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 06 - Derivative of sin x and cos x |
The two key functions of oscillation have specially neat derivatives: The slope of sin x is cos x. And the slope of cos x is -sin x. These come from one crucial fact: (sin x)/x approaches 1 at x = 0. This checks that the slope of sin x is cos 0 = 1 at the all-important point x = 0.
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