University Calculus III Double Integrals — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 7 definitions and 5 theorems, 7 worked examples, 3 diagrams, in 13 printable pages. This page lists what the notes cover. The notes themselves come with the University Calculus III bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Double Integrals — 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.
What you need
Also in this section: 1 note on method and common errors.
Double integrals over rectangles and iterated integrals
- Definition — Double integral over a rectangle
- Theorem — Fubini's theorem for a rectangle
- Theorem — Properties of the double integral
Also in this section: 1 worked example, 1 note on method and common errors.
Double integrals over general regions
- Definition — Type I and type II regions
- Theorem — Iterated integrals over a general region
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Reversing the order of integration
- Theorem — Changing the order of integration
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Polar coordinates and polar curves
- Definition — Polar coordinates
- Definition — Standard polar curves
- Definition — Polar region
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Double integrals in polar coordinates
- Theorem — Double integral in polar coordinates
Also in this section: 1 worked example, 1 note on method and common errors.
Area and volume by double integration
- Definition — Area and volume by double integration
Also in this section: 1 worked example, 1 note on method and common errors.
Mass and centre of mass of a lamina
- Definition — Mass and centre of mass of a lamina
Also in this section: 1 worked example, 1 note on method and common errors.
Where the notes are
The notes are one of the documents in the University Calculus III Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Double Integrals practice worksheet is free and stays free.
Every University Calculus III topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 9 University Calculus III 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.
Double Integrals practice worksheet About the Double Integrals unit test