One-Dimensional Dynamical Systems
Reference: Logan, A First Course in Differential Equations, 3rd ed., §1.5 "One-Dimensional Dynamical Systems", pp. 54-78
Textbook Reference
| Primary source | Logan, A First Course in Differential Equations, 3rd ed., §1.5 “One-Dimensional Dynamical Systems”, pp. 54-78 |
| Read this week | Week 3 of the quarter: pages 54 to 78 |
Bring your copy of Logan to this topic. The section and pages above are the exact reading for this skill.
Objectives
By the end of this section you should be able to:
- Write an autonomous equation in the standard form x prime equals f of x and find its equilibria
- Draw the phase line and read the direction of motion between equilibria
- Classify each equilibrium as stable or unstable from the sign of f prime at that point
- Read the logistic equation and a falling body as one-dimensional dynamical systems
Prerequisite Check
Before this section, make sure you are comfortable with:
- Solving a simple first-order equation by separation
- Computing a derivative and reading its sign
- Sketching the sign of a function
Status
A guided stub for now. Above you have the exact Logan reading with page numbers, the week it lands in the quarter, the learning targets, and what to review first. The full worked examples and the leveled practice set for this section are being written and will appear here.