MATH-15 · Undergraduate · ENGLISH · PLANNED
Build the picture, explain the rule, work an example, then justify it.
Study time is an initial activity estimate, excluding extra reading, revision and extended laboratory or project work. Videos and question bodies have not been produced by adding this outline.
Complete these courses or demonstrate equivalent knowledge. These are recommended prerequisites, not enforced enrolment locks.
YouTube playlist: ARK Mathematics | Differential Equations and Dynamical Systems
Playlist title reserved in the plan; no YouTube playlist or upload has been created yet.
Sign in to save this learning pathPractical outcome: Fit and critique a cooling model.
Explain separable equations using a visual and one worked real-world example. Context: Fit and critique a cooling model. End with a prediction or check-for-understanding.
Explain first-order linear equations using a visual and one worked real-world example. Context: Fit and critique a cooling model. End with a prediction or check-for-understanding.
Explain integrating factors using a visual and one worked real-world example. Context: Fit and critique a cooling model. End with a prediction or check-for-understanding.
Explain existence and uniqueness using a visual and one worked real-world example. Context: Fit and critique a cooling model. End with a prediction or check-for-understanding.
Use the first concepts from this section. Fit and critique a cooling model. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain second-order homogeneous equations using a visual and one worked real-world example. Context: Fit and critique a cooling model. End with a prediction or check-for-understanding.
Explain forced oscillators using a visual and one worked real-world example. Context: Fit and critique a cooling model. End with a prediction or check-for-understanding.
Explain undetermined coefficients using a visual and one worked real-world example. Context: Fit and critique a cooling model. End with a prediction or check-for-understanding.
Explain variation of parameters using a visual and one worked real-world example. Context: Fit and critique a cooling model. End with a prediction or check-for-understanding.
Fit and critique a cooling model. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Separable equations, First-order linear equations, Integrating factors and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Compare stable and unstable feedback models.
Explain linear differential systems using a visual and one worked real-world example. Context: Compare stable and unstable feedback models. End with a prediction or check-for-understanding.
Explain phase portraits using a visual and one worked real-world example. Context: Compare stable and unstable feedback models. End with a prediction or check-for-understanding.
Explain equilibria using a visual and one worked real-world example. Context: Compare stable and unstable feedback models. End with a prediction or check-for-understanding.
Explain stability using a visual and one worked real-world example. Context: Compare stable and unstable feedback models. End with a prediction or check-for-understanding.
Use the first concepts from this section. Compare stable and unstable feedback models. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain laplace transform using a visual and one worked real-world example. Context: Compare stable and unstable feedback models. End with a prediction or check-for-understanding.
Explain inverse laplace transform using a visual and one worked real-world example. Context: Compare stable and unstable feedback models. End with a prediction or check-for-understanding.
Explain impulse response using a visual and one worked real-world example. Context: Compare stable and unstable feedback models. End with a prediction or check-for-understanding.
Explain convolution using a visual and one worked real-world example. Context: Compare stable and unstable feedback models. End with a prediction or check-for-understanding.
Compare stable and unstable feedback models. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Linear differential systems, Phase portraits, Equilibria and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Simulate a population model and test step-size sensitivity.
Explain logistic equation using a visual and one worked real-world example. Context: Simulate a population model and test step-size sensitivity. End with a prediction or check-for-understanding.
Explain linearisation using a visual and one worked real-world example. Context: Simulate a population model and test step-size sensitivity. End with a prediction or check-for-understanding.
Explain bifurcations using a visual and one worked real-world example. Context: Simulate a population model and test step-size sensitivity. End with a prediction or check-for-understanding.
Explain limit cycles using a visual and one worked real-world example. Context: Simulate a population model and test step-size sensitivity. End with a prediction or check-for-understanding.
Use the first concepts from this section. Simulate a population model and test step-size sensitivity. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain euler method using a visual and one worked real-world example. Context: Simulate a population model and test step-size sensitivity. End with a prediction or check-for-understanding.
Explain runge-kutta methods using a visual and one worked real-world example. Context: Simulate a population model and test step-size sensitivity. End with a prediction or check-for-understanding.
Explain stiffness using a visual and one worked real-world example. Context: Simulate a population model and test step-size sensitivity. End with a prediction or check-for-understanding.
Explain sensitive dependence using a visual and one worked real-world example. Context: Simulate a population model and test step-size sensitivity. End with a prediction or check-for-understanding.
Simulate a population model and test step-size sensitivity. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Logistic equation, Linearisation, Bifurcations and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Combine all three sections: Simulate a population model and test step-size sensitivity. Submit an original worked artifact, evidence or tests, assumptions and a reflection. Rubric: correctness, method, practical usefulness, reproducibility and communication. Self-reviewed, not certified.
6–12 balanced questions sampling every section of Differential Equations and Dynamical Systems, including interpretation, calculation or reasoning, a misconception and a new application. Passing is 70%; review errors before retrying.
Visual constructions, worked problems and proofs. Guided work leads to an independent attempt, with a diagram, explanation, trace, calculation or tested artifact. Question bodies are generated when opened in your private learning path. Programming submissions are stored as text; the platform does not execute submitted code.
Use original or appropriately licensed datasets. Practical science activities use models or supplied data unless a qualified supervisor has reviewed a physical experiment.
Open the interactive practice sampler →