Derivatives (12 videos)

Differential Equations of Growth

The key model for growth (or decay when c < 0) is  dy/dt = c y(t)
The next model allows a steady source (constant s in dy/dt = cy + s )
The solutions include an exponential e^ct  (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 sP^2  (so P won’t grow forever)
This is nonlinear but luckily the equation for y = 1/P is linear and we solve it

Population P follows an “S-curve” reaching a number like 10 or 11 billion (???)
Great lecture but Professor Strang should have written e^-ct in the last formula

Professor Strang’s Calculus textbook (1st edition, 1991) is freely available here.

Subtitles are provided through the generous assistance of Jimmy Ren.

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