In Praise of Simple Physics

The Science and Mathematics behind Everyday Questions

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 1400880513

Category: Science

Page: 272

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Physics can explain many of the things that we commonly encounter. It can tell us why the night is dark, what causes the tides, and even how best to catch a baseball. With In Praise of Simple Physics, popular math and science writer Paul Nahin presents a plethora of situations that explore the science and math behind the wonders of everyday life. Roaming through a diverse range of puzzles, he illustrates how physics shows us ways to wring more energy from renewable sources, to measure the gravity in our car garages, to figure out which of three light switches in the basement controls the light bulb in the attic, and much, much more. How fast can you travel from London to Paris? How do scientists calculate the energy of an atomic bomb explosion? How do you kick a football so it stays in the air and goes a long way downfield? Nahin begins with simpler problems and progresses to more challenging questions, and his entertaining, accessible, and scientifically and mathematically informed explanations are all punctuated by his trademark humor. Readers are presumed to have some background in beginning differential and integral calculus. Whether you simply have a personal interest in physics' influence in the world or you're an engineering and science student who wants to gain more physics know-how, this book has an intriguing scenario for you. In Praise of Simple Physics proves that if we look carefully at the world around us, physics has answers for the most astonishing day-to-day occurrences.

Digital Dice

Computational Solutions to Practical Probability Problems

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 1400846110

Category: Mathematics

Page: 288

View: 2083

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Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations. Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the odds of coin-flipping games to figuring out the behavior of elevators. Problems build from relatively easy (deciding whether a dishwasher who breaks most of the dishes at a restaurant during a given week is clumsy or just the victim of randomness) to the very difficult (tackling branching processes of the kind that had to be solved by Manhattan Project mathematician Stanislaw Ulam). In his characteristic style, Nahin brings the problems to life with interesting and odd historical anecdotes. Readers learn, for example, not just how to determine the optimal stopping point in any selection process but that astronomer Johannes Kepler selected his second wife by interviewing eleven women. The book shows readers how to write elementary computer codes using any common programming language, and provides solutions and line-by-line walk-throughs of a MATLAB code for each problem. Digital Dice will appeal to anyone who enjoys popular math or computer science. In a new preface, Nahin wittily addresses some of the responses he received to the first edition.

Duelling Idiots and Other Probability Puzzlers

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 1400843049

Category: Mathematics

Page: 304

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What are your chances of dying on your next flight, being called for jury duty, or winning the lottery? We all encounter probability problems in our everyday lives. In this collection of twenty-one puzzles, Paul Nahin challenges us to think creatively about the laws of probability as they apply in playful, sometimes deceptive, ways to a fascinating array of speculative situations. Games of Russian roulette, problems involving the accumulation of insects on flypaper, and strategies for determining the odds of the underdog winning the World Series all reveal intriguing dimensions to the workings of probability. Over the years, Nahin, a veteran writer and teacher of the subject, has collected these and other favorite puzzles designed to instruct and entertain math enthusiasts of all backgrounds. If idiots A and B alternately take aim at each other with a six-shot revolver containing one bullet, what is the probability idiot A will win? What are the chances it will snow on your birthday in any given year? How can researchers use coin flipping and the laws of probability to obtain honest answers to embarrassing survey questions? The solutions are presented here in detail, and many contain a profound element of surprise. And some puzzles are beautiful illustrations of basic mathematical concepts: "The Blind Spider and the Fly," for example, is a clever variation of a "random walk" problem, and "Duelling Idiots" and "The Underdog and the World Series" are straightforward introductions to binomial distributions. Written in an informal way and containing a plethora of interesting historical material, Duelling Idiots is ideal for those who are fascinated by mathematics and the role it plays in everyday life and in our imaginations.

Mrs. Perkins's Electric Quilt

And Other Intriguing Stories of Mathematical Physics

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 9781400833467

Category: Mathematics

Page: 424

View: 5573

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What 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.

