Differential Equations Demystified 1st Edition by Steven G. Krantz (PDF)

Description

Here’s the perfect self-teaching guide to help anyone master differential equations–a common stumbling block for students looking to progress to advanced topics in both science and math. Covers First Order Equations, Second Order Equations and Higher, Properties, Solutions, Series Solutions, Fourier Series and Orthogonal Systems, Partial Differential Equations and Boundary Value Problems, Numerical Techniques, and more.

User’s Reviews

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

⭐At only $12 this book might be worth the wealth of inspiring examples about how important DE’s (both ODEs and PDEs) are to most descriptions of nature (physics, motion, dynamics, electronics, etc). However, if you really want to LEARN DE’s, get the for dummies series with workbook:

⭐. It’s about the same price and FAR clearer.The problem with Krantz, both here and in his other books, is that he’s a great mathematician but a TERRIBLE teacher. It’s like going to a lecture and finding that the speaker keeps switching between English, French, Russian and Arabic– in the MIDDLE of each sentence! The math version of this is Krantz showing a Laplace or Fourier transform, and in every other step something new appears without explanation– a switch to polar coordinates, notation changes between d superscript 2, to y” (which to even a smart beginner can look like the addition of a new variable rather than a simple mid-formula change of notation), the sudden appearance of a trig function (with no graphic or illustration of the fact that the ball bearing falling down a tunnel – torus just reached a choke/inflection point), etc.Good math instruction blends description, pictures, formulas and applications. Krantz does a great job of showing a wealth of applications, but leaves out so many details you need a traditional text to follow which rabbit he just pulled out of the hat, and why. If you’ve watched BAD tutorials on (say) YouTube, and GOOD tutorials (say on Kahn Academy or Lynda dot com), you know that some “teachers” are just blasting through the thing to show off, while others really care that you’re learning. This book is more of the show off variety– with little concern for the fact that self-teaching requires far more detail than this provides.To end on a positive note, Krantz uses a WIDE variety of application examples, and even shows how mechanical resonance is nearly identical in formula to electrical resonance, using correlates between Mass/Inductance, Viscosity/Resistance, Stiffness/Capacitance and Displacement/Capacitor charge (74). This cross-discipline seasoning is refreshing and rare (and he does it often– showing how mathematicians view dual state equations compared to how Physicists view superposition, etc.). If you are already adept at DE’s, you’ll probably love this, but if you’re new and trying to self teach– forget it! I’m only trying to save you 12 bucks and point to the much better for dummies book and workbook (

⭐), but if you have a lot of cash and are up for inspiring applications– go for it! Had he taken “a self teaching guide” out of the title, I would have given it a couple more stars, that’s simply misleading, and Amazon buyers deserve better.On the positive side, the applications are simply delightfully creative and unexpected, including using fox/rabbit equations to suggest that competing software companies might want to model their markets with biological growth and particle decay ODE equations, or in this case, competitive ecology ala Volterra (p. 233)! Krantz gives one an astonishing peek at the importance and diversity of DE practical applications, which truly is inspiring.An off-Amazon editor called Krantz an “acquired taste.” This might explain the disparity of reviews here. Krantz goes: example (bang, bang, bang)– now you try one. This gives you good pattern recognition, but not deep understanding. For example, if you pick up the amazing Zill test bank book on ODE’s– over 2,700 problems– (

⭐) you’ll find you can do many of the multiple choice questions due to Krantz, but composing your own systems is tougher unless you get that “intuitive” grasp. For a deep, intuitive, but difficult understanding of ODEs, try a good translation of Arnold, who blends math with deep examples, for example:

⭐.

