Highlights of Calculus
Highlights of Calculus (Res.18-005, MIT OCW). Instructor: Professor Gilbert Strang. 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: 1) Introduction - Why Professor Gilbert Strang created these videos, 2) Highlights of Calculus - Five videos reviewing the key topics and ideas of calculus, Applications to real-life situations and problems, and 3) Derivatives - Twelve videos focused on differential calculus, More applications to real-life situations and problems. (from ocw.mit.edu)
| Lecture 14 - Power Series/ Euler's Great Formula |
A special power series is ex = 1 + x + x2/2! + x3/3! + ... + every xn/n!. The series continues forever but for any x it adds up to the number ex. If you multiply each xn/n! by the nth derivative of f(x) at x = 0, the series adds to f(x). This is a TAYLOR SERIES. Of course all those derivatives are 1 for ex.
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