Number-Crunching

Taming Unruly Computational Problems from Mathematical Physics to Science Fiction

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 9781400839582

Category: Mathematics

Page: 408

View: 4446

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How do technicians repair broken communications cables at the bottom of the ocean without actually seeing them? What's the likelihood of plucking a needle out of a haystack the size of the Earth? And is it possible to use computers to create a universal library of everything ever written or every photo ever taken? These are just some of the intriguing questions that best-selling popular math writer Paul Nahin tackles in Number-Crunching. Through brilliant math ideas and entertaining stories, Nahin demonstrates how odd and unusual math problems can be solved by bringing together basic physics ideas and today's powerful computers. Some of the outcomes discussed are so counterintuitive they will leave readers astonished. Nahin looks at how the art of number-crunching has changed since the advent of computers, and how high-speed technology helps to solve fascinating conundrums such as the three-body, Monte Carlo, leapfrog, and gambler's ruin problems. Along the way, Nahin traverses topics that include algebra, trigonometry, geometry, calculus, number theory, differential equations, Fourier series, electronics, and computers in science fiction. He gives historical background for the problems presented, offers many examples and numerous challenges, supplies MATLAB codes for all the theories discussed, and includes detailed and complete solutions. Exploring the intimate relationship between mathematics, physics, and the tremendous power of modern computers, Number-Crunching will appeal to anyone interested in understanding how these three important fields join forces to solve today's thorniest puzzles.

Time Machines

Time Travel in Physics, Metaphysics, and Science Fiction

Author: Paul J. Nahin

Publisher: Springer Science & Business Media

ISBN: 9780387985718

Category: Literary Criticism

Page: 628

View: 6882

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Time Machines takes you on an exhilarating journey through the intriguing theories of scientists and the far-flung imaginations of writers. It explores the ideas of time travel from the first account in English literature to the latest theories of physicists such as Kip Thorne and Igor Novikov. This very readable work covers a variety of topics including the history of time travel in fiction; the fundamental scientific concepts of time, spacetime, and the fourth dimension; the speculations of Einstein, Richard Feynman, Kurt Gödel, and others; time travel paradoxes, and much more. For anyone who shares a fascination with time travel, Time Machines is an engrossing study of what writers have imagined and what scientists may some day make possible. "Here's a gem of a book...all peppered with delightful notes...I can't turn a page without finding a jewel."Clifford Stoll, University of California, Berkeley, author of "The Cuckoo's Egg""...I have been struck by the richness and complexity of the tapestry of ideas that Nahin presents...may well remain the most readable and complete treatise on time travel in science and science fiction." Kip S. Thorne, The Feynman Professor of Theoretical Physics, California Institute of Technology"if, like me, you are a child at heart, the real fun lies in the zany stories and wild speculations" Physics World

The Science of Radio.

With Matlab and Electronics Workbench Demonstration, 2nd edition

Author: Paul J. Nahin

Publisher: Springer Science & Business Media

ISBN: 9780387951508

Category: Computers

Page: 466

View: 6431

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The Science of Radio explains the working and charts the development of the ordinary AM radio receiver, which has become an integral part of our lives in the 80 years since its invention. As well as showing the reader the growth of technology in this century, the story of AM radio can provide a unique insight into the basics of electrical engineering, making the primary concepts and applications visual and comprehensible. Taking a "top down" approach to the subject, Nahin starts with a broad overview of radio as a sociological and technological phenomenon, then describes specific advances in research that made radio possible, moving through deeper levels of technical detail as the story progresses. Readers will see how various concepts and theories are combined to achieve specific practical results. And the book's "just in time" method of introducing mathematical and physical theory only as needed to understand a topic, helps readers gain a firm grasp of often elusive material. By focusing specifically on the workings of AM radio, The Science of Radio offers both a fascinating history of radio as an information and entertainment medium and a practical, applications-oriented introduction to electrical engineering. This second edition, written the same witty and accessible style as the first, also includes illustrative examples based on the popular MATLAB and Electronics Workbench programs now commonly used in engineering courses, as well as new technical material on differential amplifiers, more end-of-chapters problems, and additional historical discussion. About the author Paul J. Nahin is Professor of Electrical Engineering at the University of New Hampshire, and is the author of Oliver Heaviside: Sage In Solitude (IEEE Press); Time Machines: Time Travel In Physics, Metaphysics And Science Fiction, (AIP Press); and An Imaginary Tale; The Story Of The Square Root Of Minus One, (Princeton University Press).

