# Study topics for 450 midterm

- Make a Fermi model
- Criticise a a Fermi model
- Make a geometric model using similar triangles and known functions (cycloid, trammel, nautilus)
- Use plots to recognize linear, powerlaw, or exponential behavior of data
- Know and understand the normal equations and weighted normal equations of Linear Least Squares
- Set up normal equations to fit lines, power laws, and exponential relations
- Euler's method for numerical approximation of solutions to differential equation systems
- Make or read linear compartmental models for pharmocokinetics
- Solve simple linear systems
- Read and solve the basic viral dynamics model
- Explain steady-state approximations based on seperation of time scales
- Explain why viral infection treatment can lead to bi-phasic responses
- Know the basic law of mass action as a reaction and a system of differential equations
- Build a reaction networks modelling a chemical, social, or biological process
- Convert between hypergraphs, reaction networks, and compartmental differential equation models.
- Numerically solve a compartmental model
- Know how to use rand() for simple monte carlo simulations
- Know the common interpretations of the Binomial, Hypergeometric, Geometric, and Pascal distributions
- Sterling's formula
- Derivation of the Poisson distribution
- Use of the Poisson distribution
- Use of the Normal distribution
- Use of the Extreme-value distributions (Fisher-Tippett-Gumbel)
- How to fit common distributions (Least squares, MLE) to data, and interpret the quality of the fit
- Markov chains (Digraph, Matrix, solution, steady-state)