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 (R) is used throughout the book, with simple codes to quickly and easily generate transient response curves.

This book tells the story of the probability integral, the approaches to analyzing it throughout history, and the many areas of science where it arises. The so-called probability integral, the integral over the real line of a Gaussian function, occurs ubiquitously in mathematics, physics, engineering and probability theory. Stubbornly resistant to the undergraduate toolkit for handling integrals, calculating its value and investigating its properties occupied such mathematical luminaries as De Moivre, Laplace, Poisson, and Liouville. This book introduces the probability integral, puts it into a historical context, and describes the different approaches throughout history to evaluate and analyze it. The author also takes entertaining diversions into areas of math, science, and engineering where the probability integral arises: as well as being indispensable to probability theory and statistics, it also shows up naturally in thermodynamics and signal processing. Designed to be accessible to anyone at the undergraduate level and above, this book will appeal to anyone interested in integration techniques, as well as historians of math, science, and statistics.

A mathematical journey through the most fascinating problems of extremes and how to solve them What is the best way to photograph a speeding bullet? How can lost hikers find their way out of a forest? Why does light move through glass in the least amount of time possible? When Least Is Best combines the mathematical history of extrema with contemporary examples to answer these intriguing questions and more. Paul Nahin shows how life often works at the extremes-with values becoming as small (or as large) as possible-and he considers how mathematicians over the centuries, including Descartes, Fermat, and Kepler, have grappled with these problems of minima and maxima. Throughout, Nahin examines entertaining conundrums, such as how to build the shortest bridge possible between two towns, how to vary speed during a race, and how to make the perfect basketball shot. Moving from medieval writings and modern calculus to the field of optimization, the engaging and witty explorations of When Least Is Best will delight math enthusiasts everywhere.

A collection of stimulating probability puzzles from bestselling math writer Paul Nahin What are the chances of a game-show contestant finding a chicken in a box? Is the Hanukkah dreidel a fair game? Will you be alive ten years from now? These are some of the one-of-a-kind probability puzzles that popular math writer Paul Nahin offers in this lively and informative book. Nahin brings probability to life with colorful historical anecdotes and a unique puzzle-solving approach that illustrates many of the techniques mathematicians use to grapple with probability. He looks at classic puzzles-from Galileo's dice-tossing problem to a disarming dice puzzle that would have astonished even Newton-and presents a dozen challenge problems and twenty-five probability puzzlers. With wit and insight, Nahin demonstrates why seemingly simple probability problems can stump even the experts.

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 material 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.

An exploration of the idea of time travel from the first account in English literature to the latest theories of such physicists 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 Goedel, and others; time travel paradoxes, and much more.

Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics.

"Here's a gem of a book...all peppered with delightful notes from science fiction films, novels, and comics. I can't turn a page without finding a jewel." Clifford Stoll, University of California, Berkeley, author of The Cuckoo's Egg "The research that has gone into this book is impressive." Nature "For professional physicists much of the value lies in the extensive technical appendices and footnotes, and the exhaustive list of references. But if, like me, you are a child at heart, the real fun lies in the zany stories and wild speculations." Physics World Time Machines explores the idea 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 Goedel, and others; time travel paradoxes, and much more.

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.

An engrossing look at the history and importance of a centuries-old but still unanswered math problem For centuries, mathematicians the world over have tried, and failed, to solve the zeta-3 problem. Math genius Leonhard Euler attempted it in the 1700s and came up short. The straightforward puzzle considers if there exists a simple symbolic formula for the following: 1+(1/2)^3+(1/3)^3+(1/4)^3+. . . . But why is this issue-the sum of the reciprocals of the positive integers cubed-so important? With In Pursuit of Zeta-3, popular math writer Paul Nahin investigates the history and significance of this mathematical conundrum. Drawing on detailed examples, historical anecdotes, and even occasionally poetry, Nahin sheds light on the richness of the nature of zeta-3. He shows its intimate connections to the Riemann hypothesis, another mathematical mystery that has stumped mathematicians for nearly two centuries. He looks at its links with Euler's achievements and explores the modern research area of Euler sums, where zeta-3 occurs frequently. An exact solution to the zeta-3 question wouldn't simply satisfy pure mathematical interest: it would have critical ramifications for applications in physics and engineering, such as quantum electrodynamics. Challenge problems with detailed solutions and MATLAB code are included at the end of each of the book's sections. Detailing the trials and tribulations of mathematicians who have approached one of the field's great unsolved riddles, In Pursuit of Zeta-3 will tantalize curious math enthusiasts everywhere.

