Calculus is about change. One function tells how quickly another function is changing. Professor Strang shows how calculus applies to ordinary life situations.

Six Functions, Six Rules, and Six Theorems

Differential Equations of Motion

Power Series/Euler's Great Formula

Linear Approximation/Newton's Method

Derivatives of ln y and sin ^-1 (y)

Differential Equations of Growth

Growth Rates & Log Graphs

Inverse Funtions f ^-1 (y) and the Logarithm x = ln y

Product Rule and Quotient Rule

Chains f(g(x)) and the Chain Rule

Limits and Continuous Functions

Derivative of sin x and cos x

Professor Strang explains how the "magic number e" connects to ordinary things like the interest on a bank account.

The Exponential Function

Big Picture of Calculus

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.

Big Picture: Integrals

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.

Max and Min and Second Derivative

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."

Big Picture: Derivatives

Gil Strang

Gil Strang gives an overview of his video series Calculus for MIT's Highlights for High School program. Designed to give an easier introduction to calculus.

Gil Strang's Introduction to Highlights of Calculus

I could have watched these when I was still in college.  Maybe I would have passed.

I wish

Great overview, very helpful as a catchup/review tool if going back to school and need to refresh

Well Done

Highlights of Calculus - Videos

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