# infocobuild

## 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.

Go to the Course Home or watch other lectures:

 Highlights of Calculus (5) Lecture 01 - Big Picture of Calculus Lecture 02 - Big Picture: Derivatives Lecture 03 - Max and Min and Second Derivative Lecture 04 - The Exponential Function Lecture 05 - Big Picture: Integrals Derivatives (12) Lecture 06 - Derivative of sin x and cos x Lecture 07 - Product Rule and Quotient Rule Lecture 08 - Chains f(g(x)) and the Chain Rule Lecture 09 - Limits and Continuous Functions Lecture 10 - Inverse Functions f-1(y) and the Logarithm x = ln y Lecture 11 - Derivatives of ln y and sin-1(y) Lecture 12 - Growth Rate and Log Graphs Lecture 13 - Linear Approximation/Newton's Method Lecture 14 - Power Series/Euler's Great Formula Lecture 15 - Differential Equations of Motion Lecture 16 - Differential Equations of Growth Lecture 17 - Six Functions, Six Rules, and Six Theorems