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## October 1, 2011 – Dr. Branislav Kisačanin – “First Encounter with Calculus”

Many of our students have started taking Calculus or are curious about what it’s all about.  Take this opportunity to hear one of our favorite lecturers, Dr. Branislav Kisačanin, introduce even our younger students to this beautiful topic.  Here is a description of the talk in his own words:

In this session we will look at calculus and try to dispell the mistery that often surrounds it. We will begin by looking at examples of limiting processes, and show for example that as x approaches 0, the value of $\frac{\sin x}{x}$ approaches 1. Based on several other examples of limits, we will be able to determine line equations for tangets of various curves. This will bring us to the doorstep of the first derivative.

We will look at other interpretations of the first derivative and also look at how it is applied to maximization and minimization, Newton’s method of tangents for solving equations, etc. In the second hour we will look at another major part of calculus, integration, and will show how integration is used to compute areas and volumes. We will also look at the methods used by Archimedes to compute the volumes of solid spheres, which are remarkably similar to modern integration. Of course, there is much more to caclulus than we can learn in one day, but this will be a good start!