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 16 - Differential Equations of Growth|
The key model for growth (or decay when c < 0) is dy/dt = cy(t). The next model allows a steady source (constant s in dy/dt = cy + s ). The solutions include an exponential ect (because its derivative brings down c). So growth forever if c is positive, and decay if c is negative. A neat model for the population P(t) adds in minus sP2 (so P won't grow forever). This is nonlinear but luckily the equation for y = 1/P is linear and we solve it.
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