Ramakrishnan

Ramakrishnan Vaidyanathan

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7 years, 184 days

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With twenty years of Industrial experience and twenty years of teaching experience, I am now as retired Professor, using Maple to teach mathematics subject for students studying X to XII standards. Published XII Mathematics books.

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These are questions asked by Ramakrishnan

Is there any command for defining piecewise functions in 2 dimensional domain (x, y)

Say (x,y) such that ((0,0)<(x,y)<(1,1), x+y, (1,1)<(x,y)<(2,1), x-y), x=0..2, y=0..1)

 

Thanks for help.

Ramakrishnan

I am not getting the hemisphere which I thought was my expression (equation) represents.

Can anyone help me find my mistake.

with(plots);
implicitplot3d(z <= sqrt(-x^2 - y^2 + 9), x = -3 .. 3, y = -3 .. 3, z = 0 .. 3, coords = spherical);

Thanks in advance.

Doubt_ImplicitPlot.mw

I have recently received a doc from my friend in privete group in maple cloud, the table showed both eye(view) icon and download icon).When I downloaded and run, the document does not run (maple 2019). 

When I sign in maple cloud and see the doc (only view button is ahow), the same document works fine. What could be the error?

I attach  a document extract showing the errors (unable to delimt   .../  identifiers).

Can any one help us please?

Thanks. Ramki.
 

``

"Refraction Demonstration          restart:with(plots):  RefractionDemo:=proc(theta1, n2)  local theta2,ainput,ainside,aoutput,box,line1,line2,H,n2text,theta1text,theta2text;   if(theta1<0)or(theta1>Pi/(2.0001)) then return end if;   #theta1:=theta01*Pi180.;   theta2:=arcsin(1/(n2)*sin(theta1));   ainput:=arrow(?&ndash;cos(theta1),&ndash;sin(theta1)?,?cos(theta1),sin(theta1)?,color="Red"):   ainside:=arrow(?0,0?,?1,tan(theta2)?,color="DarkBlue",width=[0.05,relative=false]):   aoutput:=arrow(?1,tan(theta2)?,?cos(theta1),sin(theta1)?,color="Red"):   line1:=plot(0,x=&ndash;1..0,thickness=4,color=black);   line2:=plot(tan(theta2),x=1..2,thickness=4,color=black);   H:=1.8:   box:=plottools:&ndash;rectangle([0,&ndash;H],[1,H],color="LightBlue"):   n2text:=textplot([0.5,1.5,sprintf("n_2=%1.3 g",n2)]);   theta1text:=textplot([&ndash;0.5,0.4,sprintf("theta_1=%4.3 g",theta1)]);   theta2text:=textplot([0.5,&ndash;0.4,sprintf("theta_2=%4.3 g",theta2)]);   display([ainput,ainside,aoutput,box,line1,line2,n2text,theta1text,theta2text],scaling=constrained,view=[&ndash;1..2,&ndash;1..H]);   endproc:        Light enters from the air into a medium at an angle of theta1 relative to the normal. It is refracted to an angle of theta2and travels through the medium, returning back to the air.      You can vary two parameters:       theta1the angle of incidence       n2the index of refraction of the medium*(assuming the index of refraction of the air is essentially 1.0).     To do: Let it execute and start manipulating the sliders.     >Explore(RefractionDemo(theta1,n2),parameters=[theta1=0..Pi2.0015,n2=1..3.]);6""

Error, unable to delimit strings/identifiers

"Refraction Demonstration          restart:with(plots):  RefractionDemo:=proc(theta1, n2)  local theta2,ainput,ainside,aoutput,box,line1,line2,H,n2text,theta1text,theta2text;   if(theta1<0)or(theta1>Pi/2.0001) then return end if;   #theta1:=theta01*Pi180.;   theta2:=arcsin(1/n2*sin(theta1));   ainput:=arrow(&acirc;ï¿&frac12;&uml;&ndash;cos(theta1),&ndash;sin(theta1)&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;cos(theta1),sin(theta1)&acirc;ï¿&frac12;&copy;,color="Red"):   ainside:=arrow(&acirc;ï¿&frac12;&uml;0,0&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;1,tan(theta2)&acirc;ï¿&frac12;&copy;,color="DarkBlue",width=[0.05,relative=false]):   aoutput:=arrow(&acirc;ï¿&frac12;&uml;1,tan(theta2)&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;cos(theta1),sin(theta1)&acirc;ï¿&frac12;&copy;,color="Red"):   line1:=plot(0,x=&ndash;1..0,thickness=4,color=black);   line2:=plot(tan(theta2),x=1..2,thickness=4,color=black);   H:=1.8:   box:=plottools:&ndash;rectangle([0,&ndash;H],[1,H],color="LightBlue"):   n2text:=textplot([0.5,1.5,sprintf("n_2=%1.3 g",n2)]);   theta1text:=textplot([&ndash;0.5,0.4,sprintf("theta_1=%4.3 g",theta1)]);   theta2text:=textplot([0.5,&ndash;0.4,sprintf("theta_2=%4.3 g",theta2)]);   display([ainput,ainside,aoutput,box,line1,line2,n2text,theta1text,theta2text],scaling=constrained,view=[&ndash;1..2,&ndash;1..H]);   endproc:        Light enters from the air into a medium at an angle of theta1 relative to the normal. It is refracted to an angle of theta2and travels through the medium, returning back to the air.      You can vary two parameters:       theta1the angle of incidence       n2the index of refraction of the medium*(assuming the index of refraction of the air is essentially 1.0).     To do: Let it execute and start manipulating the sliders.     >Explore(RefractionDemo(theta1,n2),parameters=[theta1=0..Pi2.0015,n2=1..3.]);"

