Inside Interesting Integrals: A Collection of Sneaky Tricks, Sly Substitutions, and Numerous Other Stupendously Clever, Awesomely Wicked, and ... (Undergraduate Lecture Notes in Physics)

What is one to make of a book on how to do the trickier integrals? I spent hundreds of hours learning such things in my youth (at Cambridge University in the late 1960s), but what is the point today? Mathematica and similar software is still much better, certainly much faster, than I am. Part of the reason is easily discovered by playing with MSE for a while (math.stackexchange.com for the uninitiated). Jack d'Aurizio is much better than Mathematica, whilst countless students struggle to figure out what on earth is going on and could clearly make little effective use of Mathematica. Nonetheless, Paul Nahin goes rather further than they need and certainly far further than most of them would want. There is also the question of how his book compares with: (1) Irresistible Integrals; or (2) a more straightforward presentation of integration such as one might find in any number of standard textbooks; or (3) with some of the more specialised presentations such as the books on geometric algebra or (my favourite) Shilov & Gurevich Integral, Measure and Derivative. I bought Irresistible Integrals first and will try to review it separately. It is misleading. It states prominently in the Preface that "the original idea was ... to write a text in which we would prove eveery formula in Table of Integrals, Series and Products by Gradshteyn & Rhyzik (the standard reference work from the era before math software became ubiquitous, and still useful). Actually, it presents a rather laid-back collection of useful techniques with much emphasis on using Mathematica for "exploration". The dunces on MSE would find it much easier going than Nahin's book. They would also dislike Nahin because he generally does not bother to state the obvious. Exactly how some technique can be justified, well those boring details are for you to fill in. By the same token there is little overlap between Nahin and the typical College text. He assumes you already know how integrals are defined, and have met (or can easily figure out for yourself) standard properties like linearity. (3) proceed in a quite different direction exploring different ways of defining the integral to achieve greater generality or simplicity. So both Nahin and (3) are excellent supplementary material for the better student. I like Nahin's style. Not all his books work equally well (I discovered him last year and have been busy acquiring his oeuvre). This is one of the best. Absolutely brilliant.

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.

Vastly entertaining for and old-timer like me or anyone with with A-level maths or !st year university math/physics and a reasonable curiosity. Takes me back to my undergraduate struggles and makes me wish I had been ale to read it then (50 years ago!)

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.

An excellent book capable of being read cover to cover, or opened at a random page, with enjoyment in either case. It's a very accessible book, full of many classic trick for unlocking difficult integrals.

A very interesting book for maths teachers (and lecturers) to help broaden your own outlook on school- and college-level calculus.

„Differenzieren ist Handwerk, Integrieren ist Kunst“ ist eine der Spruchweisheiten, aus einer Zeit da Analysis noch 'Höhere Mathematik' genannt wurde – in diesem Sinne ist das vorliegende Buch von Paul J. Nahin, emeritierter Professor für Electrical Engineering an der Universität von New Hamshire, eine Sammlung von exzellenten Kunstwerken. Wie der Untertitel nahelegt, handelt es sich um eine Kollektion raffinierter Tricks, listiger Substitutionen, und vielfältiger anderer erstaunlich verführerischer Manöver zur Brechung von fast 200 bestimmten Integralen aus Physik, Engineering und Mathematik, nebst 60 anspruchsvollen Problem mit vollständigen und ausführlichen Lösungen – in Anhang. Darunter findet sich auch ein Kapitel über Differentiation unter dem Integral; einem der Lieblingstricks von Richard Feynman, wie dieser in seinen autobiographischen Schriften 'preisgibt'; damit brillierte Feynman bereits während seines Studiums am MIT, und diese Fähigkeit, Integrale zu 'knacken', vor denen andere schon längst kapituliert hatten, wurde zu einem Handwerkzeug, mit dem er immer wieder meisterlich bei der Ausarbeitung der QED jonglierte. Der Autor beschränkt sich auf bestimmte Integrale und führt gleich in Einleitungskapitel ein Beispiel für ein bestimmtes Integral an, das keine Stammfunktion (aus Standardfunktionen) besitzt, das aber – mit einem Symmetrisierungs- Trick – berechenbar ist. Allen Beispielen ist gemeinsam, dass sie auf den ersten Blick, viele davon auch auf dem zweiten, 'untrckable' erscheinen – aber nach einer geschickten Umformung, oder einer indirekten Betrachtung, zeigt sich dann doch ein Weg. Der Autor hat das Material aus einer großen Zahl von Originalarbeiten zusammengetragen und wunderschön aufbereitet, leider fehlt eine ebenso übersichtliche Bibliographie, die Referenzen sind auf diversen Fußnoten verteilt. Das Buch will dabei den üblichen 'Integaltafeln' keine Konkurrenz machen, hier geht es nicht in erster Linie um den Wert eines bestimmten Integrals, sondern vor allem um den – mitunter verschlungenen – Weg, die Lösung aufzufinden; Vorkenntnisse sind kaum gefordert – von eine üblichen Einführungskurs Calculus (Analysis) natürlich abgesehen – in der Einführung werden nochmal die wichtigsten Fakten zusammengestellt.

A brilliant book with interesting integral tricks!

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.

Got the item as requested, and in timely manner. No complaints whatsoever. Flawless experience.

Self-pleasing author, as they come in Britain