Flux of a Vector Field through a Surface Surface Defined over a Triangle JSFH

JSFH Obtain the flux of the vector field LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY2LUkjbWlHRiQ2J1EiRkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSNtb0dGJDYtUSI9RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUC1GLDYlUSJ5RicvRjNGMS9GNlEnaXRhbGljRictRjs2LVEifkYnRj5GQEZCRkRGRkZIRkpGTC9GT1EmMC4wZW1GJy9GUkZnbi1GLDYlUSJ6RidGVkZXRlktRiw2J1EiaUYnRi9GMkY1RjgtRjs2LVEiK0YnRj5GQEZCRkRGRkZIRkpGTC9GT1EsMC4yMjIyMjIyZW1GJy9GUkZjby1GLDYlUSJ4RidGVkZXRllGaW5GWS1GLDYnUSJqRidGL0YyRjVGOEZfb0Zlb0ZZLUklbXN1cEdGJDYlRlMtRiM2JC1JI21uR0YkNiRRIjJGJ0Y+Rj4vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRlktRiw2J1Eia0YnRi9GMkY1RjhGPg== through that part of the surface 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 inside the cylinder whose cross-section in the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjeHlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn-plane is the triangle with vertices 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. JSFH

JSFH Tools\342\211\273Tasks\342\211\273Browse: Vector Calculus\342\211\273Integration\342\211\273Flux\342\211\2733-D\342\211\273Through a Surface Defined over a Triangle Flux through a Surface Defined over a Triangle JSFHJSFH For the Vector Field: use DocumentTools in Do(%ComboBox1(value) = "Select Coordinate System"): Do(%MathContainer23 = NULL); Do(%MathContainer24 = NULL); Do(%MathContainer25 = NULL); Do(%MathContainer26 = NULL); Do(%MathContainer27 = NULL); Do(%MathContainer44 = NULL); Do(%MathContainer45 = NULL); Do(%MathContainer29 = NULL); Do(%MathContainer30 = NULL); Do(%MathContainer31 = NULL); Do(%MathContainer37 = NULL); Do(%MathContainer43 = NULL); Do(%MathContainer28 = NULL); Do(%MathContainer33 = NULL); Do(%MathContainer35 = NULL); Do(%MathContainer39 = NULL); Do(%MathContainer41 = NULL); Do(%MathContainer32 = NULL); Do(%MathContainer38 = NULL); Do(%MathContainer34 = NULL); Do(%MathContainer40 = NULL); Do(%MathContainer36 = NULL); Do(%MathContainer42 = NULL); Do(%MathContainer23(visible) = false); Do(%MathContainer24(visible) = false); Do(%MathContainer25(visible) = false); Do(%MathContainer26(visible) = false); Do(%MathContainer27(visible) = false); Do(%MathContainer44(visible) = false); Do(%MathContainer45(visible) = false); Do(%MathContainer29(visible) = false); Do(%MathContainer30(visible) = false); Do(%MathContainer31(visible) = false); Do(%MathContainer37(visible) = false); Do(%MathContainer43(visible) = false); Do(%MathContainer28(visible) = false); Do(%MathContainer33(visible) = false); Do(%MathContainer35(visible) = false); Do(%MathContainer39(visible) = false); Do(%MathContainer41(visible) = false); Do(%MathContainer32(visible) = false); Do(%MathContainer38(visible) = false); Do(%MathContainer34(visible) = false); Do(%MathContainer40(visible) = false); Do(%MathContainer36(visible) = false); Do(%MathContainer42(visible) = false); Do(%Label16(visible) = false); Do(%Label17(visible) = false); Do(%Label18(visible) = false); Do(%Label19(visible) = false); Do(%Label20(visible) = false); Do(%Label22(visible) = false); Do(%Label23(visible) = false); Do(%Label24(visible) = false); Do(%Label21(visible) = false); Do(%Label25(visible) = false); Do(%Label26(visible) = false); Do(%Label29(visible) = false); Do(%Label27(visible) = false); Do(%Label30(visible) = false); Do(%Label28(visible) = false); Do(%Label31(visible) = false); Do(%Button19(visible) = false); Do(%Button20(visible) = false); Do(%Button22(visible) = false); Do(%Button23(visible) = false); Do(%Button21(visible) = false); Do(%Button31(enabled) = false); Do(%Button32(enabled) = false); Do(%Button33(enabled) = false); Do(%Button34(enabled) = false); Do(%Button35(enabled) = false); Do(%Button25(visible) = false); Do(%Button26(visible) = false); Do(%Button27(visible) = false); Do(%Button28(visible) = false); Do(%Button30(visible) = false); Do(%Button24(visible) = false); Do(%Button29(visible) = false); end