When Least Is Best

How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 1400841364

Category: Mathematics

Page: 392

View: 3155

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What is the best way to photograph a speeding bullet? Why does light move through glass in the least amount of time possible? How can lost hikers find their way out of a forest? What will rainbows look like in the future? Why do soap bubbles have a shape that gives them the least area? By combining the mathematical history of extrema with contemporary examples, Paul J. Nahin answers these intriguing questions and more in this engaging and witty volume. He shows how life often works at the extremes--with values becoming as small (or as large) as possible--and how mathematicians over the centuries have struggled to calculate these problems of minima and maxima. From medieval writings to the development of modern calculus to the current field of optimization, Nahin tells the story of Dido's problem, Fermat and Descartes, Torricelli, Bishop Berkeley, Goldschmidt, and more. Along the way, he explores how to build the shortest bridge possible between two towns, how to shop for garbage bags, how to vary speed during a race, and how to make the perfect basketball shot. Written in a conversational tone and requiring only an early undergraduate level of mathematical knowledge, When Least Is Best is full of fascinating examples and ready-to-try-at-home experiments. This is the first book on optimization written for a wide audience, and math enthusiasts of all backgrounds will delight in its lively topics.

The Logician and the Engineer

How George Boole and Claude Shannon Created the Information Age

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 0691151008

Category: Computers

Page: 228

View: 1601

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Examines how mathematician and philosopher George Boole and electrical engineer Claude Shannon became the fathers of the information age by advancing Boolean logic, and looks at the influence of other factors, including the Turing machine.

Inside Interesting Integrals

A Collection of Sneaky Tricks, Sly Substitutions, and Numerous Other Stupendously Clever, Awesomely Wicked, and Devilishly Seductive Maneuvers for Computing Nearly 200 Perplexing Definite Integrals From Physics, Engineering, and Mathematics (Plus 60 Challenge Problems with Complete, Detailed Solutions)

Author: Paul J. Nahin

Publisher: Springer

ISBN: 1493912771

Category: Science

Page: 412

View: 5220

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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.

How to Fall Slower Than Gravity

And Other Everyday (and Not So Everyday) Uses of Mathematics and Physical Reasoning

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 0691185026

Category: Mathematics

Page: N.A

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An engaging collection of intriguing problems that shows you how to think like a mathematical physicist Paul Nahin is a master at explaining odd phenomena through straightforward mathematics. In this collection of twenty-six intriguing problems, he explores how mathematical physicists think. Always entertaining, the problems range from ancient catapult conundrums to the puzzling physics of a very peculiar kind of glass called NASTYGLASS—and from dodging trucks to why raindrops fall slower than the rate of gravity. The questions raised may seem impossible to answer at first and may require an unexpected twist in reasoning, but sometimes their solutions are surprisingly simple. Nahin’s goal, however, is always to guide readers—who will need only to have studied advanced high school math and physics—in expanding their mathematical thinking to make sense of the curiosities of the physical world. The problems are in the first part of the book and the solutions are in the second, so that readers may challenge themselves to solve the questions on their own before looking at the explanations. The problems show how mathematics—including algebra, trigonometry, geometry, and calculus—can be united with physical laws to solve both real and theoretical problems. Historical anecdotes woven throughout the book bring alive the circumstances and people involved in some amazing discoveries and achievements. More than a puzzle book, this work will immerse you in the delights of scientific history while honing your math skills.

Oliver Heaviside

The Life, Work, and Times of an Electrical Genius of the Victorian Age

Author: Paul J. Nahin

Publisher: JHU Press

ISBN: 9780801869099

Category: Biography & Autobiography

Page: 318

View: 1288

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"A good book by a careful, historically minded engineer... A lively, informative narrative of Heaviside's life and work. Nahin has exhaustively resurveyed archives and contemporary sources and is very much at home in historical discussions of Victorian physics." -- Isis

