Theoria
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Immutable package version

publiccourseMCF 1.1

Ordinary Differential Equations 0.2.0

Published by @apv on August 12, 2026.

Source checksum
39ae8d054c1562e19f63e5bd166e4f902ea1632b2f82b586e8b05a6924c3a9bd
Package size
449.3 KiB
Validation
valid · 0 diagnostics
Manifest ID
courses.theoria.polytechnical.ordinary-differential-equations
Manifest version
0.2.0
Entry
undefined
Language
en-CA
License
CC-BY-4.0
Authors
APV, Theoria
Subjects
mathematics, ordinary differential equations, dynamical systems, applied mathematics, numerical methods
Level
intermediate
Structure
33 lessons · 57 activities · 168 questions

Learning outcomes

  1. Derive ODEs and state-space systems from rate laws, mechanics, balances, and interacting-state assumptions.
  2. Solve separable, first-order linear, second-order constant-coefficient, forced, Laplace-domain, and eigenvalue-system IVPs.
  3. Use slope fields, phase lines, phase portraits, equilibria, linearization, and bifurcation reasoning to predict dynamics.
  4. Classify scalar and planar stability from derivative signs, characteristic roots, eigenvalues, and numerical amplification.
  5. Analyse transients, steady-state forcing, resonance, step inputs, impulses, and transfer-style responses.
  6. Implement Euler and RK4, measure convergence/error, recognize stability restrictions, and compare analytic/numerical trajectories.
  7. Verify ODE results through substitution, units, limiting cases, exact benchmarks, invariants, and qualitative structure.

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