rlopez

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15 years, 85 days

Dr. Robert J. Lopez, Emeritus Professor of Mathematics at the Rose-Hulman Institute of Technology in Terre Haute, Indiana, USA, is an award winning educator in mathematics and is the author of several books including Advanced Engineering Mathematics (Addison-Wesley 2001). For over two decades, Dr. Lopez has also been a visionary figure in the introduction of Maplesoft technology into undergraduate education. Dr. Lopez earned his Ph.D. in mathematics from Purdue University, his MS from the University of Missouri - Rolla, and his BA from Marist College. He has held academic appointments at Rose-Hulman (1985-2003), Memorial University of Newfoundland (1973-1985), and the University of Nebraska - Lincoln (1970-1973). His publication and research history includes manuscripts and papers in a variety of pure and applied mathematics topics. He has received numerous awards for outstanding scholarship and teaching.

MaplePrimes Activity


These are answers submitted by rlopez

If I understand the question correctly, simply add the option "axes=boxed" to the plot command.

 

RJL Maplesoft

Assuming that you really have a circular cylinder ( what appears in your message isn't the equation for such), and taking a=1 and b=1/2, the following code will generate the graph I think you want.

p1:=plots:-implicitplot3d(x^2+y^2=1,x=-1..1,y=-1..1,z=0..Pi,style=surface,transparency=.1):
p2:=plots:-spacecurve([cos(t),sin(t),t/2],t=0..2*Pi,color=black,thickness=3):
plots:-display(p1,p2,scaling=constrained); 

RJL Maplesoft

Maple's top-level diff command will not take a derivative with respect to a function. In the Physics package, diff has been modified to do this task. The simplest way to access this modified version is to replace diff with Physics:-diff.

RJL Maplesoft

Look at the recorded solution from the Maple web site. It's at the end of this link:

http://www.maplesoft.com/teachingconcepts/detail.aspx?cid=3

 

RJL Maplesoft

The difficulty with the graph is the singularity at the origin. Here's a trick I learned from one of the Maplesoft programmers, and in my Red Book of Maple Magic it's dated December 19, 2012.

U:=min(3.5, 1/sqrt(x^2+y^2));

plots:-contourplot(U,x=-1..1,y=-1..1,grid=[70,70]);

 

The limit on heights imposed by the min command keeps contourplot from distorting the contours. The differing views shown in the post probably come from having evaluation points fall on the singularity or not.

 

RJL Maplesoft

An unevaluated integral constructed with the Int command can be sent to the built-in numeric integrator (an adaptive procedure) by applying the evalf command to the integral. For example:

q:=Int(x,x=0..1);

evalf(q)

 

Not sure how important it is to your work that the integral actually be evaluated by the Trapezoid rule.

RJL Maplesoft

In the Tools menu, select Tutors, then Calculus-Single Variable, then Newton's Method.

That tutor will probably give  you what you need. Notice the command at the bottom of the tutor. You can copy and paste that command and use it to fine-tune. You will h ave to load the Student Calculus 1 package to make that command work. Use the Tools menu again, but this time select Load Package and then select the Student Calculus 1 package.

 

RJL Maplesoft

The feasible region is a triangle in the first octant, vertices are (3,0,0), (0,3,0), (0,0,3);

The function value at each of the three vertices is approximately 18.4.

Now search on each edge of the triangle. The function has a minimum along each edge.

Now search for an "interior" max by eliminating z. Look for a max in f(x,y,3-x-y). Apply plot3d to see that the highest point is in the plane x=3. Therefore, look for a max in f(3,y,-y). This max is approximately 19.8 (by fsolve and the usual techniques of the calculus).

RJL Maplesoft

with(Typesetting):
interface(typesetting=extended):

Suppress(g(t)):

diff(g(t),t) will then appear as the letter g with an overdot, and no independent variable showing.

 

The Suppress command is part of the Typesetting package. The difference between Suppress and declare is that with Suppress, the independent variable can be omitted on input as well as on output. Thus, diff(g,t) will then appear as g with an overdot.

RJL Maplesoft

There are commands in the Student VectorCalculus package that make the task a bit less tedious.

with(Student:-VectorCalculus):

V:=Vector([3-3*cos(theta),theta],coords=polar);
R:=PositionVector(convert(V,list),coords=polar);
T:=TangentLine(V,theta=3*Pi/4);
q1:=PlotPositionVector(T,x=-8..2):
q2:=PlotPositionVector(R,theta=0..2*Pi):
plots:-display(q1,q2,scaling=constrained);

 

 

RJL Maplesoft

Control Enter will put a visible page break at the point where the cursor is.

 

RJL Maplesoft

Four equations in two unknowns. I suspect that there were more than just syntax problems here.

 

RJL Maplesoft

Square brackets in Maple denote lists. They should not be used as replacements for parentheses. Change "[" to "(" and "]" to ")" in the definitions of the ODEs.

RJL Maplesoft

The code for the animation resides in the button Animation 2. Unfortunately, if you are viewing the example on the web site, you can't access the code. Here's the essence of the code:

with(plots):
with(plottools):
with(VectorCalculus):
q := plot(x^2, x = 0 .. 1, filled = true):
F := transform((x,y)->[x,0,y]):
Q := plots:-display(F(q)):
V := RootedVector(root=[2,0,0],[0,0,1]):
A := PlotVector(V,color=black):
p := display([seq(rotate(Q, (2*Pi*(1/30))*k, [[2, 0, 0], [2, 0, 1]]), k = 0 .. 30)], insequence = true):
spin := display([A, p]):

p4 := translate(animate(plot3d,[[r,t,(r-2)^2],r=1..2,t=-Pi..x,coords=cylindrical,filled],x=-Pi..Pi, paraminfo=false,frames=31),2,0,0):
display([p4,spin],labels=[x,z,y],tickmarks=[4,[0],2], orientation=[-55,70], axes=frame,scaling=constrained);

 

The variable q contains a graph of the region to be rotated, but it lies in the xy-plane.

The function F changes the plot data structure q so that the y-height becomes the z-height, and the y-coordinate is set to zero.

Q is then the plot data structure for the transformed region q.

V  is the arrow used to represent the axis of rotation.

A is a graph of the arrow V.

The animation of the rotation of Q about V is given the name p. This animation has 31 frames, each of which is obtained by applying the rotate command to the image in Q.

When the animation p is joined to A, the graph of the arrow V, it is called "spin".

The animation p4 uses cylindrical coordinates to draw the ever-expanding surface of the solid of revolution. However, this animation has to be translated so its vertical axis coincides with the vector V. This is done with the translate command.

The final display joins the animation p4 with the animation "spin". The result is the given region rotated about the axis x=2, dragging along the surface of revolution generated as the region rotates.

This is not the most efficient code, and a worksheet containing all these frames is slow to load. The animation generated by Carl Love's code is less resource-intensive.

 

RJL Maplesoft

Perhaps the reference is to the ODE Analyzer Assistant, an interactive assistant that can be accessed from the Tools/Assistants menu, or via the command dsolve[interactive]().

Of course, the argument to this command could be the ODE, in which case the Assistant launches with the ODE already in it. Alternatively, first write the ODE, then use the Context Menu option Solve DE Interactively, to launch the Assistant with the ODE already in it.

In either case, this Assistant has been part of Maple for a number of releases, including Maple 17

RJL Maplesoft

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