二重积分（double integral）.doc

二重积分（double integral） In 1 Riemann - mathematician In the first section, the concepts and properties of double integral In the second section of double integral calculation Definition of double integral concept and nature in the 2. in the 2. double integral concept and property concept and nature in the 1. 1. in the introduction of the concept and properties of double integral double integral double integral in the application of 26.1 6.1 third day double integral of the introduction of the double integral The concept and properties of the double integral in 3. in 3. of the 3, 6.1 double integral double integral with a stereo its bottom is xOy plane bounded closed region D is side boundary in C region of the D bus line and parallel to the Z axis of the cylinder (L line parallel to the line and move along the fixed curve C of a track called C called cylindrical fixed curve linear cylinder alignment L called cylinder bus) on top of it is a continuous function of two variables (x, y) z=f expressed by surface and And f (x, y) = 0 this stereo called cylinder (page 6.1.1 Two) practical problems now require the volume.1. the cylinder into the double integral (1) cylinder volume 4 6.1.15 flat column is high with the formula v = constant apparatus can its size (height * bottom area) calculation. But the cylinder top is a curved the height of z=f (x, y) is a variable the volume can not be directly from the above formula. But in z=f (x, y) D is a continuous function on the and bottom area and small cases its height is small change the cylinder approximately as flat cylinder. Therefore of cylinder we can be similar to the area for curved trapezoid with segmentation, approximate, summing and limit The method for its size. The specific measures are as follows: 6 first with a group of D curve network will be divided into n small closed area... , and small closed area is recorded as... Respectively to these small closed area The boundary curve line for cylindrical parallel to the Z