rlopez

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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.

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These are answers submitted by rlopez

https://www.bing.com/videos/search?q=lines+and+planes+Maplesoft+Youtube&docid=607991258261816461&mid=5BE57C2C787E7B8ECE5E5BE57C2C787E7B8ECE5E&view=detail&FORM=VIRE

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At 52 minutes, 25 seconds into this video, Problem 10 (distance from a point to a plane) is solved via the tools in the Student MultivariateCalculus package. All 11 problems in this video illustrate a variety of tools in this package related to the typical section in a calculus text "Vectors, Lines, and Planes."

with(Student:-VectorCalculus):

p1:=<4,3,-5>:
p2:=<3,-1,4>:
v:=p2-p1:
V:=RootedVector(root=p1,v):
PlotVector([p1, p2, v, V], color = [black, red, green, gold], width = 0.2, scaling = constrained, labels = [x, y, z])

The vector V retains as an attribute the location of its initial point. The parallel transport of v to its new location is thereby built into the definition of V, and is not an artifact of how it is graphed. 

Student:-MultivariateCalculus:-LagrangeMultipliers((x-2*y)/(5*x^2-2*x*y+2*y^2), [2*x^2 - y^2 + x*y-1], [x,y])

Include the option "output=detailed" to get the values of the function

and the multipliers at the critical points.

Alternatively, 

F:=(x-2*y)/(5*x^2-2*x*y+2*y^2)+lambda*([2*x^2-y^2+x*y-1)

solve({diff(F,x)=0, diff(F,y)=0, diff(F,lambda)=0},{x,y,lambda})

I'd use the following approach.


with(Student:-VectorCalculus):
r := <cos(t), sin(t), t>;
rp := diff(r, t);
SpaceCurve(r, t = 0 .. 2*Pi);
SpaceCurve(rp, t = 0 .. 2*Pi);

 

No need to make r a function just to draw a graph. The SpaceCurve command in VectorCalculus is more robust than the spacecurve command in plots since it applies top both 2- and 3-component vectors.

For any task template that uses embedded components, the code is "behind the components." By this is meant, right-click on the component or use the Context Panel, and select the option that contains the code.

Most Math Apps are written with embedded components, but are coded with procedures defined in a start-up section, with simple function calls "behind the components." Unfortunately, it does not seem possible to access this start-up code, but some other contributor to this forum might know a trick or two that I don't.

Tutors have a command-name in the associated Student packages. Showstat can be applied to that command name.

An Assistant such as the ODE Analyzer Assistant has the command name dsolve[':-interactive'], to which the showstat command can be applied. These command names can be found as follows.

At a (red) worksheet prompt, using 1D math input, enter a differential equation and use the Context Panel to select the interactive form of solving the DE. Maple will write the command that calls the ODE Analyzer Assistant. This name can also be found by rummaging through the appropriate help page, but having the Context Panel print the name might be faster.

answer5 contains equations x=..., y=...

Your input to arctan is then the ratio of two equations, not of the two numbers on the right of the equal signs.

A simple fix would be eval(arctan(y/x),answer5)

The following lines produce the result you want.

with(Typesetting):
Settings(useprime, prime=x,typesetprime=true):
Suppress(f(x)):
D(f)(x)(0)

 

The VectorCalculus package requires explicit declaration of the coordinate system and coordinate names. These names are used, for example, when Maple then computes a gradient.

The Student VectorCalculus package defines default variable names in the Cartesian, polar, cylindrical and spherical coordinate systems. Hence, there is far less need for declaring coordinate systems and their associated variable names. (In Cartesian coordinates, the default coordinate names are x, y, z.)

So, what you tried in VectorCalculus would have worked in the Student package, without the need to include differentiation variables in the call to gradient of f. The default names x and y would have been used in both instances of the nabla.

The error you are  making is not understanding the help page for pdsolve/numeric, wherein the very first line is

PDEsys-single or set or list of time-dependent partial differential equations in two independent variables.

This line means that only evolution equations (i.e., heat and wave equations) can be solved numerically. There is no numeric elliptic solver in Maple.
 

From the Maple Application Center, find Prof Werner's Fourier Series package:

Symbolic Computation of Fourier Series

It contains a command for generating and animating the graph of Fourier series. I highly recommend this package and had always hoped that something like it would be added to Maple.

If the equations are independent but are greater in number than the number of variables, then your system is a candidate for a least squares solution. If that is what you want to pursue, then let us know - Maple has tools for such.

In the Tools menu, select Tutors/Calculus-Single Variable/Derivatives

This pop-up too will accept an expression, provide its derivative, and graph both the expression and its derivative just by clicking the appropriate buttons. No need to learn or look up syntax.

Try either of the following Tutors:

TangentSecantTutor (in the Student:-Calculus1 package)

FunctionSlopeTutor (in the Student:-Precalculus package)

To get help on either of these, execute ?TangentSecantTutor or ?FunctionSlopeTutor. The help pages will show the correct syntax for implementing these syntax-free tools.

Assign the differential equation a name such as de.

Apply the dsolve command with the option numeric.

Assign this a name such as Q.

Apply the odeplot to Q.

de:=diff(y(t),t)=y(t);
Q:=dsolve({de,y(0)=1},y(t),numeric):
plots:-odeplot(Q,t=0..2)

With the numeric option, the dsolve command creates a procedure that will calculate the numeric solution of the initial value problem. The odeplot command applies all the necessary coding to extract that numeric solution and graph it. The odeplot command lives in the plots package and can be called as shown above. If the plots package is brought into Maple's active memory via the command "with(plots):", then the call to odeplot does not need the prefix plots:-

Finally, don't hesitate to consult the help pages by executing ?dsolve,numeric or ?odeplot. At the bottom of each help page there are examples of how to use the command. Additionally, you might consult the Student Portal that contains some 150 questions (with answers) of the form "How do I...?" An easy way to get to the Student Portal is to execute the command ?StudentPortal

What you want to look up are the two commands listed in the title. Define the curve with the PositionVector command, and use the PlotPositionVector command to graph the curve and a variety of vector fields along the curve.

This pair of commands was especially created to serve exactly the purpose you express.

If you need help setting this up, let us know.

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