Carlota Bonnet

Calculus is used in physics, engineering, economics, statistics, and medicine. It is used to create mathematical models in order to arrive into an optimal solution. We can thank two mathematicians for this discovery: Sir Isaac Newton, and Gottfried Leibniz. Both men discovered calculus almost simultaneously. Because of this, they started a war to know which one had actually discovered it, each one accusing the other of plagiarism. Through this presentation, we talk about Newton's and Leibniz's lives, and the methods they used to develop calculus. Then, we explain why their feud was so important, and how it ended.

Through many years, we have dealt with the Cartesian coordinate system. Although this systems is more broadly used, the polar coordinate system plays a strong role in calculus and mathematics in general. In the Cartesian coordinates system, we can find parabolic, hyberbolic, and conic functions, among others. Similarly, we can also find families of curves in the polar coordinate system. Throughout this presentation, we expose three of these families: Rosette curves, Spring curves, and Ovals of Cassini.

Blaise Pascal was a French mathematician, physicist, inventor, writer, and philosopher. He contributed greatly to physics, and he even gave him name to an unit of pressure, the Pascal. In mathematics, he invented a new form of proof, the induction method, particularly useful in Numbers Theory, and he developed the study of what we now call Pascal's triangle. This triangle is full of patterns, and can be used in a large variety of fields. 

A pursuit curve is a curve showing the path an object takes as it pursues another object. In real life, it may be a hound chasing a rabbit, an outfielder running towards a pop-fly, or a guided missile pursuing a jet. Graphically, the velocity vector of the pursuer is aimed directly towards prey (on the prey’s tangent), and therefore is a straight line. Through this project, we will explain how to model pursuit curves using differential equations.