Differential equations

Learning objectives

  • What is a differential equation and how can you represent it visually?
  • Distinguish between dy/dt = kt and dy/dt = k y
  • Use initial values to single out an individual solution
  • Work with the shifted exponential DE: dy/dt = k  y + b
  • Solve separable DEs:  f(x) dx = g(y) dy
  • Explore algebraic solutions of the logistic DE:  dy/dt =ky (1-y/L) where k >0 and L> 0.
  • Solve differential equations with Mathematica
  • Use the Euler method to create numerical approximations of solutions of DEs

Resources

In class