Mrs. Perkins’s Electric Quilt: And Other Intriguing Stories of Mathematical Physics by Paul J. Nahin (PDF)

Description

An incomparable collection of stimulating math puzzles from bestselling author Paul NahinWhat does quilting have to do with electric circuit theory? The answer is just one of the fascinating ways that best-selling popular math writer Paul Nahin illustrates the deep interplay of math and physics in the world around us in his latest book of challenging mathematical puzzles, Mrs. Perkins’s Electric Quilt. With his trademark combination of intriguing mathematical problems and the historical anecdotes surrounding them, Nahin invites readers on an exciting and informative exploration of some of the many ways math and physics combine to create something vastly more powerful, useful, and interesting than either is by itself.In a series of brief and largely self-contained chapters, Nahin discusses a wide range of topics in which math and physics are mutually dependent and mutually illuminating, from Newtonian gravity and Newton’s laws of mechanics to ballistics, air drag, and electricity. The mathematical subjects range from algebra, trigonometry, geometry, and calculus to differential equations, Fourier series, and theoretical and Monte Carlo probability. Each chapter includes problems—some three dozen in all—that challenge readers to try their hand at applying what they have learned. Just as in his other books of mathematical puzzles, Nahin discusses the historical background of each problem, gives many examples, includes MATLAB codes, and provides complete and detailed solutions at the end.Mrs. Perkins’s Electric Quilt will appeal to students interested in new math and physics applications, teachers looking for unusual examples to use in class—and anyone who enjoys popular math books.

User’s Reviews

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

⭐I have now read six of Paul Nahin’s books and enjoyed them all. The one difference with this book is perhaps that it dosn’t have a single underlying theme other then being a collection of very interesting problems in basic physics. They were all good but the first chapter hooked me: what is the position after five seconds of a particle with an applied force of kx**2? Sound trivial? It sure surprised me. In solving these problems he provides a perfect mix of math, physics, history, and anecdotes. As for prerequisites, a familiarity but not expertise with calculus and high school physics should be sufficient. By the way, another author very similar in style (except more towards theoretical than applied math) is John Derbyshire. Both gentlemen remind me of that one professor who could make any lecture so interesting that you were sad when the class ended.

⭐If you have, or a student has, any interest in mathematics in itself or related to other areas, read anything Paul Nahin writes. I have found each of his books full of wonderful surprises. He almost always fills in all the detail a reader needs but also makes you think about it [meaning and solution] instead of just laying out the final answers. He makes you think, not only about what the particular ‘case’ is but how similar problems can be attached and even how to “know what to do when you don’t know what to do”—which is the best definition of genius that I’ve heard.I think the only writer I can think of who has his skill, in the last 20 years, was Ian Stewart.

⭐Has many interesting topics

⭐I have many books written by Paul Nahin and every one is a gem. He is a phenomenal writer and every topic was clearly explained. I wish I had taken one of his electrical engineering classes.

⭐I have purchased several books by the author but havealways purchased paper versions. I thought I’d try this one on Kindle 3.Big mistake! The equations are blurry and petty much illegible.The equations must be images and when enlarged become more unreadable!I guess I’ll go back to paper books for readability.

⭐An enjoyable trip through some fun physics problems! There is some overlap with Nahin’s book In Praise of Simple Physics, but the analysis remains fun and conversational. You get to see how even very simple physics problems can have surprising connections (Mrs. Perkin’s Quilt is related to circuit diagrams, for example). It covers a good variety of problems with a focus on a combination of math and physics rather than just one or the other being preeminent in solving problems. It covers gravity, circuits, air drag/ballistics, and random walks. Each chapter is self-contained (though it is definitely helpful to go through in order), and the problems are worked out in full detail with challenge problems that have solutions at the back of the book.I quite enjoy this type of thing, and often learn interesting or clever ways of solving problems that seem extremely difficult at first. You get to see how to be creative in looking at problems and how problems in one domain can translate into others. You will need to understand calculus and all prerequisites in order to follow the book, however. If you have a weak math background, this will be a struggle.

⭐My only regret about buying this book is that I didn’t do so sooner. I’m still reading it, but very much enjoying what I’ve read so far. Nahin never disappoints. I particularly liked the comment about viscosity: “if you can see it, and see it moving then it’s a v-squared rule”. This certainly makes me wonder about the accuracy of all those high school physics books and their Stoke’s Law experiments.

⭐Paul J. Nahin is a retired professor of Electrical Engineering with more than a casual interest in Math & Physics. Being trained as a student in the 60es by some of the proverbial “rocket scientists” he does not shy away from cumbersome derivations, embarrassing quizzes, and “impossible” integrals. So he is the right person to present this collection of excursions into Mathematical Physics. Both the Preface and First Chapter of Nahin’s book make it clear that the reader should be mathematically educated to what would be as of recent a second year proficiency in calculus. This is especially true for most of the 35+ challenge problems contained in this book, so it is good, that one can resort to extensive solutions for all.Nahin starts with two kinematic problems in which he illustrates that Math goes wrong, when either an unphysical law is used or the right one from dynamics is not observed. Actually most of the book (nine out of 18 chapters) is on gravity and movements with and without air drag. For the latter topics Nahin states, solves, and discusses most all of the relevant differential equations, and points out the relevance to historic free fall experiments, sports and high-speed atmospheric entry. I was not aware, that there is a closed and (almost) analytic solution for a long fall through an atmosphere following the barometric law involving a certain special function, the exponential integral Ei(x). The stratospheric supersonic jumps happened too late to be included in the 2009 edition of Nahin’s book, howeverThe title of this book comes alive in Chapter 3, in which the author discusses some linearly infinite networks of resistances and reactances, which were once solved by the great physicist Richard Feynman, although he escaped failure only by the intuition of a genius. The real quilting then starts in Chapter 13 after a discussion of the geometrical puzzle of tiling rectangles by all-different squares. Nahin “electrifies” these quilts by replacing each square regardless of its size with a 1-ohm resistor, the network of which nevertheless divides the current between any pair of sidewise terminals proportional to the areas of said tiling. The task to calculate resistances of complicated networks reappears in a later chapter, with Nahin showing that they can be solved by a Monte Carlo simulation of the random walks of a multitude of charge carriers. Before this, Nahin whets the readers’ appetite with historic examples of random walks from epidemiology, gambling and Victorian riddles to Brownian motion and derives probability density functions and geometrical probabilities for quite a few of these problems. He also provides Matlab code for readers inclined to further study similar problems, whereas non-programmers will feel excluded.As a break from the more fully developed subjects, the reader is offered chapters on the zeta function, nearest neighbor problems, a noise-focusing supersonic flight path and a bonus discussion of resistor networks in the fourth dimension.All in all this book, which is type-set and printed in an unobtrusive and eye-friendly way, is very much recommended for any math aficionado, although sometimes hard to read, because it comes over in places as a somewhat haphazard collection of subjects, not all of which have a link to real-world physics, this way lacking the coherence of the author’s more mathematical books.

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