From H.G. Wells to Isaac Asimov to Ursula K. Le Guin, time travel has long been a favorite topic and plot device in tales of science fiction and fantasy. But as any true SF fan knows, astounding stories about traversing alternate universes and swimming the tides of time demand plausible science. That's just what Paul J. Nahin's guide provides.

An engineer, physicist, and published science fiction writer, Nahin is uniquely qualified to explain the ins and outs of how to spin such complex theories as worm holes, singularity, and relativity into scientifically sound fiction. First published in 1997, this fast-paced book discusses the common and not-so-common time-travel devices science fiction writers have used over the years, assesses which would theoretically work and which would not, and provides scientific insight inventive authors can use to find their own way forward or backward in time. From hyperspace and faster-than-light travel to causal loops and the uncertainty principle and beyond, Nahin's equation-free romp across time will help writers send their characters to the past or future in an entertaining, logical, and scientific way.

If you ever wanted to set up the latest and greatest grandfather paradox--or just wanted to know if the time-bending events in the latest pulp you read could ever happen--then this book is for you.

"He was a man who often was incapable of conducting himself properly in the most elementary social interactions. His only continuing contacts with women were limited to his mother, nieces, and housekeepers. He was a man who knew the power of money and desired it, but refused to work for it, preferring to live off the sweat of his family and long-suffering friends, whom he often insulted even as they paid his bills." -- from the book

This, then, was Oliver Heaviside, a pioneer of modern electrical theory. Born into a low social class of Victorian England and dying in poverty as a recluse, Heaviside (in between) made advances in mathematics, by introducing the operational calculus; in physics, where he formulated the modern-day expressions of Maxwell's Laws of electromagnetism; and in electrical engineering, through his duplex equations. This acclaimed biography is the only one devoted to Oliver Heaviside. Now available in paperback with a new preface by the author, it will appeal to historians of technology and science, as well as to scientists and engineers who wish to learn more about this remarkable man.

What are the chances of a game-show contestant finding a chicken in a box? Is the Hanukkah dreidel a fair game? Will you be alive ten years from now? These are just some of the one-of-a-kind probability puzzles that acclaimed popular math writer Paul Nahin offers in this lively and informative book.

Nahin brings probability to life with colorful and amusing historical anecdotes as well as an electrifying approach to solving puzzles that illustrates many of the techniques that mathematicians and scientists use to grapple with probability. He looks at classic puzzles from the past--from Galileo's dice-tossing problem to a disarming dice puzzle that would have astonished even Newton--and also includes a dozen challenge problems for you to tackle yourself, with complete solutions provided in the back of the book.

Nahin then presents twenty-five unusual probability puzzlers that you aren't likely to find anywhere else, and which range in difficulty from ones that are easy but clever to others that are technically intricate. Each problem is accompanied by an entertaining discussion of its background and solution, and is backed up by theory and computer simulations whenever possible in order to show how theory and computer experimentation can often work together on probability questions. All the MATLAB(r) Monte Carlo simulation codes needed to solve the problems computationally are included in the book.With his characteristic wit, audacity, and insight, Nahin demonstrates why seemingly simple probability problems can stump even the experts.

How a modern radio works, told through mathematics, history, and selected puzzles The modern radio is a wonder, and behind that magic is mathematics. In The Mathematical Radio, Paul Nahin explains how radios work, deploying mathematics and historical discussion, accompanied by a steady stream of intriguing puzzles for math buffs to ponder. Beginning with oscillators and circuits, moving on to AM, FM, and single-sideband radio. Nahin focuses on the elegant mathematics underlying radio technology rather than the engineering. He explores and explains more than a century of key developments, placing them in historical and technological context. Nahin, a prolific author of books on math for the general reader, describes in fascinating detail the mathematical underpinnings of a technology we use daily. He explains and solves, for example, Maxwell’s equations for the electromagnetic field. Readers need only a familarity with advanced high school–level math to follow Nahin’s mathematical discussions. Writing with the nonengineer in mind, Nahin examines topics including impulses in time and frequency, spectrum shifting at the transmitter, the superheterodyne, the physics of single sideband radio, and FM sidebands. Chapters end with “challenge problems” and an appendix offers solutions, partial answers, and hints. Readers will come away with a new appreciation for the beauty of even the most useful mathematics.

