University Calculus III Triple Integrals and Change of Variables — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 5 definitions and 6 theorems, 6 worked examples, 3 diagrams, in 14 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.
Triple Integrals and Change of Variables — what the notes cover
7 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.
Triple Integrals in Cartesian Coordinates
- Definition — Triple integral
- Theorem — Fubini's theorem for a box
Also in this section: 1 worked example, 1 note on method and common errors.
Setting Up the Limits for a Solid Region
- Theorem — Integral over a simple solid
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Triple Integrals in Cylindrical Coordinates
- Definition — Cylindrical coordinates
- Theorem — Triple integral in cylindrical coordinates
Also in this section: 1 worked example, 1 note on method and common errors.
Triple Integrals in Spherical Coordinates
- Definition — Spherical coordinates
- Theorem — Triple integral in spherical coordinates
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Volume, Mass and Centre of Mass of a Solid
- Definition — Mass and centre of mass
- Theorem — Symmetry and the centre of mass
Also in this section: 1 worked example, 1 note on method and common errors.
The Jacobian and Change of Variables
- Definition — Jacobian
- Theorem — Change of variables in a double integral
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 Calculus III Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Triple Integrals and Change of Variables 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.
Triple Integrals and Change of Variables practice worksheet About the Triple Integrals and Change of Variables unit test