Calculus 3: Multivariable Calculus
Contains dynamic resources that help illustrate concepts students in a Multivariable Calculus (Calculus 3) course often encounter.
Table of Contents
- 3D Coordinate Systems
- Plotting Points in 3D: Dynamic Illustrator
- 3D BATTLESHIP !!!
- Cylindrical Coordinates: Dynamic Illustrator
- Spherical Coordinates: Dynamic Illustrator
- Partial Derivatives
- Partial Derivatives: Graphical Illustrator
- Quadric (and Other) Surfaces
- Sphere Investigation
- Circular Paraboloid of Revolution
- Animation 111
- Special Spheroid Action: Locus Illustration
- Animation 112
- Special Hyperboloid of 1 Sheet as a Locus
- Special Hyperboloid of 2 Sheets as a Locus
- Catenoid
Plotting Points in 3D: Dynamic Illustrator
[size=150]Location in space is represented using an ordered triple: [math]\left(x,y,z\right)[/math]. [br]This app illustrates how we plot various points in 3-space. [/size]
To move the point up and down (parallel to the zAxis), click on it first before dragging it up and down. Click it again to move it around at the same level above or below the grid.
Partial Derivatives: Graphical Illustrator
You can enter your own multivariable function in the input box at bottom right.[br][b][br][color=#1e84cc]To explore in Augmented Reality, see the directions below the applet. [/color][/b]
TO EXPLORE IN GEOGEBRA AUGMENTED REALITY:
1) Open up GeoGebra 3D app on your device. [br][br]2) Go to MENU (3 horizontal bars in upper left hand corner). [br][br]3) Select OPEN. Under search, type: [b]fgzyyx8x[/b][br][br]4) The sliders [b]a & b[/b] control the [b]x & y[/b] coordinates of the point (respectively).[br] You will also see [b]FILLING sliders [/b]to fill in the surface itself or the tangent plane. [br][br]5) To switch from partial derivative with respect to [i]x[/i] and partial derivative with respect to [i]y[/i], [br] adjust the slider named [b]whichpartialderiv [/b]at the bottom of the algebra pane.
Sphere Investigation
TO EXPLORE IN AUGMENTED REALITY:
1) Open GeoGebra 3D app on your device. [br][br]2) Press the 3 horizontal bars (upper left corner). Select OPEN. [br][br]3) In the SEARCH TAB that appears, type [b]D4hmNy9M[/b][br] Note this string of characters can be found in the URL here. [br] Be sure to either copy & paste this code or type it just the way you see it here. [br][br]4) The slider named [b]i[/b] does the animation.[br] [color=#ff7700]Slider [b]e[/b] alters the opacity (shading of the sphere)[/color]. [br] You can move the white point on the sphere to change its radius when in 3D view.