## 1400 Reputation

17 years, 289 days
University of Twente (retired)
Enschede, Netherlands

My "website" consists of a Maple Manual in Dutch

## don't use square brackets...

In eq5 and eq6 you used square brackets [F1/V1]. This means that you created a ?list (containing only one element). Replace these by common parentheses (F1/F1).

## mtaylor...

Your example doesn't have a laurent series expansion, because the function doesn't exist for x=0 or y=0.
For a function of more variables, you can use ?mtaylor:

`mtaylor( sin(x^2)/cos(y), [x,y], 12 );`

If you want an asymptotic expansion, you could use a nested ?series command:

` convert( series( convert(series( sin(x)/x^2/sin(y), x ), polynom), y ), polynom ) ; expand(%);`

## Programmer indexing...

You can build orbit as a dynamic Vector, that is: adding as much entries as needed, by "programmer indexing", using round parentheses instead of the common square brackets. See ?Indexing.

`restart;Orbit:=proc(Map,ic,Nit)  local orbit,z,t:  orbit:=Vector(1):  z:=ic:  for t to Nit while z<>ic or t=1 do    orbit(t):=z;    z:=Map(z):  end do;  orbit(t):=z:  return convert(orbit,list);end proc:F := x -> [-x[2],x[1]]:Orbit (F,[1,0],20);               [[1,0], [0, 1], [-1, 0], [0, -1], [1, 0]]`

## Sqrt...

The equation must be entered as

`eq := LengthOfRafter = sqrt(rise^2 + run^2);`

Notice that names of variables must not contain spaces. Now you have to ?solve this equation for the variable rise

## Most natural way...

The output of sole or dsolve is formatted in a way that makes it easy to use in a subs command. So in your example:

`ode1:=2*diff(x(t),t)+x(t)+diff(y(t),t)+2*y(t)=exp(t):ode2:=3*diff(x(t),t)-7*x(t)+3*diff(y(t),t)+y(t)=0:sol:=dsolve({ode1,ode2},{x(t),y(t)}):A:=<< -10/3|-5/3>,<17/3|4/3>>:A.subs( sol, <x(t),y(t)> );`

## mul...

`L := [seq(i,i=1..50)]:for i to 10 do A[i] := mul( s[j]/(s[i]-s[j]), j=remove( n->n=i, L ) ) end do:`

Now A is a ?table. Perhaps you want it to be a list:

`B := convert(A,list):`

## powers of cos(x)...

`expand(sin(4*x)^2); expand( applyrule(sin(x)^2=1-cos(x)^2, %) );`

## RealDomain...

(1) I suspect that you omitted some multiplicationsigns in the definition of h

(2) To simplify a ln of an exponential, Maple has to know that all variables are real. So use the simplify command from the RealDomain package

`h := r -> exp(f1 + f2*r + f3*r^2 + f4*r^3 + f5*r^4 + f6*r^5);A := 0.2:h(A); # Because A is a float, evalf is not neededRealDomain:-simplify(ln(h(A)));`

## Indeed 2003...

See Andre Heck's own homepage of the book.

## " One of these lines consists of 2 diffe...

In that case you should use a ?piecewise function to define such a line. I give an example:

`restart;f := x -> piecewise( x<2, x/2+1, 2*x -2 ):g := x -> x+1:plot([f,g], -1..4 );X := solve( f(x)=g(x) );Intersection := [X[1],f(X[1])], [X[2],f(X[2])];`

## Select...

You can remove the critical points outside the domain by a select-command:

`L := CriticalPoints(f(x)):select( x -> is(x>0), L );`

## Only the trivial way...

`simplify( subs( y= -(x^2+x*y)/2, test6 ) );                             x + y`

(perhaps it is also better not to use the name gamma, because it is an ?Initially known constant.)

## Hint...

Read the article on Lagrange Multipliers. You may also use the package ?VectorCalculus to calculate gradients, etc.

## display(sphere(C(2,Pi/2,1),1));

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