Obtain the gradient for the scalar field 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.
JSFH
<Text-field style="Heading 1" layout="Heading 1">Solution via Task Template</Text-field>JSFH
Compute the Gradient Vector in Cartesian CoordinatesEnter a scalar field as an expression in Cartesian coordinates:use DocumentTools in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# GetProperty( component_name, attribute_name )
# and
# SetProperty( component_name, attribute_name, value )
# to access any of the attributes of the component.
# See ?CustomizingComponents for more information.
module()
SetProperty(MathContainer0,value,NULL);
end module;
end use;
use DocumentTools in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# GetProperty( component_name, attribute_name )
# and
# SetProperty( component_name, attribute_name, value )
# to access any of the attributes of the component.
# See ?CustomizingComponents for more information.
module()
SetProperty(MathContainer1, value, NULL);
end module;
end use;
Choose Coordinate System: Cartesian - [x\134, y],Cartesian - [x\134, y\134, z],Cartesian - otheruse DocumentTools in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# GetProperty( component_name, attribute_name )
# and
# SetProperty( component_name, attribute_name, value )
# to access any of the attributes of the component.
# See ?CustomizingComponents for more information.
xxC := GetProperty(ComboBox0,value);
if xxC="Cartesian - [x, y]" then XXC:=cartesian[x,y];SetProperty(MathContainer2,value,MathML[Export]([x,y]));xxY:=0;
elif xxC="Cartesian - [x, y, z]" then XXC:=cartesian[x,y,z];SetProperty(MathContainer2,value,MathML[Export]([x,y,z]));xxY:=0;
elif xxC="Polar - [r, theta]" then XXC:=polar[r,theta];SetProperty(MathContainer2,value,MathML[Export]([r,theta]));xxY:=0;
elif xxC="Cylindrical - [r, theta, z]" then XXC:=cylindrical[r,theta,z];SetProperty(MathContainer2,value,MathML[Export]([r,theta,z]));xxY:=0;
elif xxC="Spherical - [rho, phi, theta]" then XXC:=spherical[rho,phi,theta];SetProperty(MathContainer2,value,MathML[Export]([rho,phi,theta]));xxY:=0;
elif xxC="Spherical - [rho, theta, phi]" then XXC:=spherical[rho,theta,phi];SetProperty(MathContainer2,value,MathML[Export]([rho,theta,phi]));xxY:=0;
elif xxC="Cartesian - other" then XXC:=cartesian;SetProperty(MathContainer2,value,NULL);xxY:=1;
elif xxC="Polar - other" then XXC:=polar;SetProperty(MathContainer2,value,NULL);xxY:=1;
elif xxC="Cylindrical - other" then XXC:=cylindrical;SetProperty(MathContainer2,value,NULL);xxY:=1;
elif xxC="Spherical - other" then XXC:=spherical;SetProperty(MathContainer2,value,NULL);xxY:=1;
end if;
end use;
Coordinate Variables: use DocumentTools in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# GetProperty( component_name, attribute_name )
# and
# SetProperty( component_name, attribute_name, value )
# to access any of the attributes of the component.
# See ?CustomizingComponents for more information.
module()
_EnvDisableGlobalBindings := true:
xxf := op(2,Typesetting:-Parse(Typesetting:-FromMathML(DocumentTools:-GetProperty('MathContainer0','value'))));
xxC := GetProperty(ComboBox0,value);
if xxC="Cartesian - [x, y]" then XXC := [x,y];SetProperty(MathContainer1,value,MathML[Export]([x,y]));xxY:=0;
elif xxC="Cartesian - [x, y, z]" then XXC := [x,y,z];SetProperty(MathContainer1,value,MathML[Export]([x,y,z]));xxY:=0;
elif xxC="Cartesian - other" then xxY:=1;
end if;
if xxY=0 then xxG:=Student[MultivariateCalculus][Gradient](xxf,XXC);
else
temp:=op(Typesetting:-Parse(Typesetting:-FromMathML(DocumentTools:-GetProperty('MathContainer2','value'))))[2..-1];
if nops([temp])>1 then XXCC := [temp];
elif type(temp,list) or type(temp,set) then XXCC := temp;
else XXCC := [temp];
end if;
xxG:=Student[MultivariateCalculus][Gradient](xxf,XXCC);
end if;
SetProperty(MathContainer1,value,MathML[Export](xxG));
end module;
end use;
JSFH
<Text-field style="Heading 1" layout="Heading 1">Solution via Gradient Tutor</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
Control-drag the expression for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=Context Menu: Assign to a Name\342\211\273LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=JSFHTools\342\211\273Tutors\342\211\273Calculus - Multi-Variable: Gradients
Enter LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, and the point
Tools\342\211\273Tasks\342\211\273Browse: Calculus - Vector\342\211\273Vector Algebra and Settings\342\211\273Set Coordinates\342\211\273The More Common SystemsJSFH
The More Common Coordinate SystemsCartesian [x\134,y],Cartesian [x\134,y\134,z],Cartesian - other,polar,cylindrical,sphericaluse DocumentTools in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# Do( %component_name );
# and
# Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
# Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.
