or “close” to describe variables in this book made some simple concepts seem much more complicated than they actually are. This book also had a penchant for only half describing how to do things like draw phase lines or interpret graphs. I would not recommend this book. I had to buy this book for a class and I hope no one else has to because it is useless. If you have a choice I would recommend the book on ODE’s by Tennenbaum and Pollard which is just generally better.

⭐Arrived in great condition, cover looked really nice, pages were clean with very few notes (all in pencil), overall very happy with my purchase! Wish my professor was this reliable!

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