use; JSFHJSFH Select Coordinate System,Cartesian [x\134,y\134,z],Cartesian - other,cylindrical,spherical,bipolarcylindrical,bispherical,cardioidal,cardioidcylindrical,casscylindrical,conical,ellcylindrical,hypercylindrical,invcasscylindrical,logcylindrical,logcoshcylindrical,oblatespheroidal,paraboloidal,paracylindrical,prolatespheroidal,rosecylindrical,sixsphere,tangentcylindrical,tangentsphere,toroidaluse DocumentTools in module() local q; if GetProperty(ComboBox1,value) = "Select Coordinate System" then Do(%Label16(Visible) = false); Do(%MathContainer23 =NULL); Do(%MathContainer23(visible) = false); Do(%Button19(visible) = false); Do(%MathContainer24 = NULL); Do(%MathContainer24(visible) = false); return;end if; Do(q = %ComboBox1); if q=Cartesian [x,y,z] then Do(%MathContainer23=MathML[Export]([x,y,z])); elif q=Cartesian - other then Do(%MathContainer23 = NULL); else Do(%MathContainer23 = NULL); end if: Do(%MathContainer24 = NULL); Do(%Label16(visible) = true); Do(%MathContainer23(visible) = true); Do(%Button19(visible) = true); Do(%MathContainer24(visible) = true); #Do(%MathContainer26 = NULL); #Do(%MathContainer27 = NULL); end module; end use; JSFHJSFH JSFH JSFHuse DocumentTools, StringTools in xxxVFconstruct := module() local q,q1,q2; export q3; Do(q = %ComboBox1); Do(q1 = %MathContainer23); if type([q1],'list'('list')) then q2:=q1; elif type([q1],'list') then q2:=[q1];end if; if q2=NULL then return;end if; if q=Cartesian [x,y,z] then q3 := parse(Join(["cartesian",convert(q2,string)],"")); elif q=Cartesian - other then if nops(q2)=3 then q3:=(parse(Join(["cartesian",convert(q2,string)],""))) else return;end if; else if nops(q2)=3 then q3:=(parse(Join([convert(q,string),convert(q2,string)],""))) else return;end if; end if; Do(%MathContainer24 = MathML[Export]([op(0,q3),[op(q3)]])); Do(%Label17(visible) = true): Do(%Label18(visible) = true): Do(%Label19(visible) = true): Do(%MathContainer25(visible) = true); Do(%MathContainer26(visible) = true); Do(%MathContainer27(visible) = true); Do(%Button20(visible) = true); Do(%Button22(visible) = true); Do(%Button23(visible) = true); Do(%Button21(visible) = true); end module; end use; JSFH JSFH use DocumentTools in Do(%MathContainer25 = NULL); end use; JSFH JSFH JSFH JSFH JSFH JSFH JSFHJSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFHuse DocumentTools in module() local q1,q2,q3; Do(q1 = %MathContainer25); Do(q2 = %MathContainer26); Do(q3 = %MathContainer27); if nops([q1])*nops([q2])*nops([q3])=0 then return;end if; Do(%Label20(visible) = true); Do(%Label21(visible) = true); Do(%MathContainer28(visible) = true); Do(%Button24(visible) = true); end module; end use; JSFH use DocumentTools in Do(%MathContainer26 = NULL); end use; JSFH JSFH use DocumentTools in Do(%MathContainer27 = NULL); end use; JSFH JSFH JSFH JSFHuse DocumentTools in module() local q, params, R1,R2,R3; Do(q = %MathContainer28); if nops([q])=0 then return;end if; if type([q],'list'('list')) then params:=q; elif type([q],'list') then params:=[q];end if; if q=NULL then return;end if; if nops(params)<>2 then return;end if; if params[1]=params[2] then return;end