2 question

one, how do you plot two graphs together of f(x,y)= x - x - y + y and it's tanget at plane (1,1). i can do it individually but is it just simple as putting them in one notation in plot command? for f(x,y) i used plot3d(f(x,y)) from -pi to pi for both x and y but don't know how to put tangent in at plane (1,1)

two, how apporoximate f(x,y) = y / x by a polynomial of degree 6 in x-1 and y+1.

any hints or examples are much appreciated.

thx

Hey guys, I want to plot a differential equation (I'm looking for something a 2d direction field plot)
The differential equation is a composition of piecewise functions and a cubic spline. I have to use the subs() call to convert the function h(t) into a numeric (i dont really understand this part but was told to do this). Anyways I need the DEplot error explained to me. Here I show all of the relavent code leading up to the error:
with(CurveFitting):
with(DEtools):
z := t -> 4.713*sin((1/22356)*Pi*t)+.743*sin((1/21600)*Pi*t)+.964*sin((1/22788)*Pi*t)

does any one know if it is possible to solve numerically a ODE sys write in matrix form without first evaluate is as a set of equation?

for example my system is y'(x)=A(x,y).b(x,y)

where y'(x) and b(x,y) are Vectors and A(x,y) is a matrix

so i would solve it numerically without doing first the dotproduct symbolically. I woud do this because my system equation is constitudet not from a simple matrix.vector but by large matrix inversion so do it symbolically first take a lot of time and memory.

When I do an integral Maple sometimes spits out ridiculous answers.... I don't have an example off hand but oft it will give me trig functions that it SHOULD evaluate. Last night at my lab I was trying to do a taylor series that involved sine squared and to the fourth, and instead of giving me NUMBERS like I needed it left it in terms of sine which was utterly useless to me!

How can I assign an argument to the real numbers in an interval?

I have a matrix M which is 3x4. I need add a fourth row to it. I've been trying

E:=Matrix([ [M], [0,0,0,1] ])

and

E:=Matrix([ [Row(M,1)], [Row(M,2)], [Row(M,3)], [0,0,0,1] ])

But neither of them worked. How would I do this?

Thanks,

Dave

October 23 2008
zoid 8
Hi, I am trying to find a general solution for a special case of the 4x4 Riccati Equation. My worksheet chugs for 5 hours and 2gigs of memory before crashing. Am I posing the problem incorrectly? Or will more memory help (and if so, how much memory)?

```
> with(LinearAlgebra);
> A := Matrix([[ZeroMatrix(2), IdentityMatrix(2)], [ZeroMatrix(2), Matrix(2, symbol = a)]]);
> B := Matrix([[ZeroMatrix(2)], [Matrix(2, symbol = b)]]);
```

Hi all!
Please help me to simplify the following expression:
ex1 := C10*C20*a^2+2*C10*C20*a*b+C10*C20*b^2-m*u^2*a*C10+m*u^2*b*C20+1/2*e1*e2*a^2+e1*e2*a*b+1/2*e1*e2*b^2;
1, I've tried the followings:
collect(ex,e1*e2);
Error, (in collect) cannot collect e1*e2
2, then I've read some advice here in the forum, and tried this:
subs(e1*e2=z,%);
collect(%,z);
S0_temp2:=subs(z=e1*e2,%);
This doesn't works as well. It simply doesn't substitutes z for e1*e2.
My goal would be to get something like this:
(a+b)^2*(C10*C20+1/2*e1*e2)-m*u^2*(a*C10-b*C20);
Thanks!

Hi,

I'm just playing about with Maple's functions to see what they do. I'm confused by the behaviour of "evalb". When I enter:

I want to learn how to analytically and graphically analyze discrete time recursion equations such as the following:
N(t+1) = (1+b)(1-d)N(t)
in Maple 12 because Mathematica decided to crap out on me right before I have to give a professional talk (SHAME ON YOU STEPHEN WOLFRAM!!).
Does anybody have a good direction to point me in? Basically, in Mathematica, what I would do is:
N[t_, b_, d_]:=N[t,b,d]=(1+b)(1-d)N[t-1,b,d]

hey i'm trying to learn how to use maple and can't seem to figure out why this is wrong. i don't really know what "nops()" does either.

with (linalg);

*insert equations, matrix and Groebner here and get a whole bunch of z values *

zvals:=[fsolve(polz)];

for i from 1 to nops(zvals)

Error, unterminated for loop

do

Error, unable to parse

myx:=zvals[i];

October 22 2008
me85 28
The text below was encrypted with a substitution cipher. Only the letters (both

upper-case and lower-case) were substituted, leaving punctuation and spaces alone.

Can any on help me to figure out what the original message was using maple procedures.

“wA’r aBeD WUeK AP XNaB NM U rALKNP USUeAJBMA NM zUM

nPrB ZNAW U JUM ZWP’r XBUeMNMO AP SXUD AWB aNPXNM.”

yWUA’r ZWUArWBAPXK AWB SPXNCB ZWBMrWBWUMKBK AWBJ

AWB BJSAD eBaPXaBe.

lNCWUeK heULANOUM, “yWB zCUeXUAAN yNXA”

I have no clue...

How do you calculate the final velocities and the angles when two objects collide into one another...any help/info would be highly appreciated.