University Calculus III Vector Fields and Line 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 7 theorems, 7 worked examples, 4 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.
Vector Fields and Line 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.
Vector fields
- Definition — Vector field
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Line integrals of scalar functions
- Definition — Line integral with respect to arc length
- Definition — Mass and centre of mass of a wire
Also in this section: 1 worked example, 1 note on method and common errors.
Line integrals of vector fields and work
- Definition — Line integral of a vector field
- Theorem — Direction and pieces
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Conservative fields and potential functions
- Definition — Conservative field and potential function
- Theorem — Tests for a conservative field
Also in this section: 1 worked example, 1 note on method and common errors.
The fundamental theorem for line integrals
- Theorem — Fundamental theorem for line integrals
- Theorem — Path independence
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Green's theorem
- Definition — Positive orientation
- Theorem — Green's theorem
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Curl and divergence
- Definition — Divergence and curl
- Theorem — Curl and conservative fields
- Theorem — Vector forms of Green's theorem
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 Vector Fields and Line 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.
Vector Fields and Line Integrals practice worksheet About the Vector Fields and Line Integrals unit test