《高数双语》课件section 10.1.pptx
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1、Section 10.11Riemann,Bernhard2Mass of a Thin Rectangular Sheet MetalSuppose a thin rectangular sheet metal lieson the xOy-plane and its density is a functionthen,how(,),(,),x yf x y of the point can we find the mass of this sheet metal?To find the mass,we suppose that(,)f x yis defined on a rectangu
2、lar region given by:,.axbcydWe divide into small pieces of areaand number them in some A order 12,.nAAAkA 3Mass of a Thin Rectangular Sheet Metalin each piece(,)kkxyWe choose a point kA and form the sum1(,).nnkkkkSf xyA If f is continuous throughout,then,aswe refine the mesh(or two-dimensional piece
3、 go to zero,partition)width to make the“norm”of eachsum should have a limit and the limit shouldbe the mass of the thin rectangular steelmetal.(,)kkxykA we can expect that the01lim(,).nkkkdkSf xyA 4Volume of a Cylindrical bodycylindrical body in threedimensional space.How can we find thevolume of th
4、is body?then it can be think of aSuppose that(,)0,(,)(),zf x yx y 5Volume of a Cylindrical bodycylindrical body in threedimensional space.How can we findthe volume of this body?then it can be think of aSuppose that(,)0,(,)(),zf x yx y 6Volume of a Cylindrical bodycylindrical body in threedimensional
5、 space.How can we find thevolume of this body?then it can be think of aSuppose that(,)0,(,)(),zf x yx y 7Volume of a Cylindrical bodycylindrical body in threedimensional space.How can we find thevolume of this body?then it can be think of aSuppose that(,)0,(,)(),zf x yx y 8Volume of a Cylindrical bo
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