HUNTERTUTORING

Study Guide — First-order and planar systems

View PDF →

Dynamical systems

Undergraduate study guide for First-order and planar systems.

What this standard means

  • Autonomous ODEs; equilibrium points and phase lines
  • Bifurcations in one-dimensional systems (saddle-node, transcritical)
  • Planar linear systems: classification via eigenvalues
  • Phase plane analysis and nullclines
  • Liapunov functions (introduction)

_See printable PDF for diagram._

How to use the 20 practice sets

| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |

Pacing: 10–15 minutes per session.

How to practice

1. Define variables with units 2. Check that answers are reasonable 3. Separate setup from computation

_See printable PDF for diagram._

Common mistakes

  • Unit errors
  • Solving without interpreting parameters

Review and practice tests

1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for First-order and planar systems.

  • [ ] Builds models from context
  • [ ] Solves standard applied problems
  • [ ] Interprets solutions with units

Materials for this standard

  • Practice Problems — 20 printable sets
  • Review — 10 difficulty levels
  • Practice Test — 10 difficulty levels
  • Answer key — for parents and tutors

For your personal study only. Copying, printing, screenshotting, or sharing this material is not permitted and may result in loss of access.

Back to unit