## Hide variables in results of Jacobian / Diff ...

Hi,

for my simulation I have to calculate several gradients and jacobian matrices. The equations are quite complex and with my current setup hard to read.

Here is some exampel code:

restart;
with(VectorCalculus);
SetCoordinates(cartesian[x, y, z]);
alias(u = u(t, x, y, z), v = v(t, x, y, z), w = w(t, x, y, z)); alias(eta = eta(t, x, y, z));
U := VectorField(`<,>`(u, v, w));
Divergence(U);
Jacobian(U);
Diff(U, t);

The Divergence operator gives me a very compact result:

But Jaobian and Diff look like:

To achive a better readability I want to do two things (if possible):

1) hide the independet variables (t,x,y,z) in the result of Jacobian, Diff

2) display the result of Diff in a row vector (3x1) instead

Is this possible?

## January’s Featured Live Webinars

by:

Maplesoft regularly hosts live webinars on a variety of topics. Below you will find details on an upcoming webinars we think may be of interest to the MaplePrimes community.  For the complete list of upcoming webinars, visit our website.

Creating Questions in Maple T.A. – Part #2

This presentation is part of a series of webinars on creating questions in Maple T.A., Maplesoft’s testing and assessment system designed especially for courses involving mathematics. This webinar, which expands on the material offered in Part 1, focuses on using the Question Designer to create many standard types of questions. It will also introduce more advanced question types, such as sketch, free body diagrams, and mathematical formula.

The third and final webinar will wrap up the series with a demonstration of math apps and Maple-graded questions.

Clickable Calculus Series – Part #1: Differential Calculus

In this webinar, Dr. Lopez will apply the techniques of “Clickable Calculus” to standard calculations in Differential Calculus.

Clickable Calculus™, the idea of powerful mathematics delivered using very visual, interactive point-and-click methods, offers educators a new generation of teaching and learning techniques. Clickable Calculus introduces a better way of engaging students so that they fully understand the materials they are being taught. It responds to the most common complaint of faculty who integrate software into the classroom – time is spent teaching the tool, not the concepts.

## Error in calculus sheet...

Hello Maple

I am preparing for an examination in Calculus, but my worksheet in Maple 18 doesn't cooperate.

A lot of my studypartners use Maple 16 and they have no problems.

I meet the following error:

- Error, (in solve) invalid input: hastype expects 2 arguments, but received 1

I'm totally sure, that I'm typing correctly, because I write just the same as my studypartners.
So is it an error, which only is seen in Maple 18 and can I do anything to solve the problem?

Kind regards
Anders Kristensen

PS: I can't figure out how to add a picture

## how do you do a vertical disk method?...

I have to find the volume of a solid using the disk/washer method and the shell method.  I think I have the first part(disk/washer) right.   I think the shell is off. The problem is "the region in the first quadrant that is bounded above by the curve y = 1/x^1/4, on the left by the line x = 1/16, and below bythe line y = 1 is revolved about the x-axis to generate a solid."    I am having computer problems so any help is appreciated. Thanks

## update to Clickable Calculus Study Guide

by: Maple

For those who have the Clickable Calculus Study Guide for Maple 18, please note that we have released an update to this ebook, which provides corrections and improvements to the text and examples.

eithne

## using maple to find the dimensions of a right cyli...

I under stand how to do the calculus that's easy enough, but Maple is stil giving me a hard time.  The math par t is let the radius of the cylinder be r cms. 0<r<10 Then the height is 2 * Sqrt 100-r^2, the volume is V(r)=2PIr^2* sqrt 100-r^2 cm^3

Differentiante V(r) with respect to r we get V' (r) =2PIr^2(1/(2*sqrt(100-r^2)))(-2r) + (2PIsqrt(100-r^2))(2r)

V'(r)=(-2PIr^3 +4PIr(100-r^2))/sqrt (100-r^2)      V'(r)=2PIr(200-3r^2)/sqrt 100r^2         to find the critical point find the value of r when V(r) =0     2PI(200-3r^2)/sqrt 100-r^2 =0   2PIr(200-3r^2) = 0   r(200-3r^2)=0

r=0 or 200-3r^2 =0     r=0 or r^2=200/3 r=sqrt(200/3) =10sqrt(2/3)   r is not in the interval so ignore it.  The critical point for 0<r<10 occurs at r = 10sqrt(2/3)       Since V'(r) >0 for 0<r<10sqroot(2/3) and V'(r) <0<10sqrt(2/3)<10

The dimensions are r=10sqrt(2/3) =8.16 cm and h=20/sqrt3 = 11.55 cm the volume is 4000PI/3*sqrt3=2418.4 cm^3

So how do I translate this into maple? Any help is greatly appreciated.

