In this video lecture, Prof. Gilbert Strang discusses Limits and Continuous Functions. What does it mean to say that a sequence of numbers a1, a2, ... approaches a LIMIT A? This means: For any little interval around A, the numbers eventually get in there and stay there.The numbers a1 = 1/2, a2 = 2/3, a3 = 3/4, ... approach the limit 1. The first a's don't matter. Change 2000 a's and the limit is still 1. What about powers of the a's like a1^b1 a2^b2...? If the b's approach B then those powers approach A^B except danger if B = 0 or infinity. For calculus the important case where you can't tell by just knowing A and B is A/B = 0/0. If f(x) and g(x) both get small (f/g looks like 0/0) then l'Hopital looks at slopes: f/g goes like f '/g'. When is f(x) continuous at x=a? This means: f(x) is close to f(a) when x is close to a.
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.