module()
local q;
Do(q = %ComboBox4):
if q=Cartesian [x,y] then Do(%MathContainer185=MathML[Export]([x,y]));
elif q=Cartesian [x,y,z] then Do(%MathContainer185=MathML[Export]([x,y,z]));
elif q=Cartesian - other then Do(%MathContainer185=NULL);
elif q=polar then Do(%MathContainer185=NULL);
elif q=cylindrical then Do(%MathContainer185=NULL);
elif q=spherical then Do(%MathContainer185=NULL);
end if:
Do(%MathContainer186 = NULL);
end module;
end use;
use DocumentTools,VectorCalculus in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# Do( %component_name );
# and
# Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
# Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.
module()
local q,q1,q2,q3;
Do(q = %ComboBox4);
if q<>Cartesian [x,y] and q<> Cartesian [x,y,z] then Do(q1 = %MathContainer185);
if type([q1],'list'('list')) then q2:=q1;
elif type([q1],'list') then q2:=[q1];end if;
if q2=NULL then return;end if;
end if;
if q=Cartesian [x,y] then SetCoordinates(cartesian[x,y]);
elif q=Cartesian [x,y,z] then SetCoordinates(cartesian[x,y,z]);
elif q=Cartesian - other then if nops(q2)=3 then SetCoordinates(parse(StringTools:-Join(["cartesian",convert(q2,string)],""))) else return;end if;
elif q=polar then if nops(q2)=2 then SetCoordinates(parse(StringTools:-Join(["polar",convert(q2,string)],""))) else return;end if;
elif q=cylindrical then if nops(q2)=3 then SetCoordinates(parse(StringTools:-Join(["cylindrical",convert(q2,string)],""))) else return;end if;
elif q=spherical then if nops(q2)=3 then SetCoordinates(parse(StringTools:-Join(["spherical",convert(q2,string)],""))) else return;end if;
end if;
q3 := GetCoordinates();
Do(%MathContainer186 = MathML[Export]([op(0,q3),[op(q3)]]));
end module;
end use;
JSFHUse the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEmJkRlbDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMTExMTExMWVtRidGLw==-operator from the
Common Symbols palette.Context Menu: Evaluate at a PointJSFH
Tools\342\211\273Tasks\342\211\273Browse: Calculus - Vector\342\211\273Vector Algebra and Settings\342\211\273Set CoordinatesJSFH
Set Coordinatesuse DocumentTools in
Do(%MathContainer3 = NULL);
Do(%MathContainer4 = NULL);
Do(%ComboBox1(enabled) = true);
Do(%ComboBox2(enabled) = false);
Do(%ComboBox3(enabled) = false);
Do(%Label0(enabled) = true);
Do(%MathContainer3(visible) = true);
SetProperty(Button3,enabled,true);
Do(%MathContainer4(visible) = true);
if Do(%ComboBox1) = Cartesian [x,y] then
Do(%MathContainer3 = MathML[Export]([x,y]));end if;
end use;
JSFHuse DocumentTools in
Do(%ComboBox1(enabled) = false);
Do(%ComboBox2(enabled) = true);
Do(%ComboBox3(enabled) = false);
Do(%Label0(enabled) = true);
Do(%MathContainer3(visible) = true);
SetProperty(Button3,enabled,true);
Do(%MathContainer4(visible) = true);
Do(%MathContainer3 = NULL);
Do(%MathContainer4 = NULL);
end use;
JSFHuse DocumentTools in
Do(%ComboBox1(enabled) = false);
Do(%ComboBox2(enabled) = false);
Do(%ComboBox3(enabled) = true);
Do(%Label0(enabled) = true);
Do(%MathContainer3(visible) = true);
SetProperty(Button3,enabled,true);
Do(%MathContainer4(visible) = true);
Do(%MathContainer3 = NULL);
Do(%MathContainer4 = NULL);
end use;
JSFHCartesian [x\134,y],Cartesian [x\134,y\134,z],Cartesian - other,polar,cylindrical,sphericaluse DocumentTools in
module()
local q;
Do(q = %ComboBox1):
if q=Cartesian [x,y] then Do(%MathContainer3=MathML[Export]([x,y]));
elif q=Cartesian [x,y,z] then Do(%MathContainer3=MathML[Export]([x,y,z]));
elif q=Cartesian - other then Do(%MathContainer3=NULL);
elif q=polar then Do(%MathContainer3=NULL);
elif q=cylindrical then Do(%MathContainer3=NULL);
elif q=spherical then Do(%MathContainer3=NULL);
