## maple code generation...

hi everyone,

i need help to write a maple code to generate an animation sequence showing the taylor series approximation of tan(x) from

N=1..5.

plot the animation from x=-2pi to 2pi and y=-5 to 5.

## Mathematics and Maple...

hi everyone,

I need help writing a maple code to calculate the normal to the curve X^2-2X at x=1

and also display the curve, the tangent, and the normal on the same plot in the range x=[-2,2].

## question on notation.... abs(1,x) vs x/abs(x)...

When I take the derivative of abs(x), I use the chain rule and get this

When I ask Maple to differentiate abs(x), I get this:

I read the help file on "signum", and I expected this to work, but it does not.

How can I represent signum in normal calculus syntax when working the derivative of functions involving abs(x)?

## find values of a at which an implicit function has...

I've got

f(x,y)= a.exp(1+xy) +( a^2 )*sin(x)+1

for which I've shown that there exists an implicit function x=g(y). ( df/dx <>0)

and df/dx = a*exp(1+xy) +( a^2 )*cosx now in the neighborhood of P=(0,0) for the implicit function to exist I'd need a*exp(1+xy)*y <>0 but at P, wouldn't this be 0?

Given, g(y)=x, how do I find the max,min,saddle points?

## Integration with u, du and erfc erro term...

Hi all,

I'm having a challenge solving an integration that has some error functions associated with it.

Description:

I am trying to find the Riemann midpoint of the integral. All the parameters are known except the u and du terms which came into the expression following a laplace transform.

the output I get from the above input is shown below, and as it can be seen, the u and du terms coupled with a complimentary error function still exist. I have tried the "simplify" function and it returns similar output expression.

Any help will really be appreciated.

Thanks :)

## Mean value theorem by maple 13...

Hi there,

I want to use maple 13 for calculating mean value theorem for differentiable function  f:=piecewise(-2≤x≤0, -x2 ,0≤x≤2,x2

on the interval [-2,2]. But an error occured, that is,"function must be continuous".Any help will be appreciated.

REGARDS

Yegan

## How to write a simple code...

Hello,

How can I write a code to calculate the Rieman Sum for  y=x^1/2 [0..4] using

left hand rule and 100 subdivision.

Thank you

## minimum of a function using determinants...

Determine using determinants the range of values of a (if any) such that
f(x,y,z)=4x^2+y^2+2z^2+2axy-4xz+2yz
has a minimum at (0,0,0).

From the theory, I understand that if the matrix corresponding to the coefficients of the function is positive definite, the function has a local min at the point. But, how do I get the range of values of a such that f is a min? Is this equivalent to finding a such that det(A) > 0?

2.

Now modify the function to also involve a parameter b: g(x,y,z)=bx^2+2axy+by^2+4xz-2a^2yz+2bz^2. We determine conditions on a and b such that g has a minimum at (0,0,0).
By plotting each determinant (using implicitplot perhaps, we can identify the region in the (a,b) plane where g has a local minimum.

Which region corresponds to a local minimum?

Now determine region(s) in the (a,b) plane where g has a local maximum.

I don't understand this part at all..

## 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

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