Unit 12 - Sections 12.5 to 12.7

Module Overview

The beginning of the study of vector-valued functions mirrors precisely the study of parametric equations. Most of the material in this week is nearly identical to what we had in the previous chapter.

Learning Outcomes

Section 12.5: Vector-valued functions are just an extension of parametric curves. In this section, we (re-)define the basics.
Section 12.6: The calculus of vector-valued functions also follows the work we did in the previous chapter.
Section 12.7: As discussed earlier, movement through space has obvious interpretations with vector-valued functions. The example video allows us to see that we have been doing math like this previously, but that our new setting makes things easier.

Type: Video Links
Title	Author	Description
Vector-Valued Functions \| Vector-Valued Functions	Shai Cohen
Vector-Valued Functions Example - Line Segments \| Vector-Valued Functions Example - Line Segments	Shai Cohen
Calculus on Vector-Valued Functions - Limits of Vector-Valued Functions \| Calculus on Vector-Valued Functions - Limits of Vector-Valued Functions	Shai Cohen
Calculus on Vector-Valued Functions - Derivatives of Vector-Valued Functions \| Calculus on Vector-Valued Functions - Derivatives of Vector-Valued Functions	Shai Cohen
Calculus on Vector-Valued Functions - The Unit Tangent Vector \| Calculus on Vector-Valued Functions - The Unit Tangent Vector	Shai Cohen
Calculus on Vector-Valued Functions - Properties of the Derivative \| Calculus on Vector-Valued Functions - Properties of the Derivative	Shai Cohen
Calculus on Vector-Valued Functions - Integrals of Vector-Valued Functions \| Calculus on Vector-Valued Functions - Integrals of Vector-Valued Functions	Shai Cohen
Calculus on Vector-Valued Functions Example - N-Dimensional Functions \| Calculus on Vector-Valued Functions Example - N-Dimensional Functions	Shai Cohen
Calculus on Vector-Valued Functions Example - Derivatives and the Unity Tangent Vector \| Calculus on Vector-Valued Functions Example - Derivatives and the Unity Tangent Vector	Shai Cohen
Motion in Space Example - New Related Rates Problems \| Motion in Space Example - New Related Rates Problems	Shai Cohen