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.

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.

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, now in its second edition, 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. New material in the second edition includes 25 new challenge problems and solutions, 25 new worked examples, simplified derivations, and additional historical discussion.

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 material 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.

Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use--from our computers and cars, to home appliances. How did a system of mathematics established in the Victorian era become the basis for such incredible technological achievements a century later? In The Logician and the Engineer, Paul Nahin combines engaging problems and a colorful historical narrative to tell the remarkable story of how two men in different eras--mathematician and philosopher George Boole and electrical engineer and pioneering information theorist Claude Shannon--advanced Boolean logic and became founding fathers of the electronic communications age. Nahin takes readers from fundamental concepts to a deeper and more sophisticated understanding of modern digital machines, in order to explore computing and its possible limitations in the twenty-first century and beyond.

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 (R) is used throughout the book, with simple codes to quickly and easily generate transient response curves.

This book contains a broad overview of time travel in science fiction, along with a detailed examination of the philosophical implications of time travel. The emphasis of this book is now on the philosophical and on science fiction, rather than on physics, as in the author's earlier books on the subject. In that spirit there are, for example, no Tech Notes filled with algebra, integrals, and differential equations, as there are in the first and second editions of TIME MACHINES. Writing about time travel is, today, a respectable business. It hasn't always been so. After all, time travel, prima facie, appears to violate a fundamental law of nature; every effect has a cause, with the cause occurring before the effect. Time travel to the past, however, seems to allow, indeed to demand, backwards causation, with an effect (the time traveler emerging into the past as he exits from his time machine) occurring before its cause (the time traveler pushing the start button on his machine's control panel to start his trip backward through time). Time Machine Tales includes new discussions of the advances by physicists and philosophers that have appeared since the publication of TIME MACHINES in 1999, examples of which are the chapters on time travel paradoxes. Those chapters have been brought up-to-date with the latest philosophical thinking on the paradoxes.

Can a computer have a soul? Are religion and science mutually exclusive? Is there really such a thing as free will? If you could time travel to visit Jesus, would you (and should you)? For hundreds of years, philosophers, scientists and science fiction writers have pondered these questions and many more. In Holy Sci-Fi!, popular writer Paul Nahin explores the fertile and sometimes uneasy relationship between science fiction and religion. With a scope spanning the history of religion, philosophy and literature, Nahin follows religious themes in science fiction from Feynman to Foucault and from Asimov to Aristotle. An intriguing journey through popular and well-loved books and stories, Holy Sci-Fi! shows how sci-fi has informed humanity's attitudes towards our faiths, our future and ourselves.

An entertaining mathematical exploration of the heat equation and its role in the triumphant development of the trans-Atlantic telegraph cable Heat, like gravity, shapes nearly every aspect of our world and universe, from how milk dissolves in coffee to how molten planets cool. The heat equation, a cornerstone of modern physics, demystifies such processes, painting a mathematical picture of the way heat diffuses through matter. Presenting the mathematics and history behind the heat equation, Hot Molecules, Cold Electrons tells the remarkable story of how this foundational idea brought about one of the greatest technological advancements of the modern era. Paul Nahin vividly recounts the heat equation's tremendous influence on society, showing how French mathematical physicist Joseph Fourier discovered, derived, and solved the equation in the early nineteenth century. Nahin then follows Scottish physicist William Thomson, whose further analysis of Fourier's explorations led to the pioneering trans-Atlantic telegraph cable. This feat of engineering reduced the time it took to send a message across the ocean from weeks to minutes. Readers also learn that Thomson used Fourier's solutions to calculate the age of the earth, and, in a bit of colorful lore, that writer Charles Dickens relied on the trans-Atlantic cable to save himself from a career-damaging scandal. The book's mathematical and scientific explorations can be easily understood by anyone with a basic knowledge of high school calculus and physics, and MATLAB code is included to aid readers who would like to solve the heat equation themselves. A testament to the intricate links between mathematics and physics, Hot Molecules, Cold Electrons offers a fascinating glimpse into the relationship between a formative equation and one of the most important developments in the history of human communication.

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).

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.