In a follow up lecture on mathematical functions, we will explore more stories and problems related to polynomials, trigonometric functions, and functional equations. Furthermore, we will dive deeper into the original historical context of functions – curves such as cycloids, cardioids, catenaries, circles, ellipses, hyperbolas, parabolas. Finally, we will try to understand why exponential and trigonometric functions turn up in solutions of so many fundamental problems in math, physics, and engineering. Come and learn with us!
Posts Tagged ‘catenary’
February 16, 2013 – Dr. Branislav Kisačanin – “A Tour of Mathematical Functions II”
Posted in math circle, meeting, tagged Branislav Kisacanin, cardioid, catenary, curves, cycloid, ellipses, hyperbola, math circle, parabola on February 13, 2013| Leave a Comment »
February 2, 2013 – Dr. Branislav Kisačanin – “A Tour of Mathematical Functions”
Posted in math circles, meeting, tagged AMC 10, AMC 12, Archimedes, brachistochrone, Branislav Kisacanin, cardioid, catenary, cicloid, circle, ellipses, euler, exponential functions, hyperbolas, hyperbolic functions, logarithmic functions, Newton, parabolas, tautochrone, trigonometric functions on January 27, 2013| 1 Comment »
In this lecture we will retrace the steps of Archimedes, Newton, Euler, and other great mathematicians and learn about important mathematical functions, their properties, history, and applications. We will look at several interesting competition topics that often show up on AMC 10/12, related to exponential, logarithmic, trigonometric, hyperbolic, and other functions. We will also see how these functions turn up in solutions of some fundamental problems in math, physics, and engineering. We will have fun using them to draw important curves: cicloids, cardioids, catenaries, circles, ellipses, hyperbolas, parabolas, and will discover which one of them is brachistochrone and which one is tautochrone.