Systems of Differential Equations
Students analyze systems of linear differential equations and their phase portraits. They use eigenvalues and eigenvectors to determine the nature of critical points.
About This Topic
Students analyze systems of linear differential equations and their phase portraits. They use eigenvalues and eigenvectors to determine the nature of critical points.
Key Questions
- How do eigenvalues determine the stability of a system of DEs?
- What information does a phase portrait provide?
- How can systems of DEs model interacting populations?
Active Learning Ideas
See all activities→Activities & Teaching Strategies
See all activities
Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
More in Differential Equations and Mathematical Modelling
First-Order Differential Equations
Students solve complex first-order differential equations using integrating factors and substitution methods. They analyze the stability of equilibrium solutions.
8 methodologies
Second-Order Linear Differential Equations
This topic covers homogeneous and non-homogeneous second-order linear differential equations with constant coefficients. Students explore applications in physics, such as damped harmonic motion.
8 methodologies
Advanced Mathematical Modelling
Students synthesize their knowledge to construct, refine, and critique mathematical models of complex real-world phenomena. They evaluate the assumptions and limitations of their models.
8 methodologies