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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.
- Sales Rank: #53775 in Books
- Published on: 2014-08-28
- Released on: 2014-08-28
- Original language: English
- Number of items: 1
- Dimensions: 9.26" h x 1.03" w x 6.11" l, .0 pounds
- Binding: Paperback
- 412 pages
Review
“The main purpose of the author is not to calculate specific integrals and obtain specific answers, but to present several tricks and methods which are used to obtain those answers. … The book is published in the series Undergraduate Lecture Notes in Physics and it will probably be physicists and students of physics who will be the majority of its readers. … mathematicians also may find many interesting things there.” (Krzysztof Ciesielski, Mathematical Reviews, July, 2015)
From the Back Cover
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.
About the Author
Paul Nahin was born in California, and did all of his schooling there (Brea-Olinda High 1958, Stanford BS 1962, Caltech MS 1963 and - as a Howard Hughes Staff Doctoral Fellow - UC/Irvine PhD 1972, with all degrees in electrical engineering). He has taught at Harvey Mudd College, the Naval Postgraduate School and the Universities of New Hampshire (where he is now emeritus professor of electrical engineering) and Virginia.
Prof. Nahin has published a couple of dozen short science fiction stories in ANALOG, OMNI and TWILIGHT ZONE magazines, and has written 14 books on mathematics and physics. He has given invited talks on mathematics at Bowdoin College, the Claremont Graduate School, the University of Tennessee and Caltech, has appeared on National Public Radio's "Science Friday" show (discussing time travel) as well as on New Hampshire Public Radio's "The Front Porch" show (discussing imaginary numbers) and advised Boston's WGBH Public Television's "Nova" program on the script for their time travel episode. He gave the invited Sampson Lectures for 2011 in Mathematics at Bates College (Lewiston, Maine).
Most helpful customer reviews
56 of 56 people found the following review helpful.
Book is a "Must Have" for scientists and engineers
By Robert William Hosken
This book is very unusual. It reads like a novel but every engineer and researcher should consider having it at arm's reach. The coverage of integrals is not that of a mathematician but that of a person calculating in the trenches. Rigor is not the focus but wide coverage and great utility is. Riemann and Lebesgue integrals are both defined, but the latter is quickly dismissed as not being important to his readers.
Nahin treats almost all of the areas of science and engineering where integrals arise. The book can easily be used a reference by jumping in at a topic one needs to work on now. In a short time the reader is able to be functional in an analysis at hand. Every step of each method is shown. There are Challenge Problems at the end of every chapter with solutions in the back of the book.
Mathematical niceties such as convergence, singularities, and interchange of integration order are noted but set aside until the end of each method. Then numerical check cases are calculated in Matlab to determine if there has been a problem along the way. The reader can of use Mathematica or Wolfram Alpha if that is suitable.
This book is not littered with gratuitous pictures of mathematicians with a brief caption. Instead there are copious references that discuss how early practitioners solved an integral and comparisons of different approaches. The contributions of GH Hardy and Richard Feynman occur throughout the book.
Knowledge of complex arithmetic and basic calculus are assumed at the beginning. At the next to last chapter Contour Integration is covered with a theoretical introduction.
11 of 11 people found the following review helpful.
A wonderfully unique book on integrals
By LegionOnomaMoi
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.
15 of 16 people found the following review helpful.
The book is wonderful in its depth and variety of proof techniques
By Gary Kenosha
The book is wonderful in its depth and variety of proof techniques. It is also a plus that the proofs are step-by-step exercises in achieving the results. It is a genuine blend of the application and the art of problem solving coupled with historical perspective.
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