## Old Maple MWS vs. new Maple 12 results differ !...

hi, 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) restart; T := ->(1/8)*sqrt(x^2+225)+(1/3)*sqrt((20-x)^2+625); dT := D(T); solve(dT(x) = 0, x); evalf(%); Sols := %; Xbest := Sols[1]; solve(25/(20-x) = 15./x, x); T(%)-T(Xbest) 0.28031703 when i run in with Maple 12 Student Edition, the result I get is 11.41326364-(1/8)*sqrt(13.51659367[1]^2+225)-(1/3)*sqrt(1025-40*13.51659367[1]+13.51659367[1]^2)

## simplify(%) don't simplify...

Good morning.

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?

Thank you

S.

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

## Calculus of variations, fixed endpoint problem...

Any tips on how to solve fixed endpoint problems in the calculus of variations?

For instance,

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.

## Clairaut's (Young's) theorem

by: Maple

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);
0
```

Continuity of integrands isn't generally assumed by int (there's a separate optional parameter which enables it...

## Can't get package to work...

Okay, I'm just really starting to get into Maple again, but I'm having a little trouble getting a package to work.

I'm trying to take a look and review the precalculus package from the application center but it doesn't seem to work.

It's from maple 7.  The new version doesn't seem to follow through on the commands made.

## Cum laude

by:

No, the title does not come from hornybitches.com, nor does it mean something related to sex.

## General Relativity

by:

Special Relativity has been around for ~100 years, General Relativity for ~90 years.  I'm hoping that with the assistance of Maple and Mapleprimes I may be able to do some tensor calculus to better understand Einstein.  Perhaps the twin paradox is within my reach.  Perhaps even the orbit of Mercury.

## Do you know any antiderivative that maple can't...

by:

I need to find an example of a function of one variable that has an antiderivative that can be expressed very simply in terms of fuctions that a 1st-year calculus student would know, but int (command name in maple) can't find an antiderivative.

Hint: Start with the antiderivative F(x), and get f(x) by differentiating it and simplifying. You might try something involving a few square roots and logarithms or exponentials or trigonometric functions.

## Do you know any antiderivative that maple can't fi...

I need to find an example of a function of one variable that has an antiderivative that can be expressed very simply in terms of fuctions that a 1st-year calculus student would know, but int (command name in maple) can't find an antiderivative.

Hint: Start with the antiderivative F(x), and get f(x) by differentiating it and simplifying. You might try something involving a few square roots and logarithms or exponentials or trigonometric functions.

## Do you know any antiderivative that maple can't fi...

I need to find an example of a function of one variable that has an antiderivative that can be expressed very simply in terms of fuctions that a 1st-year calculus student would know, but int (command name in maple) can't find an antiderivative.

Hint: Start with the antiderivative F(x), and get f(x) by differentiating it and simplifying. You might try something involving a few square roots and logarithms or exponentials or trigonometric functions.

## Maplesoft Great Application Contest - Winners!

by:

We are pleased to announce the winners of the Great Application Contest. First prize is awarded to Dr. Jason Schattman, for his entry Can a Square Roll?, an exploration of the "Renaissance Man of calculus problems", the square wheel problem. The runner-up is Prof. Mario Lemelin, for his Pré-test en Mathématique, a Maple-based questionnaire that lets beginning differential calculus students test their secondary school mathematics comprehension. These and many other Maple applications can of course be viewed on the Maple Application Center. Congratulations to both!

## Gradients, Jacobians, Hessians, and higher order...

Inspired by the post "finding the Hessian (third order tensor) and higher order derivatives", I have written the following function which treats gradients, Jacobians, Hessians, and higher order derivatives in a unified way, implementing tensors as multidimensional Arrays:
```multiDiff := proc(expr::Array(algebraic),vars::list(symbol),n::posint)
local i,result;
if n > 1 then result := multiDiff(multiDiff(expr,vars,n - 1),vars,1)
else
result := Array(ArrayDims(expr),1..nops(vars),order = C_order);
```

## How to compute the integral for the inverse of...

by:
The recipe is quite simple to understand looking at an example (and it is understood best by having paper and pencil to follow it): f:= x -> x^2 the parabola with its inverse g:= y -> sqrt(y). Say you want the integral of g over 0 ... 2, which (here) is the area between the graph and its horizontal axis. That is the same as the area of the rectangle minus the area between the graph of g and the vertical axis, where the rectangle has corners 0, 2 and g(0)= f^(-1)(0) and g(2)= f^(-1)(2). Now recall the geometric interpretation of the compositional inverse of a function: it is reflection at the diagonal.