## How to Take Partial Derivative of a Mapping?...

Here's how to break Maple's 'D' function:

```~\$ cmaple mapleBug.mpl
|\^/|     Maple 2018 (X86 64 WINDOWS)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2018
<____ ____>  Waterloo Maple Inc.
|       Type ? for help.
> D[1]((x, y) ->x^2-y^2);
(x, y) -> 2 x

> D[2]((x, y) ->x^2-y^2);
(x, y) -> -2 y

> with(VectorCalculus):
> assume(x, 'real');
> assume(y, 'real');
> D[1]((x, y) ->x^2-y^2);
(x, y) -> 0

> D[2]((x, y) ->x^2-y^2);
(x, y) -> 0

> quit
memory used=2.4MB, alloc=8.3MB, time=0.06

~\$```

What if a person needs to have these lines:

```> with(VectorCalculus):
> assume(x, 'real');
> assume(y, 'real');```

and then he wants to take partial derivatives? Not possible? Once you load VectorCalculus and declare x and y real, Maple stops doing partial derivatives? Why.

## Results from op...

Sorry,

I have been away from Maple for a year.
Then, when I used op command, I am puzzed to notice the results were different from those I know.

>op((x+5)^2*(x+y));
_EXPSEQ((x+5)^2, x+y)

Result I know is

(x+5)^2, x+y

Has a modifire such as _EXPSEQ   automatically come to be attatched?
Or, can I have maple express it  in the form I know:  (x+5)^2, x+y?

taro

## Question in 3D Space...

A mathematical friend wrote to me recently with the following problem:

a + b + c = 1

a² + b² + c² = 2

a³ + b³ + c³ = 3

Find the values of  a^4 + b^4 + c^4 and a^5 + b^5 + c^5.

Note the question doesn’t ask for the values of a, b and c, but can you find them?

## How do I write this differential equation (Newtons...

Hi all, I would be most grateful if I could get some help with solving the tasks below using Maple.

Given the function: mx''(t)+cx'(t)+kx(t)= F_y(t)

1. Rewrite the equation above to a system of 1. order differential equations, by defining the two variables x_1(t) = x(t) and x_2(t)=x'(t) (Hint what is x'(t)?) This gives the first differential equation in the system. What is x_2'(t)?

2. Write the equations as a linear system when the outer force F_y(t) is the influence and the position x_1(t) is the answer, in other words give the system matrix A and the vectors b and r.

3. I'm given the constants m = 5kg, c = 3Ns/m and k = 20 N/m and I'm trying to find the transfer function of the system.

4. Give the systems transfer function H(s) and draw the graphs for the amplitude and phase characteristic.

Thank you!