 

``

``

``

``Dear Prof.

The following code seems not copying properly (my communication error be allowed please)

 

"ainput:=arrow(?&"

Error, unable to delimit strings/identifiers

"ainput:=arrow(&acirc;ï¿&frac12;&uml;&ndash;cos(theta1),&ndash;sin(theta1)&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;cos(theta1),sin(theta1)&acirc;ï¿&frac12;&copy;,color="Red"):ainside:=arrow(&acirc;ï¿&frac12;&uml;0,0&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;1,tan(theta2)&acirc;ï¿&frac12;&copy;,color="DarkBlue",width=[0.05,relative=false]):aoutput:=arrow(&acirc;ï¿&frac12;&uml;1,tan(theta2)&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;cos(theta1),sin(theta1)&acirc;ï¿&frac12;&copy;,color="Red"):"

 

``

``

"I checked by typing separately. It works as below."

``

``

a1 := arrow([-cos(theta1), -sin(theta1)], color = "LightBlue")

 

``ainput := arrow([-1, 0], color = "Red")

 

"But the copied from your code does not work."

"ainput:=arrow([-1, 0],color= "`Red"`)"

Error, unable to delimit strings/identifiers

"ainput:=arrow([-1, 0],color= "`Red"`)"

 

``


 

Download forScotgould_Error_arrow.mw

It is easy to draw all the types of arcs in plots. Hence a multiple plot may help under such situations. I attempted to draw for a few problems, but found it difficult. Can any one help in drawing the same to get neat and clean output drawings for me to explain the answer to students.

Thanks
 

Find the area of the shaded portion (b) . (portion b not shaded)

 

 

 

 

Find the area of the shaded portion.

 

 

 

 

 

 Area b = Area (a+b) - Area a =    -     =

 

 

Find the radius of the circle.

 

 

 

 Mistake : It shd be 0.25 and not 4 times (x+...)

 

 

Find the height of the cone.

 

``

``

A circle with radius 1 is tangent to 2 points of the parabola y = x2   What is the area between the circle ana parabola?

 

 

 

 

 

 

 

NULL


Maple drawing shows all outer portions of circles.I used snipping tool to get cropped picture for first problem.

I already got a similar problem and got a response that i should use being forward and backward, but that seems to be not worth it many a times since figures become bigger in maple drawing with outer rectangles used for eliminating portions. (Ex: problem 1, not shown here)

Thanks.

Download GeometryProblems_Sketches_Problems.mw

Can any one find why the first code works and not the second code?
The same code, but not shown in the upload below.

reset; with(Plot)
plot(tan(x), x = -Pi .. Pi, y = -(1/2)*Pi .. (1/2)*Pi, color = ["blue"], legend = Graph*of*inverse*tan*`function"`, caption = " Domain = [-&infin;, &infin;]; Principal range = [-&pi;/2, &pi;/2]")

 

``

``

``

"plot(tan^()(x),x=-Pi..Pi, y = -Pi/(2)..Pi/(2),color = ["blue"],legend = "\"inverse tan (""x"")\"", title= "Graph of inverse tan function", caption  =" Domain = [-infinity, infinity]; Principal range = [-&pi;/2, &pi;/2]")"

Error, invalid =

"plot(tan(x),x=-Pi..Pi, y = -Pi/2..Pi/2,color = ["blue"],legend = , title= "Graph of inverse tan function", caption  =" Domain = [-infinity, infinity]; Principal range = [-&pi;/2, &pi;/2]")"

 

``


 

Download SyntaxErrorinlegend.mw

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