Seventeen Equations that Changed the World

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Important work by mathematicians Vladimir Arnold and Stephen Smale helped with the realization that chaos is a consequence of differential equations. There was no overarching theme other than each one is important, nor did I feel was there any attempt to flow from equation to equation. Auch Mathematiker*innen (so wie ich es eine bin) können beim Lesen des Buches noch etwas lernen - mir waren ca drei Viertel der Formeln bekannt, aber ihr historischer Kontext und ihre gesellschaftlichen Implikationen nicht unbedingt. The Wave Equation is one of the most important equations in physics, and is crucial for engineers studying the vibrations in vehicles and the response of buildings to earthquakes.

Die behandelte Mathematik ist absolut nicht einfach (manches in den ersten Kapiteln schon, aber es wird recht schnell happig). History: The initial concept was discovered by the Scottish Laird John Napier of Merchiston in an effort to make the multiplication of large numbers, then incredibly tedious and time consuming, easier and faster. The arguments suggest a lack of understanding of fundamental economic theory particularly with regard to the need for derivatives in providing optimal allocations in an economy. Importance: Once computers became powerful enough to approximately solve this equation, it opened up a complex and very useful field of physics.He has that valuable grasp of not only what it takes to make equations interesting, but also to make science cool. He explores how Pythagoras’s Theorem led to GPS and Satnav; how logarithms are applied in architecture; why imaginary numbers were important in the development of the digital camera, and what is really going on with Schroedinger’s cat.

In the book Stewart traced a history of the role of mathematics in human history, beginning with the Pythagorean theorem (Pythagorean equation) [4] to the equation that transformed the twenty-first century financial market, the Black–Scholes model. Euclid turned geometry into logic by making his basic assumptions explicit and invoking them to give systematic proofs for all of his theorems.

History: Joseph Fourier discovered the equation, which extended from his famous solution to a differential equation describing how heat flows, and the previously described wave equation. He also modified the equations of trigonometry to reflect the spherical nature of the Earth’s surface, an important step towards effective navigation.