The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.

Example 1: Circular Cylinder

Sketch the portion of the cylinder x2 + y2 = 1 where 1 ≤ z ≤ 2 (Figure 11.1.12).


Draw the curve x2 + y2 = 1 in the (x, y) plane. The curve is a circle of radius one.

11_partial_differentiation-24.gif Draw the three coordinate axes and the horizontal planes z = 1, z = 2.
11_partial_differentiation-25.gif Draw the circles x2 + y2 = 1 where the surface intersects the two planes z = 1,z = 2.


Figure 11.1.12

Complete the sketch by drawing heavy lines for all edges which would be visible on an "opaque" model of the given surface. This surface is called a circular cylinder.


Last Update: 2006-11-15