Visualizing Functions of Two Variables
This Applet can be used to Visualizing Functions of Two Variables onto its xy-projection . Here are explored:
-Extrema lines. Points of intersection of these lines are critical points.
-Two methods of drawing contour lines:
Implicit method. In this case colours of painting are dependent on the heights with respect to the x-y Plane. Lines of the same color are contour lines -similar to the lines of equal thickness in Optical Interference. You can use the "Frequency" parameter to adjust the distance between the lines. Increasing the frequency, you can examine in more details the functions region with small changes of coordinates z.
Explicit method. In this case contour lines are drawn directly on a x-y Plane. Both methods can be used for all points in x-y Plane and for a small area near the selected point.
-Critical points of the function y=f(x,y) and its projection onto the x-y plane.
Attention: You can download the applet to your computer and Java applet will run faster.
1. Slope Feld, level Curve, Critical Points
2. 3D Surface, level curve, critical Points
3. Extrema lines and Critical points
4. Contour lines in x-y Plane-Implicit Method
5. Extrema, Contour lines in x-y Plane-Implicit Method
6. Extrema, Contour lines in x-y Plane-Implicit Method, Critical Points
7. Contour lines in x-y Plane- Implicit Method with local additions
8. Contour lines in x-y Plane- Implicit Method with local additions, Critical Points
9. Level Curve
10. Contour lines in x-y Plane- Explicit Method
11. Contour lines in x-y Plane- Explicit Method with local additions
12 Contour lines- two Methods
