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