about(_Z)

Why do you want plotting in Maple and computing in Excel? Excel has nice plotting tools and there should be a good reason why to operate through 2 different software systems

perhaps he just wants that to have it written in the following form: F:= t -> f(x(t)); # define your composite function

diff(F(t),t);     # differentiate it

                                   /d      \
                         D(f)(x(t)) |-- x(t)|
                                    \dt     /

That's what Schivnorr says by "as you do it by hand"

well ... just do substitute "dp=dy*Diff(p(y),y)" as done by the Mariner ... but it is brute and what you say ist just: handling it as fraction is not differentiating and that's what Maple says just remember that kind of manipulations (usually) are more mnemonic than mathematical

  eq1:=p*A-(p+dp)*A-rho*g*A*dy=0;
  eq2:=dp_by_dy=dp/dy;

               eq1 := p A - (p + dp) A - rho g A dy = 0

                                           dp
                        eq2 := dp_by_dy = ----
                                           dy

  isolate(eq2,dp); eval(eq1,%); 
  isolate(%,dp_by_dy): simplify(%);
  eval(%, eq2);

                             dp
                            ---- = -rho g
                             dy

evaluate either to floats or rational numbers (but do not forget precision through Digits:=16), something like evalff(myExpression) then should be feed into codegeneration

Again somebody starting with Maple trapped by the standard interface? That's the way to find fans friends for products ...

do not know Maple T A, but it sounds like the separator problem on German machines I know from Excel + Maple: StringTools[SubstituteAll]("0,78",",","."); parse(%); gives 0.78 (i.e. read in data as strings and replace; take care if there is a 1000 separator as well)

In such a case I look at simplier cases, may be the indefinite solution.

I guess that M has 2 problems (but I am not sure): it will try to find
the formal solution has no singularities and the would try to find limits.

The first can be avoided (if you know it is allowed) like the following:

restart;
st:=time():
Int((sin(x)/x)^20,x=-infinity..infinity,'continuous');
evalf(%);
time()-st;

                             0.9635047953
                         seconds needed = 0.015

However for exponent=100 that does not help: while M finds a solution
quickly it hangs up at the limits. To cure that kick off sin and cos
terms (as they will vanish), some Sine integrals survive and now see
what happens:

st:=time():
Int((sin(x)/x)^100,x);
V:=value(%):
remove(has,V,cos): 
W:=remove(has,%,sin):
limit(W,x=infinity)-limit(W,x=-infinity);
`seconds needed`=time()-st;
evalf(%%);

                        seconds needed = 0.499
                             0.4335090115

The answer is given in 1/2 second and evaluating the quite long result
(= rational number * Pi) coincides with a purely numerical solution.

'Scanning' the book gives me the opinion: really nice! Thx for such a link! May be it is not of great help, since I learned the stuff from Math and not for Physics (and only got tortured by the symbols end of the 1st year, it was the only thing I really hated in linear Algebra ... and relearned it in different settings after Algebra later). Roughly (speaking of vector spaces) it is the same as a multilinear morphism of vector spaces (bilinear example: the scalar product) ... well may be that only makes it simplier for Algebraists ... Covariant vs contravariant then just means that one talks about a vector space or its dual (well, a bit strange, since that is a vector space as well, but there one has a 'natural' way to have functionals V ---> IR to evaluate). The symbols came in, as soon as you decide to work in coordinates of a base and one example is to write matrix multiplication with a vector in that way (forgive me to omit that details). A simple example is to have a square matrix - which is an endomorphism phi of a vectorspace V (and as such you 'abstract need' no base). Instead of viewing at phi: V ---> V one can consider it as an element in V@V*, where @ = tensor product and V* is the dual space = morphisms from V to K = linear forms, and the latter is free of coordinates. Then one can talk of the trace of phi just as for a matrix, i.e. summing the diagonal elements. Or you for Sum x_i @ f_i representing phi you do Sum f_i(x_i) (which means evaluate functionals). Within that machinery it is the same (in a 'natural' way). Most other stuff has similar interpretation (which I am not aware of). But it shows, that an 'interpretation' is difficult, especially a geometric one (since using multilinear Algebra is not so clear ...). May be the following may help as motivating example (may be it is the book as well): Decomposing a 'space' into a (local) product means also means to decompose its differentials (wedge product) and tangent space. Now as a _fact_ just accept it means to write that as tensor product. Then think of a (local) product decomposition as a way to introduce coordinates on a manifold and the convention tells you how to proceed consistently for that. NB1 here the tensor product is 'actually' given through the (local) product of the spaces (which induces a tensor product for the function algebras (it is a co-product, harhar) and that carries over to differential forms) NB2 for that example linear functionals come in through integrals, as soon as one integrates differential forms (along pathes). May be that does not really help (and is not very exact), but may be it gives some feeling, why to bear a machinery until one gets used to it (or survives until reaching other stuff). But I would not try to learn it through a CAS.

you are welcome ... just think you got trapped by some misunderstanding or typo, you will not have to integrate erf(log(x)) as you might 'see' from your desired result (and the other replies). And: you may not forget to post your own finding, if your project is finished?

in addition to Mariner's answer: you may check again the subjects matter, lognormal is *not* log(normal) and if you take the correct one Maple will give you the desired Black-Scholes formula (note there are some restrictions on the parameters as well)

Difficult to say, why it not works, it may even be your Dev installation. I append a complete Dev-C++ example with paths, which you may check and adapt, just double click the *.dev file to start the project. My project is located at D:\_Work\DevCpp\RNG_uniform, while C:\Programme\Maple11 is my Maple directory (same PC, different drives, not on a network and *NO* blank or other special characters in path names (by default there is a blank after 'Maple') on Win XP SP2). Version for the IDE is 4.9.9.2 (the latest I think), have not checked package versions (as I rarely use it, but just checkedit: it is ok here). Download 102_DevCPP_example_RNG_uniform.zip
View file details

http://www.mapleprimes.com/blog/alec/openmaple-example-with-dev-c

system("notepad") or ssystem("notepad") ... whenever a DOS system prompt can execute that (I think) ... but why from Maple?