end if:
Do(%MathContainer4 = NULL);
end module;
end use;
JSFHbipolar,cardioid,cassinian,elliptic,hyperbolic,invcassinian,logarithmic,logcosh,parabolic,rose,tangentuse DocumentTools in
Do(%MathContainer3 = NULL);
Do(%MathContainer4 = NULL);
end use;
JSFHbipolarcylindrical,bispherical,cardioidal,cardioidcylindrical,casscylindrical,conical,ellcylindrical,hypercylindrical,invcasscylindrical,logcylindrical,logcoshcylindrical,oblatespheroidal,paraboloidal,paracylindrical,prolatespheroidal,rosecylindrical,sixsphere,tangentcylindrical,tangentsphere,toroidaluse DocumentTools in
Do(%MathContainer3 = NULL);
Do(%MathContainer4 = NULL);
end use;
JSFHJSFHuse DocumentTools, VectorCalculus in
module()
local q,q1,q2,q3;
if Do(%RadioButton3) then
Do(q = %ComboBox1);
Do(q1 = %MathContainer3);
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] then q3 := parse(StringTools:-Join(["cartesian",convert(q2,string)],""));
elif q=Cartesian [x,y,z] then q3 := parse(StringTools:-Join(["cartesian",convert(q2,string)],""));
elif q=Cartesian - other then if nops(q2)=2 or nops(q2)=3 then q3:=(parse(StringTools:-Join(["cartesian",convert(q2,string)],""))) else return;end if;
elif q=polar then if nops(q2)=2 then q3:=(parse(StringTools:-Join(["polar",convert(q2,string)],""))) else return;end if;
elif q=cylindrical then if nops(q2)=3 then q3:=(parse(StringTools:-Join(["cylindrical",convert(q2,string)],""))) else return;end if;
elif q=spherical then if nops(q2)=3 then q3:=(parse(StringTools:-Join(["spherical",convert(q2,string)],""))) else return;end if;
end if;
Do(%MathContainer4 = MathML[Export]([op(0,q3),[op(q3)]]));
SetCoordinates(q3);
elif Do(%RadioButton1) then
Do(q = %ComboBox1);
Do(q1 = %MathContainer3);
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 nops(q2)<>2 then return; end if;
q3 := parse(StringTools:-Join([convert(q,string),convert(q2,string)],""));
Do(%MathContainer4 = MathML[Export]([op(0,q3),[op(q3)]]));
SetCoordinates(q3);
elif Do(%RadioButton2) then
Do(q = %ComboBox2);
Do(q1 = %MathContainer3);
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 nops(q2)<>3 then return; end if;
q3 := parse(StringTools:-Join([convert(q,string),convert(q2,string)],""));
Do(%MathContainer4 = MathML[Export]([op(0,q3),[op(q3)]]));
SetCoordinates(q3);
else return;
end if;
end module;
end use;
use DocumentTools, VectorCalculus in
Do(%RadioButton3 = true):
Do(%MathContainer3 = NULL):
Do(%MathContainer4 = NULL):
Do(%ComboBox1 = "Cartesian [x,y]"):
SetProperty(ComboBox1,enabled,false):
Do(%ComboBox2 = bipolar):
SetProperty(ComboBox2,enabled,false):
Do(%ComboBox3 = bipolarcylindrical):
SetProperty(ComboBox3,enabled,false):
SetProperty(Label0,enabled,false):
SetProperty(MathContainer3,visible,false):
SetProperty(MathContainer4,visible,false):
SetProperty(Button3,enabled,false):
SetCoordinates(cartesian);
end use;
JSFHUse the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEmJkRlbDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMTExMTExMWVtRidGLw==-operator from the
Common Symbols palette.Context Menu: Evaluate at a PointJSFH
JSFH
<Text-field style="Heading 1" layout="Heading 1">Gradient from First Principles</Text-field>JSFH
Enter the equation LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSkmaGVsbGlwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4xNjY2NjY3ZW1GJy9GTkZTRjk=Context Menu: Assign NameJSFHUsing the Matrix palette, enter a vector template.Use the partial derivative template in the Expression palette to obtain
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 and 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
Press the Enter key.Context Menu: Evaluate at a PointJSFH