Inside Interesting Integrals: A Collection of Sneaky Tricks, Sly Substitutions, and Numerous Other Stupendously Clever, Awesomely Wicked, and Devilishly … (Undergraduate Lecture Notes in Physics) 2015th Edition by Paul J. Nahin (PDF)

Description

What’s the point of calculating definite integrals since you can’t possibly do them all?.What makes doing the specific integrals in this book of value aren’t the specific answers we’ll obtain, but rather the methods we’ll use in obtaining those answers; methods you can use for evaluating the integrals you will encounter in the future.This book is written in a light-hearted manner for students who have completed the first year of college or high school AP calculus and have just a bit of exposure to the concept of a differential equation. Every result is fully derived. If you are fascinated by definite integrals, then this is a book for you.

User’s Reviews

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

⭐I like all of Paul Nahin’s math books but this one is on the top of the list. It contains material you won’t find anywhere else all together. The book is about evaluating definite integrals. I found it easy to understand. You need to know calculus and be proficient at algebraic manipulation. Some knowledge of Complex Analysis is helpful. If you aren’t ready for this start with An Imaginary Tale which is great then graduate to Dr. Euler’s Fabulous Formula. On the other hand if this is easy for you try (Almost) Impossible Integrals, Sums, and Series by Cornel Valean. If you want to learn calculus start with Yet Another Introduction to Analysis by Victor Bryant, a great book. If you want to learn Complex Analysis try Complex Analysis by Dennis Zill and Patrick Shanahan, it’s easy to understand. Finally, if you are into stuff like this look at Pi and the AGM by the Borwein brothers.

⭐I created and teach a class in Fourier Theory for an industrial firm. As one knows, the topic requires a substantial amount of integration. Integration is fun. Each integral is a puzzle. Well Nahin created a whole new level of fun. The techniques for solving integrals are rarely taught. Once you begin reading and working the problems, the reader learns new ways of solving many fascinating integral forms. As you move along, the author builds and builds again on techniques he taught in a earlier chapter to take you down another ” Yellow Brick Road”. This book is meant for people that enjoy integral calculus – Enjoy.

⭐Nahin’s book on integrals is certainly not the only book aimed for undergraduates and devoted to integration. It is, however, unique in its down-to-earth, applied treatment of integration. Other texts of comparable levels of mathematical sophistication tend to be oriented towards transitioning students from the rote, mechanical treatment of calculus problems to the deeper understanding acquired in courses on real analysis. For this reason, they invariably spend a fair amount of time on topics like measure theory, the Lebesgue integral, rigor (both in presentation and exercises), and similar content that greatly benefits the undergraduate majoring in mathematics but is of little or no use to engineers, computer scientists, and others who intend to go on to more applied fields. Nor his Nahin’s book simply a more thorough treatment of methods to find antiderivatives, of numerical integration, or in general the kind of extended nature of most books on integration that are intended for non-mathematics majors.Instead, it is an exquisitely idiosyncratic presentation of integration that provides a both deeper understanding while remaining thoroughly applied in orientation and a way, or set of ways, to problem-solving that is not at all an extension of methods learned in typical calculus courses. In short, it provides a look inside integrals- as promised.

⭐Very interesting book! The books says the target audience is undergraduates as well as professionals looking for a good technical read. I am a professional programmer with a master’s in mathematics and I really enjoyed the book, learned alot. The material is sufficiently interesting for those with a background in analysis, and accessible enough for undergraduates with Calculus 2 under their belts.

⭐Anything Paul Nahin writes I buy. He is always excellent. Many many years of teaching experience shows in his presentation and writing. I pirate his stuff all the time when I teach.

⭐If you are stuck on an island or at home in the rain, this little volume will entertain anyone interested in solving intriguing calculus problems. Nicely done.

⭐The material in the book is excellent and well presented. For those interested in solutions to a wide range of integrals, the book is will serve as a first rate reference.

⭐What an awesome book and great author. Still studying and have been working in it for 5 months. I understand power series summation from long division and e topics, among LN operation, and trig uses in calculus. Many amazing approaches and tips. Thank you Paul.

⭐This book is written in a jolly style with lots of different techniques (“tricks” as the author calls them) to help evaluate some scary looking definite integrals. I think this book is a great place for anyone to start who wants to appreciate mathematics, and as a basis for various branches of physics as well as an analytical number theory. It is a very entertaining book, deliberately in the manner that anyone who finds mathematical problems entertaining (when an insight might come or it might not). As someone who remembers many criminally dull mathematics books at university (which I will leave unmentioned here), this book helps put the magic back into mathematics.

⭐A hugely enjoyable book. I have been working through the examples and questions and thoroughly enjoying it. The only, minor, thing that lets it down is the somewhat ugly formatting of the formulae. I can’t help thinking it would have been better to have typeset it in TeX. I also found the numerical checks using Matlab to be redundant – having proved an integral mathematically I couldn’t see the point of then doing a check with a numerical calculation. But what a great mathematical exposition!

⭐An interesting book that I’m enjoying reading. It’s always a pleasure to see a clever maths trick, and this book is packed with them. Nahin’s books are always a good read, and this one is no exception. Anyone who likes their maths books full of equations will appreciate this book.

⭐This book covers a topic that I think is poorly handled else where; at in many cases not at all; differentiation under the integral, which is a beautiful and power approach to many ‘interesting’ integral solutions.

⭐Love watching black pen red pen on youtube so thought get a book on integrals but some of these really hard but good to read when i need a bit of mental stimulation

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