Ordinary Differential Equations

Learning outcomes

What learners can expect

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.