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Math · Advanced

Differential Equations

Most laws of nature don't say what something is. They say how it changes. Learn to read slope fields, put the number ee to work, model cooling coffee, growing populations and mixing tanks, solve equations step by step with Euler's method, see why springs bounce and shock absorbers don't, and draw the phase portrait of a pendulum.

8 lessons~40 min0/8 complete
1

Equations About Change

Slope fields and exponentials.

  1. Slope FieldsFollowing the arrows
  2. Growth, Decay and eThe function that is its own slope
  3. Newton’s Law of CoolingApproaching equilibrium
2

Models and Methods

Limits, steps and springs.

  1. Logistic GrowthGrowth that levels off
  2. Euler’s MethodSolving by taking small steps
  3. Springs & DampingSecond-order equations
3

Seeing Solutions

Phase portraits and mixing tanks.

  1. Phase PortraitsPosition and velocity together
  2. Tanks and MixingIn, out, and the approach to balance

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Predator–prey cycles, a fishing paradox, sustainable harvests, competition and age structure.

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