### Lecture Description

In this video lecture, Prof. Gilbert Strang discusses Six Functions, Six Rules, and Six Theorems.

This lecture compresses all the others into one fast video for review of derivatives.

Five of the 6 functions are old, the new one is a STEP function.

Slope = delta function.

The 6 rules cover f + g, f times g, f divided by g, chains f(g(x)), inverse of f, and then L'Hopital for 0/0.

The 6 theorems include the Fundamental Theorem of Calculus for Integral of Derivative of f(x).

Function 1 is f(x) Function 2 is its slope (rate of change). Add up those changes to recover f(x).

The Mean Value Theorem says that if your average speed is 70, then instant speed is 70 at least once. The Binomial Theorem tells you the series that adds up to the pth power f(x) = (1 + x)^p.

### Course Index

- Faculty Introduction
- Big Picture of Calculus
- Big Picture: Derivatives
- Max and Min and Second Derivative
- The Exponential Function
- Big Picture: Integrals
- Derivative of sin x and cos x
- Product Rule and Quotient Rule
- Chains f(g(x)) and the Chain Rule
- Limits and Continuous Functions
- Inverse Functions f ^-1 (y) and the Logarithm x = ln y
- Derivatives of ln y and sin ^-1 (y)
- Growth Rate and Log Graphs
- Linear Approximation/Newton's Method
- Power Series/Euler's Great Formula
- Differential Equations of Motion
- Differential Equations of Growth
- Six Functions, Six Rules, and Six Theorems

### Course Description

Highlights of Calculus is a series of short videos that introduces the basics 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.

The series is divided into three sections:

**Introduction**

- Why Professor Strang created these videos

- How to use the materials

**Highlights of Calculus**

- Five videos reviewing the key topics and ideas of calculus

- Applications to real-life situations and problems

- Additional summary slides and practice problems

**Derivatives**

- Twelve videos focused on differential calculus

- More applications to real-life situations and problems

- Additional summary slides and practice problems

**Acknowledgements**

Special thanks to Professor J.C. Nave for his help and advice on the development and recording of this program.The video editing was funded by the Lord Foundation of Massachusetts.