Burn Math Class

And Reinvent Mathematics for Yourself

Author: Jason Wilkes

Publisher: Basic Books

ISBN: 0465073816

Category: Mathematics

Page: 400

View: 2055

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Forget everything you’ve been taught about math. In Burn Math Class, Jason Wilkes takes the traditional approach to mathematics education—with its unwelcoming textbooks, unexplained rules, and authoritarian assertions—and sets it on fire. Focusing on how mathematics is created rather than on mathematical facts, Wilkes teaches the subject in a way that requires no memorization and no prior knowledge beyond addition and multiplication. From these simple foundations, Burn Math Class shows how mathematics can be (re)invented from scratch without preexisting textbooks and courses. We can discover math on our own through experimentation and failure, without appealing to any outside authority. When math is created free from arcane notations and pretentious jargon that hide the simplicity of mathematical concepts, it can be understood organically—and it becomes fun! Following this unconventional approach, Burn Math Class leads the reader from the basics of elementary arithmetic to various “advanced” topics, such as time-dilation in special relativity, Taylor series, and calculus in infinite-dimensional spaces. Along the way, Wilkes argues that orthodox mathematics education has been teaching the subject backward: calculus belongs before many of its so-called prerequisites, and those prerequisites cannot be fully understood without calculus. Like the smartest, craziest teacher you’ve ever had, Wilkes guides you on an adventure in mathematical creation that will radically change the way you think about math. Revealing the beauty and simplicity of this timeless subject, Burn Math Class turns everything that seems difficult about mathematics upside down and sideways until you understand just how easy math can be.

Storm in a Teacup: The Physics of Everyday Life

Author: Helen Czerski

Publisher: W. W. Norton & Company

ISBN: 0393248976

Category: Science

Page: 336

View: 7602

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“[Czerski’s] quest to enhance humanity’s everyday scientific literacy is timely and imperative.”—Science Storm in a Teacup is Helen Czerski’s lively, entertaining, and richly informed introduction to the world of physics. Czerski provides the tools to alter the way we see everything around us by linking ordinary objects and occurrences, like popcorn popping, coffee stains, and fridge magnets, to big ideas like climate change, the energy crisis, or innovative medical testing. She provides answers to vexing questions: How do ducks keep their feet warm when walking on ice? Why does it take so long for ketchup to come out of a bottle? Why does milk, when added to tea, look like billowing storm clouds? In an engaging voice at once warm and witty, Czerski shares her stunning breadth of knowledge to lift the veil of familiarity from the ordinary.

Dr. Euler's Fabulous Formula

Cures Many Mathematical Ills

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 9781400838479

Category: Mathematics

Page: 416

View: 8149

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In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula—long regarded as the gold standard for mathematical beauty—and shows why it still lies at the heart of complex number theory. In some ways a sequel to Nahin's An Imaginary Tale, this book examines the many applications of complex numbers alongside intriguing stories from the history of mathematics. Dr. Euler's Fabulous Formula is accessible to any reader familiar with calculus and differential equations, and promises to inspire mathematicians for years to come.

Data Analysis for Scientists and Engineers

Author: Edward L. Robinson

Publisher: Princeton University Press

ISBN: 1400883067

Category: Science

Page: 408

View: 8544

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Data Analysis for Scientists and Engineers is a modern, graduate-level text on data analysis techniques for physical science and engineering students as well as working scientists and engineers. Edward Robinson emphasizes the principles behind various techniques so that practitioners can adapt them to their own problems, or develop new techniques when necessary. Robinson divides the book into three sections. The first section covers basic concepts in probability and includes a chapter on Monte Carlo methods with an extended discussion of Markov chain Monte Carlo sampling. The second section introduces statistics and then develops tools for fitting models to data, comparing and contrasting techniques from both frequentist and Bayesian perspectives. The final section is devoted to methods for analyzing sequences of data, such as correlation functions, periodograms, and image reconstruction. While it goes beyond elementary statistics, the text is self-contained and accessible to readers from a wide variety of backgrounds. Specialized mathematical topics are included in an appendix. Based on a graduate course on data analysis that the author has taught for many years, and couched in the looser, workaday language of scientists and engineers who wrestle directly with data, this book is ideal for courses on data analysis and a valuable resource for students, instructors, and practitioners in the physical sciences and engineering. In-depth discussion of data analysis for scientists and engineers Coverage of both frequentist and Bayesian approaches to data analysis Extensive look at analysis techniques for time-series data and images Detailed exploration of linear and nonlinear modeling of data Emphasis on error analysis Instructor's manual (available only to professors)

