{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Finding the surface area" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "restart;with(plots): with (linalg):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Problem: Find the su rface area of a sphere of radius a:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "x:=(u,v)->a*sin(u)*cos(v);y:=(u,v)->a*sin(u)*sin(v);z :=(u,v)->a*cos(u);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "plot3 d(subs(a=1,[x(u,v),y(u,v),z(u,v)]),u=0..Pi,v=0..2*Pi,axes=boxed);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "r:=(u,v)->[x(u,v),y(u,v),z(u ,v)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "r_u:=(u,v)->diff(r (u,v),u);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "r_v:=(u,v)->di ff(r(u,v),v);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "cross:=cro ssprod(r_u(u,v),r_v(u,v));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "F0:=sqrt(dotprod(cross,cross,`orthogonal`));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "F:=simplify(F0); " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 30 "Int(Int(F,u=0..Pi),v=0..2*Pi);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 30 "int(int(F,u=0..Pi),v=0..2*Pi);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "restart;with(plots): with(linalg):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 47 "Problem: Find the surface area of an ellipsoid." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "x :=(u,v)->a*cos(u)*sin(v);y:=(u,v)->b*sin(u)*sin(v);z:=(u,v)->c*cos(v); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "plot3d(subs(a=1,b=1,c=2 ,[x(u,v),y(u,v),z(u,v)]),u=0..2*Pi,v=0..Pi,axes=boxed,scaling=constrai ned);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "r:=(u,v)->[x(u,v), y(u,v),z(u,v)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "r_u:=(u, v)->diff(r(u,v),u);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "r_v: =(u,v)->diff(r(u,v),v);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " cross:=crossprod(r_u(u,v),r_v(u,v));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "F0:=sqrt(dotprod(cross,cross,`orthogonal`));" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "F:=simplify(F0); " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Int(Int(F,u=0..Pi),v=0..2*Pi );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "int(int(subs(a=1,b=1, c=2,F),u=0..Pi),v=0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "evalf(int(int(subs(a=1,b=1,c=2,F),u=0..Pi),v=0..2*Pi));" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "evalf(ellipsoid(1,1,2));" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "15 1 0" 47 } {VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }