Learning goals

[inducer]

• Build tables of function values (by hand)
• Plot function values (by hand)
• Take differences (in a table, by hand)
• Take slopes (in a table, by hand)
• Do all of the above on a computer
• Reconstructing a function from differences
  • Given a table of differences and an initial value
• Dependency on step size, limits???
  • Activity: Explore points of a function with different step sizes
  • Connecting dots
• Reconstructing a function from slopes
  • Take differences, reconstruct (aka "fundamental theorem of calculus")
• Reconstructing from data that doesn't come from slopes
  • E.g. just take input to reconstruction to be 1, x, x**2, f (aka the function values -> expoential -> tada: differential equations! y'=y)
• Muck around with differential equations/"initial value problems"
• Systems of them (predator-prey/Lotka-Volterra)
• Harmonic Oscillator
• Second differences can be done using systems
• Taking slopes in space and time -> waves

Things that are out of scope

• Connecting dots in a way that's buttery smooth
• Limits aka "what's the correct step size"
• "Actual calculus" aka "Differentiating and Integrating"