Numbercrunching : taming unruly computational problems from mathematical physics to science fiction
 Author/Creator
 Nahin, Paul J.
 Language
 English.
 Imprint
 Princeton [N.J.] : Princeton University Press, c2011.
 Physical description
 xxvi, 376 p. : ill. ; 24 cm.
Access
Available online
 proquest.safaribooksonline.com Safari Books Online
 ebrary

Stacks

Unknown
QC20.7 .E4 N34 2011

Unknown
QC20.7 .E4 N34 2011
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Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Introduction x Chapter 1: FEYNMAN MEETS FERMAT 1 1.1 The Physicist as Mathematician 1 1.2 Fermat's Last Theorem 2 1.3 "Proof" by Probability 3 1.4 Feynman's Double Integral 6 1.5 Things to come 10 1.6 Challenge Problems 11 1.7 Notes and References 13 Chapter 2: Just for Fun: Two Quick NumberCrunching Problems 16 2.1 NumberCrunching in the Past 16 2.2 A Modern NumberCruncher 20 2.3 Challenge Problem 25 2.4 Notes and References 25 Chapter 3: Computers and Mathematical Physics 27 3.1 When Theory Isn't Available 27 3.2 The Monte Carlo Technique 28 3.3 The Hot Plate Problem 34 3.4 Solving the Hot Plate Problem with Analysis 38 3.5 Solving the Hot Plate Problem by Iteration 44 3.6 Solving the Hot Plate Problem with the Monte Carlo Technique 50 3.7 ENIAC and MANIACI: the Electronic Computer Arrives 55 3.8 The FermiPastaUlam Computer Experiment 58 3.9 Challenge Problems 73 3.10 Notes and References 74 Chapter 4: The Astonishing Problem of the Hanging Masses 82 4.1 Springs and Harmonic Motion 82 4.2 A Curious Oscillator 87 4.3 PhasePlane Portraits 96 4.4 Another (Even More?) Curious Oscillator 99 4.5 Hanging Masses 104 4.6 Two Hanging Masses and the Laplace Transform 108 4.7 Hanging Masses and MATLAB 113 4.8 Challenge Problems 124 4.9 Notes and References 124 Chapter 5: The ThreeBody Problem and Computers 131 5.1 Newton's Theory of Gravity 131 5.2 Newton's TwoBody Solution 139 5.3 Euler's Restricted ThreeBody Problem 147 5.4 Binary Stars 155 5.5 Euler's Problem in Rotating Coordinates 166 5.6 Poincare and the King Oscar II Competition 177 5.7 Computers and the Pythagorean ThreeBody Problem 184 5.8 Two Very Weird ThreeBody Orbits 195 5.9 Challenge Problems 205 5.10 Notes and References 207 Chapter 6: Electrical Circuit Analysis and Computers 218 6.1 Electronics Captures a Teenage Mind 218 6.2 My First Project 220 6.3 "Building" Circuits on a Computer 230 6.4 Frequency Response by Computer Analysis 234 6.5 Differential Amplifiers and Electronic Circuit Magic 249 6.6 More Circuit Magic: The Inductor Problem 260 6.7 Closing the Loop: Sinusoidal and Relaxation Oscillators by Computer 272 6.8 Challenge Problems 278 6.9 Notes and References 281 Chapter 7: The Leapfrog Problem 288 7.1 The Origin of the Leapfrog Problem 288 7.2 Simulating the Leapfrog Problem 290 7.3 Challenge Problems 296 7.4 Notes and References 296 Chapter 8: Science Fiction: When Computers Become Like Us 297 8.1 The Literature of the Imagination 297 8.2 Science Fiction "Spoofs" 300 8.3 What If Newton Had Owned a Calculator? 305 8.4 A Final Tale: the Artificially Intelligent Computer 314 8.5 Notes and References 324 Chapter 9: A Cautionary Epilogue 328 9.1 The Limits of Computation 328 9.2 The Halting Problem 330 9.3 Notes and References 333 Appendix (FPU Computer Experiment MATLAB Code) 335 Solutions to the Challenge Problems 337 Acknowledgments 371 Index 373 Also by Paul J. Nahin 377.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 bestselling popular math writer Paul Nahin tackles in "NumberCrunching". 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 numbercrunching has changed since the advent of computers, and how highspeed technology helps to solve fascinating conundrums such as the threebody, 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, "NumberCrunching" will appeal to anyone interested in understanding how these three important fields join forces to solve today's thorniest puzzles.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2011
 Responsibility
 Paul J. Nahin.
 Note
 "A collection of challenging problems in mathematical physics that roar like lions when attacked analytically, but which purr like kittens when confronted by a highspeed electronic computer and its powerful scientific software (plus some speculations for the future from science fiction)"
 ISBN
 9780691144252 (hbk. : alk. paper)
 0691144257 (hbk. : alk. paper)