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For the Reader | p. xi |
Preface | p. xiii |
Three Examples of the Mutual Embrace | p. 1 |
Unphysical Laws | p. 1 |
When Math Goes Wrong | p. 6 |
Math from Physics | p. 13 |
Measuring Gravity | p. 18 |
First, a Little Theory | p. 18 |
Out in the Author's Garage | p. 21 |
Feynman's Infinite Circuit | p. 24 |
An Infinity of Resistors | p. 24 |
An Infinity of Reactances, and Recursion | p. 27 |
Convergence--or Not? | p. 32 |
Three More Infinite, All-Resistor Networks | p. 36 |
Air Drag--A Mathematical View | p. 44 |
Air Drag Treated Broadly | p. 44 |
Air Drag Treated with Some Detail | p. 51 |
Air Drag--A Physical View | p. 62 |
The Quadratic Force Law | p. 62 |
Long Falls through a Real Atmosphere | p. 70 |
Really Long Falls | p. 82 |
Falling into the Sun | p. 82 |
Falling from Heaven to Hell | p. 86 |
The Zeta Function--and Physics | p. 94 |
A Curious Double Integral | p. 94 |
Fourier Series and the Zeta Function | p. 95 |
The Zeta Function in Physics | p. 100 |
Ballistics--With No Air Drag (Yet) | p. 107 |
Shooting a Cannon in a Vacuum | p. 107 |
What Makes a Champion Shot-Putter? | p. 112 |
Another Cannon Question | p. 116 |
Ballistics--With Air Drag | p. 120 |
Thin Air Cannot Be Ignored! | p. 120 |
Air Drag and Baseball | p. 126 |
Gravity and Newton | p. 136 |
The Beginnings of Modern Gravity | p. 136 |
Newton's Superb Theorems | p. 140 |
The Moon Test and Blowing-Up Planets | p. 148 |
A Surprising Gravity Calculation | p. 152 |
Gravitational Contraction | p. 157 |
Gravity Far Above the Earth | p. 170 |
Kepler's Laws of Planetary Motion | p. 170 |
Weighing the Planets | p. 175 |
Gravity Inside the Earth | p. 186 |
Newton's Experiment | p. 186 |
Gravity Inside the Earth | p. 191 |
Pressure at the Center of the Earth | p. 200 |
Travel Inside the Earth | p. 203 |
Epilogue | p. 209 |
Quilts & Electricity | p. 215 |
Recreational Mathematics | p. 215 |
Electric Quilts | p. 220 |
Three Impossibility Proofs | p. 225 |
Random Walks | p. 233 |
Ronald Ross and the Flight of Mosquitoes | p. 233 |
Karl Pearson Formulates a Famous Problem | p. 236 |
Gambler's Ruin | p. 241 |
The Monte Carlo Method | p. 245 |
Two More Random Walks | p. 261 |
Brownian Motion | p. 261 |
Shrinking Walks | p. 269 |
Nearest Neighbors | p. 285 |
Cannibals Can Be Fun! | p. 285 |
Neighbors Beyond the Nearest | p. 291 |
What Happens When We Have Lots of Cannibals | p. 294 |
Serious Physics | p. 296 |
One Last Random Walk | p. 299 |
Resistor Mathematics | p. 299 |
Electric Walks | p. 301 |
Monte Carlo Circuit Simulation | p. 305 |
Symmetry, Superposition, and Resistor Circuits | p. 313 |
The Big Noise | p. 321 |
An Interesting Textbook Problem | p. 321 |
The Polar Equations of the Big-Noise Flight | p. 322 |
The Acceleration on a Big-Noise Flight Path | p. 328 |
Solutions To The Challenge Problems | p. 333 |
Special Bonus Discussion | p. 371 |
Warning: Do Not Read before Reading Disscussion 17 | p. 373 |
Electricity in the Fourth Dimension | p. 373 |
The Tesseract | p. 373 |
Connecting a Tesseract Resistor Cube | p. 376 |
Acknowledgments | p. 385 |
Index | p. 387 |
Table of Contents provided by Publisher. All Rights Reserved. |
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The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.