⭐Differential Equations Demystified is written by Steven Krantz, the author of the not-so-popular Calculus Demystified. Admittedly, this book is not any more user friendly than Calculus demystified; he spends no time explaining jargon in informal language; he constantly uses different notation for derivatives, etc. But at this level, at least, it is more acceptable. Any reader tackling the subject of differential equations with any seriousness will have to face rigors of mathematical language at some point.Surprisingly Krantz claims in his introduction that anyone who has finished Caculus Demystified will be prepared for this book. Unfortunately by page fifteen he is using concepts from multivariable calculus (partial derivatives) that, if I’m not mistaken, were not covered in Calculus Demystified. Unless you are confident in your mathematical skills I would recommend brushing up your multivariable calculus before tackling this text.For the most part, however, the book proceeds in typical fashion. The reader will be introduced to most of the key topics covered in a typical college Diff Eq class including first and second order differential equations, series solutions, and other basic topics. If you’re just looking to get the “flavor” of Diff. Eqs then this book will suffice. However, do not expect to come away from this book with a deep knowledge of the subject matter. He concisely covers most of the basic procedures for solving and manipulating standard ordinary differential equations, and doesn’t bog the reader down in much theory. Answers are provided in the back of the book for most of the problems in each chapter.However, for readers who want a more thorough introductory look at applied differential equations I know of no better introduction than Tenenbaum’s Ordinary Differential Equations. Tenenbaum does an excellent job of introducing the theory behind the equations and covers many of the fine details that Krantz leaves out. Another strength of Tenenbaum is his resistance to undue formalism. He takes the time to flesh out the motivation behind each topic with historical asides and physical applications. Krantz does not do this. Seeing as both books are selling for the roughly the same price […] I see little justification in recommending this work over Tenenbaum’s. The only circumstance under which I would recommend Krantz is to the reader who needs a concise and breezy introduction to the methods of Differential Equations. For deeper understanding consult Tenenbaum. And if you are looking for a source for solved practice problems I would direct you to Differential Equations Prolem Solver which has thousands of solved problems.Overall, a solid, concise effort. But when compared to other books in its league like “Calculus for Dummies” and “How to Ace Calculus” it falls a bit short.PS: For a great informal brush up on Multivariable caclus I recommend “How to Ace the rest of Caculus”.

⭐We ordered this for my son who is an engineering undergraduate. His professor has a thick accent and instruction is unclear. My son has found this book very helpful in addition to Khan Academy.

⭐This is a fine book for refreshing one’s math skills. I use it to help me tutor college students. It’s easy to read and has many step-by-step examples.

⭐I chose to acquire this book after I had perused through the first few lines of the first chapter. I felt, immediately, that the author knew his “stuff” and how to deploy his skill. I was not disappointed.

⭐The Kindle version of this book is what Kindle editions of math books should be. It does not have the Kindle font size nonsense which does not work on equations. Instead you can zoom in or out like a PDF document. It took more time and money to create this edition. But it is well worth it. A job well done.

⭐I loved the first chapter but am trying to push my way through the second. I believe I am struggling because I am teaching myself mechanics and mechatronics. I mean no disrespect to the author. When the light bulb turns on, I will probably say the concepts were very accurate.

⭐I got this to help with comprehension it does a good job translating the concepts from mathinese to English very easy to follow without the pretentiousness that comes from mathematicians who forget they teaching

⭐The author makes it quite clear from the start that familiarity with calculus is essential to fully understand the material in the book, and rightfully so. Most undergraduate courses that cover differential equations require the student be erudite with calculus and its applications prior to embarking on this important topic. having stated that, it is presupposed that readers are also familiar with the topics of trigmometry, limits, power series to name but a few. In short this is not a beginners text with little more than GCSE math. It is ideal for supporting an undergraduate course for a first degree or diploma. There are plenty of exercises, with solutions, and a final “Exam” , or questions that cover the whole book. It is written in a clear style not overly rigorous, so mathematicians may squirm at this. However, the author takes care to provide practical examples from Physics and Engineering to enable to topic to be appreciated. I would fully recommend this text to anyone who is embarking on a first degree in the physical sciences or for a revision text for those who have previously studied this topic.

⭐I bought this book to help me in my studies for a mechatronics engineering course. Having been a while since I covered differential equations I needed some extra text to help. This book is very detailed but in a manageable way. It explains the course I studied very well.

⭐Esto no es una reseña del libro, más bien una queja del mal estado en que llegó. Es la primera vez que me sucede con Amazon y es decepcionante. Dejo fotos del libro.molto utile

⭐

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