AP Calculus AB Differential Equations — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 12 definitions and 4 theorems, 5 worked examples, 4 diagrams, in 13 printable pages. This page lists what the notes cover. The notes themselves come with the AP Calculus AB bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Differential Equations — what the notes cover
8 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.
Also in this section: 1 note on method and common errors.
What you need
Also in this section: 1 note on method and common errors.
Turning a situation into an equation (topic 7.1)
- Definition — Differential equation
- Definition — Constant of proportionality
Also in this section: 1 worked example.
Verifying a proposed solution (topic 7.2)
- Definition — Solution of a differential equation
Also in this section: 1 worked example.
Slope fields (topic 7.3)
- Definition — Slope field
- Theorem — One solution curve through each point
Also in this section: 1 diagram.
Reading a field: equilibrium and stability (topic 7.4)
- Definition — Equilibrium solution
- Theorem — Monotone and bounded
- Definition — Stable and unstable equilibrium
Also in this section: 1 worked example, 1 diagram.
Separation of variables (topic 7.6)
- Definition — Separable differential equation
- Definition — General solution
- Definition — Singular solution
Also in this section: 1 note on method and common errors.
Particular solutions (topic 7.7)
- Definition — Initial condition
- Definition — Particular solution
- Theorem — The initial condition fixes the branch
Also in this section: 1 worked example, 2 notes on method and common errors, 1 diagram.
Exponential models (topic 7.8)
- Theorem — Exponential change
- Definition — Relative rate of change
Also in this section: 1 worked example, 1 diagram.
Where the notes are
The notes are one of the documents in the AP Calculus AB Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Differential Equations practice worksheet is free and stays free.
Every AP Calculus AB topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 8 AP Calculus AB units: the worksheet, the reference notes, the challenge set, the unit test and every answer key — these notes included.
- Worked solutions, not answer lists — every step written out
- Covers the whole year's program at this level
- Less than the price of one hour of tutoring — for the entire year's solutions
Practise it, then test yourself
Notes on their own do not make anything stick. This unit has a free, printable practice worksheet, and an end-of-unit test that comes with the bundle.
Differential Equations practice worksheet About the Differential Equations unit test