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CPS 111 Home
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Syllabus
The number of lectures estimated for each topic below is tentative. References to
the textbook (see the readings and software page) are
given when appropriate. Additional notes will be handed out as needed.
- Introduction and motivation (1 lecture; Sec. 2.1)
- Mathematical and computational modeling
- The modeling process
- Discrete, deterministic models of change over time (5 lectures; Ch. 1)
- Stationary, first-order scalar recurrences
- Fixed points and stability
- Nonlinear, first-order scalar recurrences. Chaos
- Systems of scalar recurrences
- 2x2 systems of scalar recurrences
- Continuous, deterministic models of change over time (5 lectures; Ch. 10, 11)
- Linear, ordinary differential equations (ODEs)
- Systems of linear ODEs
- Discretization
[Midterm exam about here]
- Stochastic models (7 lectures; Sec. 5.3, 5.4, 6.1, 6.2)
- Motivation: modeling uncertainties
- Basics of probability
- Goodness of fit
- Markov chains
- Hidden Markov models
- Simulations (4 lectures; Sec. 5.1, 5.5)
- Deterministic simulations
- Stochastic simulations
- Optimization (5 lectures; Ch. 7, 12)
- Motivation
- Linear programming
- Unconstrained optimization
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