University Differential Equations Modelling with First-Order Equations — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 6 definitions and 5 theorems, 5 worked examples, 3 diagrams, in 14 printable pages. This page lists what the notes cover. The notes themselves come with the University Differential Equations bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Modelling with First-Order Equations — what the notes cover
6 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.
What you need
Also in this section: 1 note on method and common errors.
Translating a rate statement into a differential equation
- Definition — Balance law for a changing quantity
- Theorem — Four standard rate laws
- Definition — Equilibrium solution and the long-run level
Also in this section: 1 worked example, 1 note on method and common errors.
Newton's law of cooling and heating
- Definition — Newton's law of cooling
- Theorem — Cooling towards constant surroundings
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Mixing with unequal flow rates
- Definition — Mixing model with unequal flow rates
- Theorem — Solving the mixing equation
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
First-order electric circuits
- Definition — Series RL and RC circuit equations
- Theorem — Response to a constant source
Also in this section: 1 worked example, 1 note on method and common errors.
The logistic equation
- Definition — The logistic equation
- Theorem — The logistic solution
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Where the notes are
The notes are one of the documents in the University Differential Equations Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Modelling with First-Order Equations practice worksheet is free and stays free.
Every University Differential Equations topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 9 University Differential Equations 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.
Modelling with First-Order Equations practice worksheet About the Modelling with First-Order Equations unit test