University Calculus III Vector Functions and Space Curves — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 9 definitions and 4 theorems, 7 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.
Vector Functions and Space Curves — 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.
Parametric curves in the plane and in space
- Definition — Parametric curve
- Definition — Standard parametrizations
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Vector functions and their limits
- Definition — Vector function
- Definition — Limit and continuity of a vector function
Also in this section: 1 worked example, 1 note on method and common errors.
Derivatives and integrals of vector functions
- Definition — Derivative and integral of a vector function
- Theorem — Differentiation rules
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Tangent lines to a space curve
- Definition — Unit tangent and tangent line
Also in this section: 1 worked example, 1 note on method and common errors.
Arc length of a space curve
- Theorem — Arc length
- Definition — Arc length function
Also in this section: 1 worked example, 1 note on method and common errors.
Curvature
- Definition — Curvature
- Theorem — Computing curvature
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Velocity and acceleration along a curve
- Definition — Velocity, speed and acceleration
- Theorem — Motion from acceleration
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 Functions and Space Curves 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 Functions and Space Curves practice worksheet About the Vector Functions and Space Curves unit test