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How to Fall Slower Than Gravity: And Other Everyday (and Not So Everyday) Uses of Mathematics and Physical Reasoning [Pehme köide]

  • Formaat: Paperback / softback, 320 pages, kõrgus x laius: 203x133 mm, 62 b/w illus., 4 tables
  • Ilmumisaeg: 23-Nov-2021
  • Kirjastus: Princeton University Press
  • ISBN-10: 0691229171
  • ISBN-13: 9780691229171
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  • Formaat: Paperback / softback, 320 pages, kõrgus x laius: 203x133 mm, 62 b/w illus., 4 tables
  • Ilmumisaeg: 23-Nov-2021
  • Kirjastus: Princeton University Press
  • ISBN-10: 0691229171
  • ISBN-13: 9780691229171

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.

Arvustused

"This book is without a doubt the most enjoyable, stimulating book of mathematical physics (and occasionally more pure branches of maths) puzzles that I have ever read. Its essentially a series of cleverly, and occasionally fiendishly put-together mathematics and physics challenge questions, each of which gets you thinking in a new and fascinating way."---Jonathan Shock, Mathemafrica "Reading Nahin is like reading through a select library of ancient Babylonian mathematical clay tablets. Surprises abound. . . . Nahin weaves much colorful history into his narrative."---Andrew Simoson, Mathematical Intelligencer "Engaging. . . . The book contains a wealth of original problems. . . . An enjoyable read."---Antonín Slavík, Zentralblatt MATH "This reviewer found himself being drawn to a variety of unfamiliar settings with much interest and even fascination." * Choice * "I certainly enjoyed [ the book]!"---Alan Stevens, Mathematics Today "The potential audience for this book should be fairly large and go from highly talented high school students up through professionals in any STEM field."---Geoffrey Dietz, MAA Reviews

Preface xiii
PART I THE PROBLEMS
1(154)
Problem 1 A Military Question: Catapult Warfare
3(1)
Problem 2 A Seemingly Impossible Question: A Shocking Snow Conundrum
4(2)
Problem 3 Two Math Problems: Algebra and Differential Equations Save the Day
6(2)
Problem 4 An Escape Problem: Dodge the Truck
8(1)
Problem 5 The Catapult Again: Where Dead Cows Can't Go!
9(1)
Problem 6 Another Math Problem: This One Requires Calculus
10(1)
Problem 7 If Theory Fails: Monte Carlo Simulation
11(6)
Problem 8 Monte Carlo and Theory: The Drunkard's One-Dimensional Random Walk
17(2)
Problem 9 More Monte Carlo: A Two-Dimensional Random Walk in Paris
19(2)
Problem 10 Flying with (and against) the Wind: Math for the Modern Traveler
21(1)
Problem 11 A Combinatorial Problem with Physics Implications: Particles, Energy Levels, and Pauli Exclusion
22(7)
Problem 12 Mathematical Analysis: By Physical Reasoning
29(7)
Problem 13 When an Integral Blows Up: Can a Physical Quantity Really Be Infinite?
36(3)
Problem 14 Is This Easier Than Falling Off a Log? Well, Maybe Not
39(8)
Problem 15 When the Computer Fails: When Every Day Is a Birthday
47(8)
Problem 16 When Intuition Fails: Sometimes What Feels Right, Just Isn't
55(5)
Problem 17 Computer Simulation of the Physics of NASTYGLASS: Is This Serious? Maybe
60(12)
Problem 18 The Falling-Raindrop, Variable-Mass Problem: Falling Slower Than Gravity
72(9)
Problem 19 Beyond the Quadratic: A Cubic Equation and Discontinuous Behavior in a Physical System
81(12)
Problem 20 Another Cubic Equation: This One Inspired by Jules Verne
93(10)
Problem 21 Beyond the Cubic: Quartic Equations, Crossed Ladders, Undersea Rocket Launches, and Quintic Equations
103(11)
Problem 22 Escaping an Atomic Explosion: Why the Enola Gay Survived
114(8)
Problem 23 "Impossible" Math Made Easy: Gauss's Congruence Arithmetic
122(4)
Problem 24 Wizard Math: Fourier's Series, Dirac's Impulse, and Euler's Zeta Function
126(11)
Problem 25 The Euclidean Algorithm: The Zeta Function and Computer Science
137(10)
Problem 26 One Last Quadratic: Heaviside Locates an Underwater Fish Bite!
147(8)
PART II THE SOLUTIONS
155(70)
Appendix 1 MATLAB, Primes, Irrationals, and Continued Fractions 225(22)
Appendix 2 A Derivation of Brouncker's Continued Fraction for 247(4)
Appendix 3 Landen's Calculus Solution to the Depressed Cubic Equation 251(10)
Appendix 4 Solution to Lord Rayleigh's Rotating-Ring Problem of 1876 261(9)
Acknowledgments 270(3)
Index 273(8)
Also 281
Paul J. Nahin
Paul J. Nahin is the author of many popular math books, including In Praise of Simple Physics, Dr. Eulers Fabulous Formula, and An Imaginary Tale (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire. He received the 2017 Chandler Davis Prize for Excellence in Expository Writing in Mathematics.