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
Location in space is represented using an ordered triple: [math]\left(x,y,z\right)[/math]. [br][br]This applet illustrates how we plot various points in 3-space.
Quick (Silent) Demo
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.