E-Book, Englisch, 336 Seiten
Adam X and the City
Course Book
ISBN: 978-1-4008-4169-1
Verlag: De Gruyter
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
Modeling Aspects of Urban Life
E-Book, Englisch, 336 Seiten
ISBN: 978-1-4008-4169-1
Verlag: De Gruyter
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
What mathematical modeling uncovers about life in the city
X and the City, a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow through tunnels? Can you predict whether a traffic light will stay green long enough for you to cross the intersection? And what is the likelihood that your city will be hit by an asteroid?
Every math problem and equation in this book tells a story and examples are explained throughout in an informal and witty style. The level of mathematics ranges from precalculus through calculus to some differential equations, and any reader with knowledge of elementary calculus will be able to follow the materials with ease. There are also some more challenging problems sprinkled in for the more advanced reader.
Filled with interesting and unusual observations about how cities work, X and the City shows how mathematics undergirds and plays an important part in the metropolitan landscape.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Preface xiii
Acknowledgments xvii
Chapter 1
Introduction: Cancer, Princess Dido, and the city 1
Chapter 2
Getting to the city 7
Chapter 3
Living in the city 15
Chapter 4
Eating in the city 35
Chapter 5
Gardening in the city 41
Chapter 6
Summer in the city 47
Chapter 7
Not driving in the city! 63
Chapter 8
Driving in the city 73
Chapter 9
Probability in the city 89
Chapter 10
Traffic in the city 97
Chapter 11
Car following in the city--I 107
Chapter 12
Car following in the city--II 113
Chapter 13
Congestion in the city 121
Chapter 14
Roads in the city 129
Chapter 15
Sex and the city 135
Chapter 16
Growth and the city 149
Chapter 17
The axiomatic city 159
Chapter 18
Scaling in the city 167
Chapter 19
Air pollution in the city 179
Chapter 20
Light in the city 191
Chapter 21
Nighttime in the city--I 209
Chapter 22
Nighttime in the city--II 221
Chapter 23
Lighthouses in the city? 233
Chapter 24
Disaster in the city? 247
Chapter 25
Getting away from the city 255
Appendix 1
Theorems for Princess Dido 261
Appendix 2
Dido and the sinc function 263
Appendix 3
Taxicab geometry 269
Appendix 4
The Poisson distribution 273
Appendix 5
The method of Lagrange multipliers 277
Appendix 6
A spiral braking path 279
Appendix 7
The average distance between two random
points in a circle 281
Appendix 8
Informal "derivation" of the logistic
differential equation 283
Appendix 9
A miniscule introduction to fractals 287
Appendix 10
Random walks and the diffusion equation 291
Appendix 11
Rainbow/halo details 297
Appendix 12
The Earth as vacuum cleaner? 303
Annotated references and notes 309
Index 317
