Infinite Powers

How Calculus Reveals the Secrets of the Universe

Steven Strogatz

• Éditeur: Mariner Books
• Année: 2019
• ISBN:
  9781328880017
• Sujet: Mathematics
• Sous-sujet: Calculus

From preeminent math personality and author of The Joy of x, a brilliant and endlessly appealing explanation of calculus—how it works and why it makes our lives immeasurably better. Without calculus, we wouldn't have cell phones, TV, GPS, or ultrasound.We wouldn't have unraveled DNA or discovered Neptune or figured out how to put 5, 000 songs in your pocket.

Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz's brilliantly creative, down-to-earth history shows that calculus is not about complexity; it's about simplicity.It harnesses an unreal number—infinity—to tackle real-world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous.

Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes "backwards" sometimes; how to make electricity with magnets; how to ensure your rocket doesn't miss the moon; how to turn the tide in the fight against AIDS.

As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.

Index

A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z

Note: Illustrations are indicated by italics

A

Abu Sa’d al-A’la Ibn Sahl, 116

acceleration, 141–42, 172–75, 230–31, 258

Achilles and the Tortoise paradox, 17–19, 17, 162

acquired immune deficiency syndrome (AIDS), 218–25

Adams, Douglas, viii

Adams, John, 239

adequality, 106–7

aeroelastic flutter, 246–47

AIDS, 218–25

air resistance, 69–71

aircraft engineering, 244–47

algebra

Achilles and the Tortoise paradox, 19

birthplace of, 90

distance, rate and time, 145

geometry, merge with, 93–96, 98

history of, 89–93

Newton on, 102

optimization problems, 103–7

popularity of, xx–xxi

symbols vs spoken language, 67

tangents of curves, 168

Wallis on, 196

xy plane, 177

al-Khwarizmi, Muhammad Ibn Musa, 92

AlphaInfinity, 292–93, 294

AlphaZero, 292, 293

altimeter, 213–16

American Revolution, 239

Ampère, André-Marie, x–xi

Ampère’s law, xi

amplitude, 109–10, 254

analysis vs synthesis, 102–3

analytic geometry, 101–3

analytic number theory, 228

ancient civilizations

algebra and geometry, 90–91, 95

area of a circle, 7

Descartes on, 102

Egypt, 1

geography of Greece, 90

geometry vs arithmetic, 33

Greeks on curves, 3–4

instantaneous speed, 162

musical harmony, xiv, 48

planetary motion, 62, 63

synthesis vs analysis, 102

view of numbers and symbols, 95–96

Anderson, Carl, 298

animated movies, 50–53

anti-electron, 298

antimatter,...