Diff. Equations·Course
Differential Equations
Differential equations: first- and second-order ODEs, systems, PDEs, and applications in physics and engineering
6
Modules
18
Articles
~2 h
Reading
IV
CLOs
§ 01 — Curriculum
6 modules.
Each module is a small unit. Most read in sequence — but a determined reader can begin anywhere.
- M IFirst-Order ODEsSolution methods, singular solutions, geometric interpretation3 articles
18 minBegin → - M IIPicard’s TheoremExistence and uniqueness of solutions, continuation of solutions3 articles
18 minBegin → - M IIIHigher-Order Linear ODEsFundamental system of solutions, Wronskian, method of variation of parameters3 articles
18 minBegin → - M IVSystems of ODEsMatrix method, Wronskian, fundamental matrix3 articles
18 minBegin → - M VPhase Portrait and Critical PointsClassification of critical points, stability, limit cycles3 articles
18 minBegin → - M VILyapunov Stability TheoryLyapunov stability, Lyapunov functions, bifurcations3 articles
18 minBegin →
§ 02 — Learning outcomes
4 outcomes.
CLO I
First-Order ODEs
Solve separable equations, linear first-order ODEs, and the Bernoulli equation
CLO II
Higher-Order ODEs
Solve linear ODEs with constant coefficients using the method of variation of parameters
CLO III
Systems of ODEs
Study systems of ODEs, phase portraits, and stability
CLO IV
Partial Differential Equations
Solve fundamental equations of mathematical physics by the method of separation of variables
§ 03 — Practices