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 15 - Differential Equations of Motion |
These equations have 2nd derivatives because acceleration is in Newton's Law F = ma. The key model equation is (second derivative) y" = MINUS y or y" = MINUS a2y. There are two solutions since the equation is second order. They are SINE and COSINE y = sin(at) and y = cos(at). Two derivatives bring back sine and cosine with minus a2. The next step allows damping (first derivative) as in my" + dy' + ky = 0. How to solve? Just try y = eat. You find that ma2 + da + k = 0.
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