# of Controlled Variables/
# of Controlling Variables Traditional Method of Visualization |
1 | 2 | 3 | ... | 6 |
1 | Precalculus
Calculus I&II Graphs of functions |
Calc. III
Graphs of Parametric and Vector Curves in the plane- Trace and image |
Calc. III
Graphs of Parametric and Vector Curves in space- Trace and image |
Adv. Calc.
Vector Calc. |
|
2 | Calculus III
Level Curves Graph of Function |
Linear Algebra
Vector Calc. Transformation (mapping) Figure |
Calc. III
Vector Calc. Graph of parametric Surfaces in space |
Adv. Calc. | |
3 | Calculus III
Level Surfaces |
Linear Algebra
Transformation (mapping) Figure |
Linear Algebra
Transformation (mapping) Figure |
Adv. Calc. | |
... | Adv. Calc.
Vector Calc. |
Adv. Calc. | Adv. Calc. | ||
7 | Music (Guitar) |
# of Controlled Variables/
# of Controlling Variables Traditional Method of Visualization |
1 | 2 | 3 | ... | 6 |
1 | Velocity
Slope of Tangents |
Velocity Vector
Tangent Vector |
Velocity Vector
Tangent Vector |
||
2 | The Gradient
Tangent Plane |
The Jacobian (?) | The Tangent Plane | ||
3 | The tangent plane to a level surface |
|
|||
... | |||||
6 | ? |
Familiar experiences with many variables: