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CalcVR Supplemental Materials
Jeremy Becnel, Nicholas Long
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Front Matter
Acknowledgements
Calculus in Virtual Reality
1
Two Dimensional Preliminaries
1.1
Parametric Equations
1.1.1
Curves
1.1.1
Pre-class Activity on Parametric Equations in 2D
1.1.2
Circles
1.2
Derivatives of Parametric Equations
1.2.1
Derivatives of Parametric Equations
1.3
Parametric Equations of Ellipses
1.3.1
Ellipse Parametric Equation
1.4
Rectangular Regions and Inequalities
1.4.1
Inequalities for Function
1.4.2
Implicit Equations and Inequalities
1.4.3
Exercises
1.5
Polar Points and Regions
1.5.1
Polar Coordinates
2
Three Dimensional Coordinates
2.1
Rectangular 3D Coordinates
2.1.1
Rectangular Coordinates in Three Dimensions
2.1.2
Comments to Instructors
2.2
Cylindrical 3D Coordinates
2.2.1
Cylindrical Coordinate Measurements
2.2.2
Cylindrical Coordinates: Surfaces and Regions
2.2.2
Practice Graphs with Cylindrical Coordinates
2.3
Spherical Coordinates
2.3.1
Spherical Coordinate Measurements
2.3.2
Spherical Coordinates: Surfaces and Regions
2.3.2
Practice Graphs with Spherical Coordinates
2.4
Quiz on Vectors in 3D
2.5
3D Coordinate Playground
2.5.1
Controls and Options Coordinate Measurement Playground
2.5.2
Controls and Options for Constant Coordinate Graph Playground
3
Basic Graphs in 3D
3.1
Coordinates and Graphs in 3D
3.1.1
Comments to Instructors
3.2
Graphs in 3D
3.2.1
Fundamental Planes in 3D
3.2.2
More Fundamental Planes and Graphs
3.3
Lines in Space
3.3.1
Lines in Space
3.3.2
Lines in Space Quiz
3.4
Planes in Space
3.4.1
Planes in Three Dimensions
3.4.2
Exercises
3.4.3
Intersecting planes
3.4.4
Exercises
3.4.5
Planes Quiz
3.5
Cylinder Surfaces
3.5.1
CalcVR Lesson on Cylinder Surfaces
3.5.2
Comments to Instructors
3.6
Quadric Surfaces Demo
3.6.1
Selecting a Surface
3.6.2
Changing Parameters
3.6.3
Viewing Level Curves
3.6.4
Turning Level Curves of a Quadric Surfaces On/Off
3.7
Quadric Surface Explorations
4
Parameterizations of Curves and Surfaces
4.1
Parameterizations of Curves in Space
4.1.1
Parametric Curves in Space
4.2
Parameterizations of Surfaces in Space
4.2.1
Parametric Surfaces in Space
4.3
Graph Transformations and Parameterizations
4.3.1
Transformations in Graphs and Parameterizations
4.4
Surface Graphing Playground
4.4.1
Entering Parametric Equations for Surface
4.4.2
Loading and Saving Parametric Equations/Functions
4.4.3
Rotating
5
Vector Valued Functions of One Variable
5.1
Plotting Vector Valued Functions of One Variable
5.1.1
Non-Uniqueness of Parameterizations
5.2
The Velocity Vector
5.2.1
The Velocity Vector
5.3
Speed
5.3.1
Speed Explorations
5.4
Arc Length
5.4.1
Arc Length
5.5
Acceleration
5.5.1
The Acceleration Vector
5.6
The Unit Tangent Vector
5.6.1
The Unit Tangent Vector
5.7
The Unit Normal Vector
5.7.1
Unit Normal and Unit Tangent Vector Activities
5.8
Splitting the Acceleration Vector
5.8.1
Acceleration Components
5.8.1
Exercises
5.9
Curvature
5.9.1
Curvature Activities
5.10
Binormal Vector
5.10.1
The Binormal Vector
5.11
Vector Valued Function Quiz
5.12
Vector Valued Function Playground
5.12.1
Tracing the Curve
5.12.2
Displaying Vectors
5.12.3
Displaying Osculating Circle
5.12.4
Tracing and Viewing Speed, Curvature, and Arc Length Graphs
5.12.5
Entering Functions
5.12.6
Loading and Saving Parametric Equations
6
Multivariable Functions
6.1
Graphs and Properties of Multivariable Functions
6.1.1
Domain and Range
6.1.2
Exercises
6.1.3
MVF: Tables and Graphs
6.2
Change and Slopes on Non-vertical Planes
6.2.1
Vertical Change on a Plane
6.3
Sections on MVF and Contour Plots
6.3.1
Sections on Graphs of Multivariable Functions
6.3.2
Contours and Level Curves
6.3.3
Exercises
6.4
Limits and Continuity of Multivariable Functions
6.4.1
Paths on Multivariable Functions
6.4.2
Limits Multivariable Functions Not Existing
6.5
Partial Derivatives
6.5.1
Connection to Vector Valued Functions
6.6
Local Linearity and Tangent Planes
6.6.1
Local Linearity
6.6.2
Tangent Planes
6.6.3
Total Differential
6.7
Directional Derivatives
6.7.1
Connection to Vector Valued Functions
6.8
Gradients
6.8.1
Exploring the Geometry Connected to the Gradient
6.8.2
Exercises
6.9
Second Partial Derivatives
6.10
Extrema of Multivariable Functions
6.10.1
Identifying Extrema Using Contour Plots
6.11
Extrema on Compact Regions
6.11.1
Contour Plots and Extrema on the Boundary of a Region
6.12
Multivariable Function and Contour Playground
6.12.1
Entering Functions and Parametric Equations
6.12.2
Loading and Saving Parametric Equations/Functions
6.12.3
Displaying Contours
6.12.4
Gradients
7
Multiple Integration
7.1
A Chapter on Multiple Integration
8
Vector Fields
8.1
Plotting Vector Fields
8.1.1
Lesson on Plotting of Vector Fields
8.2
The Curl of Vector Fields
8.3
The Divergence of a Vector Field
8.4
Interactive Playground for Visualizing Vector Fields
8.4.1
Entering Vector Field Equations
8.4.2
Loading and Saving Vector Fields
8.4.3
Examining Particular Vectors
8.4.4
Vector Field Display Options
9
Vector Calculus
9.1
Line Integrals of Scalar Functions
9.2
Line Integrals of Vector Fields
9.3
Surface Integrals of Scalar Functions
Back Matter
A
Common Elements in
CalcVR
A.1
CalcVR Menu
A.1.1
Topics
A.1.2
Lessons, Quizzes, Playgrounds, etc.
A.1.3
Bluetooth Menu
A.2
Tutorial
A.3
Graphics Control Panel
A.4
Lesson Control Panel
A.5
Bottom Menu
A.5.1
Main Menu
A.5.2
Settings Menu
A.6
Keyboard
A.6.1
Using Controller
A.6.2
Without Controller
A.7
Sliders
Section
7.1
A Chapter on Multiple Integration
Coming soon in the
CalcVR
app and Supplmental Materials!