if; Do(%Label22(visible) = true); Do(%Label23(visible) = true); Do(%Label24(visible) = true); Do(%MathContainer29(visible) = true); Do(%MathContainer30(visible) = true); Do(%MathContainer31(visible) = true); Do(%Button25(visible) = true); Do(%Button26(visible) = true); Do(%Button27(visible) = true); Do(%Button28(visible) = true); if params[1]=x or params[2]=x then R1:=x else R1:=NULL;end if; if params[1]=y or params[2]=y then R2:=y else R2:=NULL;end if; if params[1]=z or params[2]=z then R3:=z else R3:=NULL;end if; Do(%MathContainer29 = R1); Do(%MathContainer30 = R2); Do(%MathContainer31 = R3); end module; end use; use DocumentTools in Do(%MathContainer29 = NULL); end use; use DocumentTools in Do(%MathContainer30 = NULL); end use; use DocumentTools in Do(%MathContainer31 = NULL); end use; use DocumentTools in module() local q1,q2,q3; Do(q1 = %MathContainer29); Do(q2 = %MathContainer30); Do(q3 = %MathContainer31); if nops([q1])*nops([q2])*nops([q3])=0 then return;end if; Do(%Label25(visible) = true); Do(%Label26(visible) = true); Do(%Label29(visible) = true); Do(%Label27(visible) = true); Do(%Label30(visible) = true); Do(%Label28(visible) = true); Do(%Label31(visible) = true); Do(%MathContainer32(visible) = true); Do(%MathContainer38(visible) = true); Do(%MathContainer34(visible) = true); Do(%MathContainer40(visible) = true); Do(%MathContainer36(visible) = true); Do(%MathContainer42(visible) = true); Do(%MathContainer33(visible) = true); Do(%MathContainer35(visible) = true); Do(%MathContainer39(visible) = true); Do(%MathContainer41(visible) = true); Do(%MathContainer37(visible) = true); Do(%MathContainer43(visible) = true); Do(%Button30(visible) = true); Do(%Button29(visible) = true); Do(%MathContainer32 = x[1]); Do(%MathContainer38 = y[1]); Do(%MathContainer34 = x[2]); Do(%MathContainer40 = y[2]); Do(%MathContainer36 = x[3]); Do(%MathContainer42 = y[3]); end module; end use; JSFH JSFH JSFH use DocumentTools in Do(%MathContainer33 = NULL); Do(%MathContainer39 = NULL); Do(%MathContainer35 = NULL); Do(%MathContainer41 = NULL); Do(%MathContainer37 = NULL); Do(%MathContainer43 = NULL); end use; JSFH JSFH JSFH use DocumentTools in module() local X,Y,Z, params, x1,y1,x2,y2,x3,y3; Do(X = %MathContainer29); Do(Y = %MathContainer30); Do(Z = %MathContainer31); Do(x1 = %MathContainer33); Do(y1 = %MathContainer39); Do(x2 = %MathContainer35); Do(y2 = %MathContainer41); Do(x3 = %MathContainer37); Do(y3 = %MathContainer43); Do(params = %MathContainer28); if nops([X])*nops([Y])*nops([Z])*nops([x1])*nops([x2])*nops([x3])*nops([y1])*nops([y2])*nops([y3])*nops([params])=0 then return;end if; Do(%Button31(enabled) = true); Do(%MathContainer44(visible) = true); end module; end use; JSFH use DocumentTools, VectorCalculus in module() local q, F1, F2, F3, F, X,Y,Z, Q, params, x1,y1,x2,y2,x3,y3, V1,V2,V3,CS; CS := GetCoordinates(); Do(F1 = %MathContainer25); Do(F2 = %MathContainer26); Do(F3 = %MathContainer27); if nops([F1])*nops([F2])*nops([F3])=0 then return;end if; F := VectorField([F1,F2,F3],coords=xxxVFconstruct:-q3); Do(Q = %MathContainer28); if nops([Q])=0 then return;end if; if type([Q],'list'('list')) then params:=Q; elif type([Q],'list') then params:=[Q];end if; if Q=NULL then return;end if; if nops(params)<>2 then return;end if; if params[1]=params[2] then return;end if; Do(X = %MathContainer29); Do(Y = %MathContainer30); Do(Z = %MathContainer31); Do(x1 = %MathContainer33); Do(y1 = %MathContainer39); Do(x2 = %MathContainer35); Do(y2 = %MathContainer41); Do(x3 = %MathContainer37); Do(y3 = %MathContainer43); if nops([X])*nops([Y])*nops([Z])*nops([x1])*nops([x2])*nops([x3])*nops([y1])*nops([y2])*nops([y3])=0 then return;end if; V1 := Vector([x1,y1],coords=cartesian[x,y]); V2 := Vector([x2,y2],coords=cartesian[x,y]); V3 := Vector([x3,y3],coords=cartesian[x,y]); SetCoordinates(cartesian[x,y,z]); try q := Flux(F,Surface(<X,Y,Z>,params=Triangle(V1,V2,V3),cartesian),inert); catch: q := NULL; finally SetCoordinates(CS); end try; Do(%MathContainer44 = q); if q<>NULL then Do(%Button32(enabled) = true); Do(%Button33(enabled) = true); else Do(%MathContainer45 = NULL); end if; end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer44); if nops(q)=1 then Do(%MathContainer44 = subsop([1,1] = simplify(op([1,1],q)),q)); else Do(%MathContainer44 = simplify(q));end if; end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRi8= use DocumentTools in module() local q; Do(%MathContainer45(visible) = true); Do(q = %MathContainer44); Do(%MathContainer45 = value(q)); Do(%Button34(enabled) = true); Do(%Button35(enabled) = true); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer45); Do(%MathContainer45 = simplify(q)); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer45); Do(%MathContainer45 = evalf(q)); end module; end use; JSFH TTdSMApJNlJUQUJMRV9TQVZFLzE0MDg0NjgyMFgqJSlhbnl0aGluZ0c2IjYkJSx2ZWN0b3JmaWVsZEcvJSdjb29yZHNHJiUqY2FydGVzaWFuRzYlJSZfX3hfX0clJl9feV9fRyUmX196X19HW2dsISMlISEhIiQiJEYtKiRGLiIiIyokRi9GMTYi

Initialize: 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 Vector Field F: 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 Surface 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbWlHRiQ2JVEiWkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkjbW5HRiQ2JFEiMUYnRjktRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZXLUZQNiRRIjJGJ0Y5LUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5Gam4tSSVtc3VwR0YkNiUtRiw2JVEieEYnRi9GMi1GIzYlRlkvJStleGVjdXRhYmxlR0Y9RjkvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRlMtRlA2JFEiM0YnRjlGZm4tRl1vNiUtRiw2JVEieUYnRi9GMkZib0Zmb0Zkb0Y5 Normal field: 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 Unit normal field: 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 Vertices of Triangle: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVErU3VyZmFjZUludEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYsLUYsNidRIkZGJy8lJWJvbGRHRjEvRjBRJmZhbHNlRicvRjNRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRkItSSNtb0dGJDYtUSkmbWlkZG90O0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR0ZALyUqc2VwYXJhdG9yR0ZALyUpc3RyZXRjaHlHRkAvJSpzeW1tZXRyaWNHRkAvJShsYXJnZW9wR0ZALyUubW92YWJsZWxpbWl0c0dGQC8lJ2FjY2VudEdGQC8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRmVuLUYsNidRIk5GJ0Y9Rj9GQUZDLUZGNi1RIixGJ0ZJRksvRk5GMUZPRlFGU0ZVRlcvRlpRJjAuMGVtRicvRmduUSwwLjMzMzMzMzNlbUYnLUY2NiYtRiM2KS1GLDYlUSJ4RidGL0YyRltvLUYsNiVRInlGJ0YvRjJGW28tRiw2JVEiekYnRi9GMi8lK2V4ZWN1dGFibGVHRkBGSUZJLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnLUZGNi1RIj1GJ0ZJRktGTUZPRlFGU0ZVRlcvRlpRLDAuMjc3Nzc3OGVtRicvRmduRlxxLUYsNiVRKFN1cmZhY2VGJ0YvRjItRjY2JC1GIzYqLUY2NiYtRiM2KUZnb0Zbb0Zqb0Zbby1GLDYlUSJaRidGL0YyRmBwRklGSS9GY3BRJyZsYW5nO0YnL0ZmcFEnJnJhbmc7RidGW28tRjY2Ji1GIzYnRmdvRltvRmpvRmBwRklGSUZicEZlcEZocC1GLDYlUSlUcmlhbmdsZUYnRi9GMi1GNjYkLUYjNictRiw2I1EhRictSShtYWN0aW9uR0YkNiVGW3MvJSthY3Rpb250eXBlR1E6bWFwbGVzb2Z0LmNvbTpsYWJlbChMMzYwKUYnLyUldmlld0dRJmxhYmVsRidGW3NGYHBGSUZJRmBwRklGSUZgcEZJRklGYHBGSQ== Integration Details LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoZCYjOTYzO0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGOQ==except for differentials: 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Graph of triangle: 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Equations of edges: 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