## apply convert(,exp) to matrix...

Hi all,

I am stuck with the following problem:

convert(cos(alpha), exp); works fine for me.

Once I have the trigonometric functions in a matrix, it does not work any more:

In the latter line, A keeps the trigonometric functions. Why is this the case? Is there any way to force maple to keep the complex exponentials instead of trigonometric functions?

I am using LinearAlgebra and VectorCalculus.

Best Regards

Wassja

## differentiate a function with respect to a vector ...

f:=x+y+y;

diff(f,x);
diff(f,y);
diff(f,z);

What I hope to get is a vector with i-th entry being the dervative of f, differentiated w.r.s.t the i-th parameter, like this

Vector([1,1,1]);

Is there a more efficient (built-in) command to do this?

VectorCalculus[diff] does not do what I want.

Thanks,

casper

## Clickable Calculus Study Guide

by: Maple

We have just released an all-new, second edition of the Calculus Study Guide.

This guide has been completely rewritten and greatly expanded and to take full advantage of Maple’s Clickable Math approach.  It covers all of Calculus I and Calculus II and has over 450 worked examples, the vast majority of which are solved using interactive, Clickable Math techniques.

Not only is this guide useful for students learning calculus, but it can also serve as a guide for instructors interested in pursuing a syntax-free approach to using Maple in their teaching.

eithne

## Why is there an error in Tangent command?...

Why does:

Student[Calculus1]:-Tangent(tan(3*x)-5*exp(-x^3),x=0,output=plot,gridlines=true,caption="")

produce the following error?

Error, (in plots:-display) integer or integer range expected in op list

## How do I solve a system of equations in Maple 17 f...

I was required to purchase Maple 17 for my upcoming Calculus III course, and until now, I have been using my TI-Nspire CAS CX for all of my CAS needs.  I am going through various tutorials/labs in an effort to learn how to use the Maple 17 Software. As a part of this process, I am attempting to solve a system of equations and was told to use the following command:

>solve({2*x+3*y=7,5*x+8*y=9},{x,y});

{y=-17,x=29}.

Instead, I have received the following error message, which has no help attached to it through the help page.

solve({2*x+3*y = 7, 5*x+8*y = 9}, {x, y});
Warning, solving for expressions other than names or functions is not recommended.

I am hoping this has something to do with Mac vs. Windows software, and that it has a simple solution.  I would greatly appreciate any guidance!

## How do I plot this orthogonal trajectories equatio...

I'm taking calculus and my professor introduced us to maple software. The professor asked us to plot the families of curves for this orthogonal equation:

dy/dx = (x^2) - (2y^2) - C = 0

This is what I had so far:

restart;

with(DEtools):

with(plots):

Function:=unapply(simplify(x^2-2y^2-C),(x,y)):

'Function'(x,y) = Function(x,y);

plotFunction:=C->implicitplot(eval(F(x,y),a=C),x=-5..5,y=5..5,scaling=constrained):

plot1:=display(seq(plotFunction(a),a=-5..5)):

display(plot1);

This is only display one family. How do I code for it plot the other families?

(The graph should look like curves converging from left, top and right sides toward to the origin of the axes)

## Multivariate Taylor expansion...

How can I expand the mutivariate taylor series of the functions below about the point (x,y)

f(h*a[2]+x, h*a[2]*k[1]+y);

and

f(h*a[3]+x, y+h(a[3]-b[32])*k[1]+h*b[32]*k[2]);

## Maple 17 Won't plot this ...

I copied and pasted this from the example page and I have to get this same graph for an assignment

im using maple 17

when i hit enter the return was

(1)

## Max/Min Problems in Maple 17...

Hello All,

I have had a few questions that have come up while working on a Maple Assignment for my Calculus III class. I was wondering if anybody could help me with these questions, as well as show me how to enter them in Maple. Here are the questions I have been struggling with.

1. In the xy-plane, graph the ellipse ((x-4)^2)/(4))+(y-4)^2=1 and two level curves of F(x,y)=x^3+y^3-3xy that just touch the ellipse.

a. What do we know about the gradients of F and the ellipse at those points?

b. Use your graph to approximate the minimum and maximum values of F subject to the constraint ((x-4)^2)/(4))+  (y-4)^2=1.

2. A company manufactures a product using inputs x,y,z according to the production function Q(x,y,z)=20x^(1/2)y^(1/4)z^(2/5). The prices per unit are \$7 for x, \$12 for y, and \$18 for z.

a. Create the cost function

b. The company wants to produce 2500 products. Estimate the minimum cost by using the graph of the level surfaces of the cost function (from part a) together with the production constraint.