Highlights of Calculus

Source: MIT OCW

These five Highlights of Calculus videos provide an overview of the key topics and ideas of calculus and how they apply to real-life situations and problems.

Prof. Strang’s free on-line textbook is available here.

Big Picture of Calculus: 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, growing to full adult height

Big Picture: Derivatives 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” and the “slope of a curve” and the “derivative of a function.”

Max and Min and Second Derivative:  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: 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 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. I know the speed at each moment of my trip, so how far did I go?

Derivatives (12 videos)

These twelve videos on Derivatives dig deeper into the subfield of calculus known as “differential calculus.”  Like the overview videos, Professor Strang explains how each topic applies to real-life applications.  Along with the videos, there are summary slides and practice problems available under the Related Resources tab on each video page. Visit here to watch.

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