I have recently been working on a problem using fractional calculus and have come across something in Maple's fracdiff command that makes no sense to me.
Consider the function y:=a+b*(x-q)+c*(x-q)^2
z:=subs(x=q,fracdiff(y,x,1)) gives the correct answer of z:=b, z:=subs(x=q,fracdiff(y,x,2)) gives the correct answer of z:=2c, z:=subs(x=q,fracdiff(y,x,3/2)) gives the answer of z:=4*sqrt(q)*c/sqrt(pi)
I was hoping to give my calculus III students a short introduction to using vectors in Maple. I wanted a few simple things like plotting vectors in three space. I loaded VectorCalculus. Got the dot product and cross product to work, and I can plot one vector -- although it looks more like a telephone pole with a cap than a simple arrow. But despite all my attempts to give plotvector a list of vectors, I am completely unsuccessful. There has got to be a better way. I'm quite frustrated after searching through documentation for several hours. I'm cert
Would appreciate some guidance for this question:
If q = ax + by and r = bx - ay, determine the value of:
I'm an autodidact working with calculus and Maple 9.5, I find the Maple Learning Guide more illustrative than comprehensive and the help files too oriented toward users who know more math and/or more Maple than I do. This forum has proved helpful in responding to specific questions, but I'm looking for some books that would provide guidance on the full range of Maple's potential. I'm not looking for a primer, but rather something as comprehensive as the help files that makes fewer assumptions about the reader's knowledge and is written
==> Integral calculus and differential 1
Question: Being given the function f (x) =1/(3x+1),
a) By using the definition of the derived function (and not the rules of derivation), determine f' (x).
b) Determine the slope of the tangent to the curve of f (x) at the point (1, f (1)).
Instructions: You must use Maple 12 and show your calculations.
Thank you for the assistance offered with these forums.
November 23 2008
If anyone can advise me about how to create the tool that I describe below, that would be great. I am a novice to Maple and object-oriented programming, but I can program in C and I suspect that I can write a Maplet, if that is indeed the best way to achieve my goal. This is what I want to do.
How does one do the indeterminate vector product with and Dyadic calculus operations with Maple 12?
I have a function when expressed in polar coordinates such that a trig function resides inside a trig function. In calculus 101 we all learned that integrating the product or quotient of 2 or more trig functions requires integration by parts but I have never run across the case where a trig function is a function of another trig function. Any one have any references I should consult on to learn how to handle this?
Let be q(x) some polynomial of degree = 2 in several, n variables x[i],
x to be thought as (row) vector
Can Maple provide the quadratic normalform for q (real resp. complex)?
By this it is meant that q ° f (x) equals one of
Sum( c[i]*x[i], i=1..n)
Sum( c[i]*x[i], i=1..n) + 1
Sum( c[i]*x[i], i=1..n) + x[n+1]
where c[i] in K, K = Reals or Complex (should not matter so much, except
char(K), and square roots have to exist, so Rationals(squareRoots) is fine),
and f: K^n -> K^n is affine ( = bijective and linear + shift vector)?
My calculus book says that y = (x^2 - 2)/(x - sqrt(2)) is discontinuous at 2, but Maple finds a limit of
My calculus text says that a function cannot have an ordinary limit at an endpoint of its domain, but it can have a one-sided limit. So, in the case of f(x) = sqrt(4 - x^2), the text says (a) that it has a left-hand limit at x = 2 and a right-hand limit at x = -2, but it does not have a left-hand limit at x = -2 or a right-hand limit at x = 2 and (b) that it does not have ordinary two-sided limits at either -2 or 2.
So there are six possibilities. Maple gives limit = 0 for all six. Why the discrepancy?
i'm using an existing Maple mws that was created by some unknow version of Maple.
the Maple text is show below, and the old result is the last line (0.28031703)
T := ->(1/8)*sqrt(x^2+225)+(1/3)*sqrt((20-x)^2+625);
dT := D(T);
solve(dT(x) = 0, x);
Sols := %;
Xbest := Sols;
solve(25/(20-x) = 15./x, x);
when i run in with Maple 12 Student Edition, the result I get is
I've this funny problem with maple11. I get an expression as output from a calculus, and I try to simplify it with simplify(%), but simplify don't simplify and give the same expression as result.
On the other hand, If I copy the expression and paste it as argument of simplify it work fine.
Anyone know why this happens?
ps: the expression to simplify (in fact is more simple than a simplification: there are terms equals but with different sign to cancel togheter) is
Any tips on how to solve fixed endpoint problems in the calculus of variations?
Find the extremal for:
int(diff(x(t),t)^2/(t^3),t=1..2) with x(1)=2 and x(2)=17.
The correct answer is x(t) = t^4 + 1.
How can Maple arrive at the following, for an unspecified function f(x,y), without knowing sufficient conditions (eg. whether the 2nd partials are continuous)?
> # From the ?diff help-page
> diff(f(x,y),x,y) - diff(f(x,y),y,x);
Continuity of integrands isn't generally assumed by int (there's a separate optional parameter which enables it...