二重积分毕业论文

我不太清楚你问的，如果是图里最后一项为何为零，你考虑对称，或者你算也是零啊

国内：现如今二重积分基础理论的研究已经相当成熟，在实际应用中的研究还比较少，任何一门学问在历史发展过程中都会与时俱进，所以二重积分的发展趋势会在现有的基础上日益完善，尤其是在物理学、经济学等应用方面的研究会越来越深入，整个微积分体系会越来越完备

开题报告主要是“泛泛而谈”，你的题目要介绍二重积分的起源发展，重要意义，简略的介绍下二重积分的一些算法，不用具体介绍算法，再稍微介绍点应用方面的知识，都只需简略的介绍。

The second surface integral calculation is a difficulty and key content of higher mathematics. The second curved surface integral, also known as sitting target surface integral, it said the physical significance of the steady flow of incompressible fluid flow to the surface side of the flow. The second kind of surface integral calculation problem is a comprehensive calculus problem, involves the surface side and the normal vector, partial derivative of function of many variables, double integral and triple integrals, the first kind of curved surface integral and gauss formula, and other article, we respectively from two traditional calculation method and an innovative method to calculate the direction of generalizations about the second type of surface integral calculation method, and combined with typical examples illustrate the use of different methods, easy to master by the techniques of.

D : x^2+y^2 ≤ 4, 积分域既对称于 x 轴， 又对称于 y 轴，则 x, y 的奇函数积分为 0，二重积分I = ∫∫(x-2y)^2dxdy = ∫∫(x^2-4xy+4y^2)dxdy= ∫∫(x^2+4y^2)dxdy = ∫<0, 2π>dt∫<0, 2>r^3[(cost)^2+4(sint)^2]dr= ∫<0, 2π>[1+3(sint)^2]dt∫<0, 2>r^3dr= 4∫<0, 2π>[5/2-(3/2)cos2t]dt = 4[5t/2-(3/4)sin2t]<0, 2π> = 20π