The Physics of Nascar

The Science Behind the Speed

Author: Diandra Leslie-Pelecky

Publisher: Penguin

ISBN: 1101213949

Category: Sports & Recreation

Page: 304

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A physicist explores the science of speed racing and the #1 spectator sport in America, with 75 million fans. Every NASCAR fan—at one time or another—asks the same question: Why isn’t my favorite driver winning? This is your chance to discover how much more there is to NASCAR than “Go fast, turn left and don’t crash.” If you’ve ever wondered why racecars don’t have mufflers, how “bump drafting” works, or what in the world “Let’s go up a pound on the right rear and add half a round of wedge” means, The Physics of NASCAR is for you. In this fast-paced investigation into the adrenaline-pumping world of NASCAR, a physicist with a passion uncovers what happens when the rubber hits the road and 800-horsepower vehicles compete at 190 miles per hour only inches from one another. Diandra Leslie-Pelecky reveals how and why drivers trust the engineering and science their teams literally build around them not only to get them across the finish line in first place, but also to keep them alive. Leslie-Pelecky is a physicist in love with the sport’s beauty and power and is uniquely qualified to explain exactly how physics translates into winning races. Based on the author’s extensive access to race shops, pit crews, crew chiefs and mechanics, this book traces the life cycle of a race car from behind the scenes at top race shops to the track. The Physics of NASCAR takes readers right into the ultra competitive world of NASCAR, from the champion driver’s hot seat behind the detachable steering wheel to the New Zealander nicknamed Kiwi in charge of shocks for the No. 19 car. Diandra Leslie-Pelecky tells her story in terms anyone who drives a car—and maybe occasionally looks under the hood--can understand. How do drivers walk away from serious crashes? How can two cars travel faster together than either car can on its own? How do you dress for a 1800°F gasoline fire? In simple yet detailed, high-octane prose, this is the ultimate thrill ride for armchair speed demons, auto science buffs, and NASCAR fans at every level of interest. Readers, start your engines.

The Mathematics of Secrets

Cryptography from Caesar Ciphers to Digital Encryption

Author: Joshua Holden

Publisher: Princeton University Press

ISBN: 0691184550

Category: Computers

Page: N.A

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The Mathematics of Secrets takes readers on a fascinating tour of the mathematics behind cryptography—the science of sending secret messages. Using a wide range of historical anecdotes and real-world examples, Joshua Holden shows how mathematical principles underpin the ways that different codes and ciphers work. He focuses on both code making and code breaking and discusses most of the ancient and modern ciphers that are currently known. He begins by looking at substitution ciphers, and then discusses how to introduce flexibility and additional notation. Holden goes on to explore polyalphabetic substitution ciphers, transposition ciphers, connections between ciphers and computer encryption, stream ciphers, public-key ciphers, and ciphers involving exponentiation. He concludes by looking at the future of ciphers and where cryptography might be headed. The Mathematics of Secrets reveals the mathematics working stealthily in the science of coded messages. A blog describing new developments and historical discoveries in cryptography related to the material in this book is accessible at http://press.princeton.edu/titles/10826.html.

Transients for Electrical Engineers

Elementary Switched-Circuit Analysis in the Time and Laplace Transform Domains (with a touch of MATLAB®)

Author: Paul J. Nahin

Publisher: Springer

ISBN: 3319775987

Category: Technology & Engineering

Page: 189

View: 4002

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This book offers a concise introduction to the analysis of electrical transients aimed at students who have completed introductory circuits and freshman calculus courses. While it is written under the assumption that these students are encountering transient electrical circuits for the first time, the mathematical and physical theory is not ‘watered-down.’ That is, the analysis of both lumped and continuous (transmission line) parameter circuits is performed with the use of differential equations (both ordinary and partial) in the time domain, and the Laplace transform. The transform is fully developed in the book for readers who are not assumed to have seen it before. The use of singular time functions (unit step and impulse) is addressed and illustrated through detailed examples. The appearance of paradoxical circuit situations, often ignored in many textbooks (because they are, perhaps, considered ‘difficult’ to explain) is fully embraced as an opportunity to challenge students. In addition, historical commentary is included throughout the book, to combat the misconception that the material in engineering textbooks was found engraved on Biblical stones, rather than painstakingly discovered by people of genius who often went down many wrong paths before finding the right one. MATLAB® is used throughout the book, with simple codes to quickly and easily generate transient response curves.