# 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)