Mathematics for Dynamic Systems
Stage I, Course 2 · 4 credits · 14 weeks · From observation to equation
Course Purpose
Students learn to represent systems mathematically. This course transforms the qualitative systems thinking from Course 1 into the formal language that allows precise reasoning and solution.
By end: Students can choose variables for any system, write equations governing their behavior, analyze both linear and simple nonlinear systems, and use multiple representations (equations, matrices, state-space) to understand system dynamics.
Learning Outcomes
- Choose appropriate variables for a system
- Write differential and difference equations from system description
- Analyze linear systems mathematically (eigenvalues, stability)
- Understand state-space representation and matrix formulation
- Solve ODEs analytically (for simple cases) and numerically
- Analyze stability and behavior from equations
- Use multiple mathematical representations — equations, matrices, graphs
- Understand when mathematics breaks down — nonlinearity, chaos, limits
Core Concepts
variable, equation, function, differential-equation, state-space, matrix, eigenvalue, stability, equilibrium, linearity, feedback-equation, rate-of-change
Course Structure (14 weeks)
| Week | Topic | Major Assignment |
|---|---|---|
| 1-3 | Variables and functions | Define variables, write functions for systems |
| 4-5 | Equations and relationships | Write equations from system descriptions |
| 6-7 | Differential equations | Solve ODEs, analyze behavior |
| 8 | Difference equations (discrete time) | Discrete vs. continuous models |
| 9-11 | Matrices and linear systems | Matrix operations, eigenvalues, stability |
| 12 | State-space models | Reformulate systems in state-space |
| 13 | Behavior from structure | Stability analysis, prediction |
| 14 | Integration and synthesis | Major modeling project |
Prerequisites for Subsequent Courses
This course provides the mathematical foundation needed for Course 3 (NCFCA), where formal proofs and structural properties are studied, and Course 4 (Programming), where equations are implemented.
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