# Highlights of Calculus

Massachusetts Institute of Technology

Highlights of Calculus is a series of short videos that introduces the basic ideas of calculus — how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject.

• ##### Professor Strang Introduces the Series
Gilbert Strang

Professor Gilbert Strang talks informally in his office at MIT about why he created this video series, and how MIT OpenCourseWare users can benefit from these materials.

• ##### Big Picture of Calculus
Gilbert Strang

Calculus is about change. One function tells how quickly another function is changing. Professor Strang shows how calculus applies to ordinary life situations, such as driving a car, climbing a mountain, and growing to full adult height.

• ##### Big Picture: Derivatives
Gilbert Strang

Calculus finds the relationship between the distance traveled and the speed — easy for constant speed, not so easy for changing speed. Professor Strang is finding the rate of change, the slope of a curve, and the derivative of a function.

• ##### Max and Min and Second Derivatives
Gilbert Strang

At the top and bottom of a curve (Max and Min), the slope is zero. The second derivative shows whether the curve is bending down or up. Here is a real-world example of a minimum problem: What route from home to work takes the shortest time?

• ##### The Exponential Function
Gilbert Strang

Professor Strang explains how the magic number e connects to ordinary things like the interest on a bank account. The graph of y = e^x has the special property that its slope equals its height (it goes up exponentially fast!). This is the great function of calculus.

• ##### Big Picture: Integrals
Gilbert Strang

The second half of calculus looks for the distance traveled even when the speed is changing. Finding this integral is the opposite of finding the derivative. Professor Strang explains how the integral adds up little pieces to recover the total distance.