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Home Partial Differentiation Surfaces Examples Example 3: Elliptic Paraboloid
 
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Example 3: Elliptic Paraboloid

Sketch the part of the surface

z = x2 + y2

where

- 1 ≤ z ≤ 1.

This is an elliptic paraboloid (Figure 11.1.15).

11_partial_differentiation-29.gif

Draw the topographic map. The level curves are circles.

11_partial_differentiation-30.gif

Draw the axes and the planes z = - 1, z = 1.

11_partial_differentiation-31.gif

Draw the intersections of the surface with the planes z = - 1, z = 1 and also the planes x = 0 and y = 0.

z = - 1: No intersection. z = 1: The circle x2 + y2 = 1. x = 0: The parabola z = y2. y = 0: The parabola z = x2.

11_partial_differentiation-32.gif

Figure 11.1.15

Complete the figure with heavy lines for visible edges.

 
Home Partial Differentiation Surfaces Examples Example 3: Elliptic Paraboloid

Last Update: 2006-11-15