## Solving a simultaneous equation with angles and di...

After analysing a sketch I came up with two equations describing the sketch.

My first equation looks like: eq1 := tan(X/2) = Vt/Hr;
My second equation looks like: eq2 := tan(X) = (V-Vt)/Hl;

I know the values for Hr, Hl, V so I am left with two unknown values which is angle X and distance Vt.

I have typed these equations in Maple 8 and when I substitute the values Hr, Hl, V then Maple does come up with the correct solution to either angle X or distance Vt. My problem is that I do not want the specific answer to this problem. I need a general answer. That means I want an equation where I can put in any legal values for Hr, Hl, V and then the equation will calculate either Vt or X for me.

Is is possible to add comments in Maple code without gyrating through the LanguageDefinition? Below is a sample that shows an embedded comment - it would be nice if this were possible.
```fn := proc(n)
local x;

# here's my math
x := n + n;

end proc;

C(fn);

int fn(int n)
{

// here's my math
x = n + n;

return x;
}
```

## piecewise functions with vectors...

Hello,

I'm trying to create a piecewise function with vectors instead of constants. So far I have

vf := 3*vx[1] < [6, 1] and vx[1] < [-2, 5], [3, 4]+3*vx[1], 2*vx[1] < [8, -4] and -vx[1] < [2, -5], [1, 9]+2*vx[1], -3*vx[1] < [-6, -1] and -2*vx[1] < [-8, 4], [9, 5]

This won't convert to a piecewise function. However, if the vectors are in the form (1,2) instead of [1,2] (ie. with parentheses instead of braces), it works. Is there any way to convert them at this stage or earlier, when I have then as individual functions (for example: 3*vx[1] < [6, 1])?

Thanks for the help,

Am

## Linear Differential Operators...

Hi Friends My name is Sayed Hoseini and I am PhD student in University of Wollongong. Could you please have a look on this problem and let me know about any package/s which might be used for solving that? I came across to this problem in my research: We have a linear system including two differential equations and two variables; For example consider the following system: L*U=H Where: [diff(,x\$2)+I*w q ] L=[ ] [q diff(,x\$2)- I*w] and [u(x)] U=[ ] [v(x)] that u and v are functions of x and w, q and H are functions of x too, but fixed and I is the complex argument .

## speed up calculation using the interpolant option ...

Looking for faster ways to make chi^2 nonlinear fit calculations, for functions involving integrals, I have compared timings of calculation of chi^2 at a pair of sample points evaluating the integrals by three numerical methods. In the attached worksheet they are called as follows: 1. chin, using evalf(Int(...)) 2. chin2, using the interpolant option (`dsolve/numeric`(sys, range=...)) 3. chin3, using evalf(Int(...,method=_d01ajc)) I have obtained timings with Maple 9.5 using first a Celeron 333 MHz under RH7.1 and then a P4 1.8 GHz under Win XP. My expectation was that the method of the interpolant function were the

## External Callling and new Watcom compiler...

How do I create a shared library for use with the define_external command?

In the examples,ExternalCalling help page the following command is used.

> ssystem("cl test1.c -Fetest1.dll -Gz -link -dll -export:f1"):

But this assumes the Microsoft Visual C/C++ compiler.

I want to use the new Watcom compiler included in Maple 10 for Windows.

Bob.

## Implied Multiplication Question...

I'm wondering if a Maple guru would comment on the behavior of Implied Multiplication. I was working through an exercise with Maple and ran into the following behavior. Initially I had this: limit(sum(3((1+3*i/n)^3-2(1+3*i/n))/n, i = 0 .. n), n = infinity) = 231/4 which didn't look right since I expected a different result. Ater messing about I tried looking at the operators and when I did this: limit(sum(3((1+3*i/n)^3-(2)*(1+3i/n))/n, i = 0 .. n), n = infinity) = 195/4 I got the answer I expected to see. [note that Maple Primes has distributed the 2 inside the brackets above. In my document it is 2*(1+3/n)]

## Problem with FunctionChart...

When using the FunctionChart call from Student[Calculus1] I keep running into a strange problem. As soon as I attempt to change the display size with the view=[x1..x2,y1..y2] option I get a tiny little graph that is no larger than an ordinary icon. Does anyone have a work around for this? As an example this misbehaves on my Maple 10 install: with(Student[Calculus1]) with(Plots) FunctionChart(x^2, x, view = [-2 .. 2, 0 .. 9]) Tim

## formal parameters in procedures - why formal?...

In the Help section under procedures (or proc) it states:
argseq - the formal parameter names
I just wondered about the use of the word 'formal'.
eg in this simple Maple code
maxim:=proc (a,b,c,d)
max(a,b)+max(c,d)
end proc:
maxim(2,3,5,4);
. . . the formal parameters are a, b, c, d. Is the word 'formal
' being used as "officially recognised" and a=2, b=3 etc. (ie the
order is important or is there
some deeper meaning? I'd appreciate a short example of a proc using
something else besides variable values, or Null.
Thanks
David

## ODE Curve fitting...

Ok, I have the following equations: c'[t] = a[t]*b[t]*k1 - c[t]*k2, a'[t] = (-a[t])*b[t]*k1 + c[t]*k2, b'[t] = (-a[t])*b[t]*k1 + c[t]*k2, c[0] =0, a[0] =10, b[0] =10. I have data for concentration of "c" at all time intervals from 0-16. Here is the data: {0, 0}, {1, 4.98112}, {2, 6.61986}, {3, 7.42423}, {4,7.89529}, {5, 8.20004}, {6, 8.41008}, {7, 8.56123}, {8,8.67342}, {9, 8.7586}, {10, 8.82442}, {11, 8.87595}, {12, 8.91671}, {13, 8.94923}, {14, 8.97535}, {15, 8.99643}, {16, 9.01351}. I need Maple to Solve the ODE's and optimize the values for k1 and k2 to fit the data usins a least-square method or something along the lins of that. Can someone send me the code for that?

## How do I make Maple Code run faster after its conv...

We were wondering if you could help us with a question to Maple: We have converted a C code directly into Maple code and have found that Maple runs about a thousand times slower than the C version (the code is a numerical simulation). 1) Why is this so? 2) How do we make it run faster?

## print dsolve[numeric] result to file?...

Hi, All, I'm a Maple primer. I want to solve an ODE numerically and then save the data to file. I use: dsol := dsolve({deq,ic}, numeric, range=0..100); or dsol := dsolve({deq,ic}, numeric, range=0..100, output=operator); then how can I print the formated data for some specified t (=1..100, for example) to a data file? Thanks. David

## missing symbol...

I need the symbol for the partial derivative (something like @) in a .mws worksheet. Well, I found this feature as an operator on the new .mw platform, but I need it as a symbol. If I write a name (say PartialD) in the worksheet I want to get the symbol similar to @ at the screen.

What can I do?

Florian