# Visualizing Functions of Two Variables

*This Applet can be used to Visualizing Functions of Two Variables onto its xy-projection .*__Here are explored__:

*-*__E__

__xtrema 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.***E**

**xplicit 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.*

*-***of the function y=f(x,y) and its projection onto the x-y plane.**__Critical points__*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

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