## How can get a point M(x,y,z) in side the triangle ...

I have triangle TAD. Now I want to take any point inside the triagle TAD. How can I take it? I tried

```restart;
with(Student:-MultivariateCalculus);
A := [1, 2, 3];
DD := [-2, 1, 0];
T := [1/2, 1/2, 3/2];
P := Plane(T, A, DD);
GetRepresentation(P)```

I got the quation of the plane TAD is

`-3*x-3*y+4*z = 3`

With the point P(x,y,z). What is the condition of x, y, z?

## Mean Value Theorem ...

Given the following functions and respective intervals graph them and determine all values of in the interval (a,b) such that

f'(c) =f(b)-f(a)/b-a (apply the Mean Value Theorem)

Question 1: f(x)=x^3-2*x      [0,2]

Question 2 : g(x)= cuberoot(x-3)^2     [-3,4]

## ColorTools not really precise on gamuts and Color ...

Dear All

I wanted to use the ColorTools of Maple to study the conversions between color spaces and different color definitions, but I find the tool very limited and rather confusing.

My main issue is to understand really which "RGB" definition is used ?
I assume it's a "RGB" = sRGB from Adobe(r) that is then translate to CIE 1931 values XYZ, xyz, Lab and more recent Luv values, all based on D65 illumination ? This must be really better defined in the help !!!

This is really not clearly stated as today "RGB" means mostly Adobe 1998 RGB, the larger gamut color space from Adobe and not the older and more reduces sRGB.

Color Space and Color understanding is subtile and require really a clear differentiation about illumination, color mappings, input, and output devices, and more ...

This issue applies to the "HSV" and "CMYK" these are all HW associated devices, and at least the standard illumination considered here must be defined, from my undersanding (and within the CIE definitions there are at least half a dozen of illumination standards, the most common, for me, are the D50, & D65).

It would be great if the ColorTables allowed us to really study colors in a correct way and following more the appraoch of i.e. "Digital Color Management, ENCODING SOLUTIONS" by Edward J. Giorgianni and Thomas E. Madden, Wiley (2.Ed, 2008) or some of the other serious book on color management.

Sincerely

Ivar

## how I can write a program code for newmark method...

how I can write a program code for newmark method.

in this method time has 3 order derivation

## Table properties...

I have made a table and did a programme to do calculations inside.

While converting into a pdf, i found that the table cells being continuous overlaps on pages. I now want to trim the table or split the table to convenient size. Any suggestion.

How do I convert a 7 x 3 table into a 4 x 3 and 3x3 table? Reducing font size does not alter the row and cell size. Is there a way to alter the columnwidth and row height in maple?

Thanks for suggestion.

## interface(Typesetting) issue bug...

Why does this happen

interface(Typesetting)

interface(Typesetting=standard)

interface(Typesetting)

a2

## How do I write a subscript/superscript into text s...

I've looked up previous answers to this but __ double underscore only works in math input, and ctrl + shift + ^ or ctrl + shift + _ does not seem to work. I'm using Maple 18, windows computer.

## How to set all cells in table to text?...

I'm using a maple doc to do a homework assignment that is mostly text with only a few equations and math sections. I need to draw a table of material properties in, and when I create a table all the cells default to math inputs. Because of this if I try to evaluate the entire document I get tons of blue evaluation numbers in the table that I don't want, since all the mateial properties show up as math. I can set each cell to text one by one but there are like 30 cells and it's tedious. How do I set the entire table so that each cell is a text cell?

## Is it possible to Explore the solution of a parame...

Hi,

Suppose I numerically solve an ODE systems with formal parameters.
Is it possible to use Explore to visualize the solution?
(the goal is to associate for instance sliders to these parameters and to visualize easily how they act)

Here is a notional problem with only one unset parameter "a".
What I usually do to analyse the role of the parameters corresponds to the for loop.

 > restart:
 > sys := { diff(x(t), t) = a*t, x(0)=0 }:
 > sol := dsolve(sys, numeric,parameters=[a])
 (1)
 > A := [seq(1..3, 1)]: for n from 1 to numelems(A) do   sol(parameters=[A[n]]):   pic||n := plots:-odeplot(                             sol,                             [t, x(t)],                             t=0..1,                             color=ColorTools:-Color([rand()/10^12, rand()/10^12, rand()/10^12]),                             legend=A[n]                           ): end do:
 > plots:-display(seq(pic||n, n=1..numelems(A)))
 >

## Is well defined this "recursive" function?...

Hi!

Let F(z) (with z complex) a given function. I want to compute F^n(z0), i.e. the composition of F with itself n-times, where z0 is a given point (complex).

Is correct the following procedure to compute F^k(z0)?

App := proc (k, z0) local z1, z2, j; z1 := z0; z2 := NULL; for j to k do z2 := F(z1); z1 := z2 end do; return z2 end proc

## solve inequation with piecewise function ...

Hi

Consider the piecewise function

f:=x->piecewise(x≤0,−3,0<x≤1,x^2,1<x,-x)

can Maple solve the inequation  in R:   f(x)> a

where "a" is a given number in R

Of course the results depend on parameter a