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P\303\251ld\303\241k: pol\303\241r-, henger- \+ \303\251s g\303\266mbi koordin\303\241t\303\241k." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "Jacobian(,[r,phi],'determinant'=true);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-I'MatrixG6$%*protectedGI(_syslibG6\"6#/I$%idGF(\"*3Yf \\\",&*&)-I$cosGF%6#I$phiGF(\"\"#\"\"\"I\"rGF(F5F5*&F6F5)-I$sinGF%F2F4 F5F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "simplify(%[2],trig) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"rG6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "Jacobian(,[r,phi,z],'dete rminant'=true);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-I'MatrixG6$%*prote ctedGI(_syslibG6\"6#/I$%idGF(\"*g9u[\",&*&)-I$cosGF%6#I$phiGF(\"\"#\" \"\"I\"rGF(F5F5*&F6F5)-I$sinGF%F2F4F5F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "simplify(%[2],trig);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"rG6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "Jacobian(,\n" }{MPLTEXT 1 0 34 "[r,phi,theta],'determinant'=true);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-I'MatrixG6$%*protectedGI(_syslibG6\"6#/I$%idGF(\"*wK_S\",**()-I $cosGF%6#I$phiGF(\"\"#\"\"\")-F16#I&thetaGF(\"\"$F5)I\"rGF(F4F5F5*()-I $sinGF%F2F4F5F6F5F;F5F5**F;F5F>F5F7F5)-F@F8F4F5F5**F;F5F/F5F7F5FBF5F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "simplify(%[2],trig);" }} {PARA 11 "" 1 "" {XPPMATH 20 "*&-I$cosG6$%*protectedGI(_syslibG6\"6#I& thetaGF(\"\"\")I\"rGF(\"\"#F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "with(Student[MultivariateCalculus]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "77I5Add2DCoordinateNamesG6\"I5Add3DCoordinateNamesGF$I/Ap proximateIntGF$I4ApproximateIntTutorGF$I-CenterOfMassGF$I2ChangeOfVari ablesGF$I-CrossSectionGF$I2CrossSectionTutorGF$I6DirectionalDerivative GF$I;DirectionalDerivativeTutorGF$I0FunctionAverageGF$I)GradientGF$I.G radientTutorGF$I)JacobianGF$I4LagrangeMultipliersGF$I)MultiIntGF$I'Rev ertGF$I5SecondDerivativeTestGF$I,SurfaceAreaGF$I4TaylorApproximationGF $I9TaylorApproximationTutorGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "ChangeOfVariables(x^2+y^2,['cartesian'[x,y],'polar'[r,phi]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&)I\"rG6\"\"\"#\"\"\")-I$cosG6$%*p rotectedGI(_syslibGF&6#I$phiGF&F'F(F(*&F$F()-I$sinGF,F/F'F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "simplify(%,trig);" }}{PARA 11 "" 1 "" {XPPMATH 20 "*$)I\"rG6\"\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "ChangeOfVariables(Int(Int(x^2+y^2,x),y),\n" } {MPLTEXT 1 0 35 "['cartesian'[x,y],'polar'[r,phi]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I$IntG6$%*protectedGI(_syslibG6\"6$-F#6$*$)I\"rGF'\" \"$\"\"\"I$phiGF'F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "Chan geOfVariables(x^2+y^2-z^2,['cartesian'[x,y,z],\n" }{MPLTEXT 1 0 25 "'c ylindrical'[r,phi,z]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&)I\"rG6\" \"\"#\"\"\")-I$cosG6$%*protectedGI(_syslibGF&6#I$phiGF&F'F(F(*&F$F()-I $sinGF,F/F'F(F(*$)I\"zGF&F'F(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "simplify(%,trig);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",& *$)I\"zG6\"\"\"#\"\"\"!\"\"*$)I\"rGF&F'F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "ChangeOfVariables(Int(Int(Int(x^2+y^2-z^2,x),y),z) ,\n" }{MPLTEXT 1 0 45 "['cartesian'[x,y,z],'cylindrical'[r,phi,z]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I$IntG6$%*protectedGI(_syslibG6\"6$-F #6$-F#6$*&,&*$)I\"zGF'\"\"#\"\"\"!\"\"*$)I\"rGF'F2F3F3F3F7F3I$phiGF'F7 F1" }}}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 89 "2.3.32. 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