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

• Hughes-Hallett: 11.1-11.7
• Solving differential equations with Mathematica
• Solutions of exponential, shifted exponential, and logistic equations

In class

• Introduction, with some vocabulary
• Problems: growth and decay models, separable DEs
• A model of atmospheric temperature
• Population modeling: page 7
• Solving a DE numerically with a spreadsheet
• Euler method with Mathematica