University Calculus III Surface Integrals and Integral Theorems — 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, 6 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.
Surface Integrals and Integral Theorems — 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.
Parametric surfaces
- Definition — Parametric surface
- Theorem — Tangent vectors and the normal vector
- Definition — Standard parametrizations
Also in this section: 1 worked example, 1 note on method and common errors.
Surface area
- Theorem — Surface area of a parametric surface
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Surface integrals of scalar functions
- Definition — Surface integral of a scalar function
- Definition — Mass and average value on a surface
Also in this section: 1 worked example, 1 note on method and common errors.
Flux integrals of vector fields
- Definition — Orientation of a surface
- Definition — Flux of a vector field across a surface
Also in this section: 1 worked example, 1 note on method and common errors.
Stokes' theorem
- Definition — Positive orientation of the boundary
- Theorem — Stokes' theorem
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
The divergence theorem
- Theorem — The divergence theorem
- Theorem — Divergence as outflow per unit volume
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 Surface Integrals and Integral Theorems 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.
Surface Integrals and Integral Theorems practice worksheet About the Surface Integrals and Integral Theorems unit test