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Matrix models -- discrete time, linear maps:
- Introduction to population biology
- Linear algebra concepts: matrix multiplication and eigenvalues
- Dominant eigenvalues and population growth
- Euler-Lotkerra formula and root-finding
Stochastic models:
- Coin flipping & binomial distribution
- Transition probabilities and Markov chains
- Dominant eigenvalues return
- Central limit theorem and deterministic limits
- Diffusion equation: applications in neuroscience of decision making
Continuous time models:
- Ordinary differential equations and vector "arrow" fields -- visualizing flows in
- Nullclines
- Equilibria: Newton's method in
- Stability and oscillations
- Numerical solution methods, implementation
- Applications in gene networks, oscillators, and genetic toggle switches
- Applications in population biology and epidemiology
- Applications in neuroscience models and action potentials
Fitting and testing models:
- Least squares fits, concept of maximum likelihood
- Model optimization in
- Building models: model vs. parameter error
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