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.

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...

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.

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

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.

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.

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.

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.

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!

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.

Basically, I am considering buying Maple 11 as I am a college student hwo will soon be taking college-level math courses. But I am weak in these old areas of mathematics, the stuff you explore in high school. I want to know if Maple 11 will serve the majority of my math needs as a student, whether it is pre-algebra, algebra, geometry, calculus, etc.

Have you ever plotted a function in Maple and then found that the range you plotted it on wasn't really what you wanted? You can always re-execute the command, of course, but that means working out exactly what the range is for that interesting feature you want to investigate, and if you've made changes to the plot those will be lost. However Maple has the ability to zoom in on a plot interactively, without re-executing the command.
The Axis Properties dialog lets you change the range numerically, but you can also do so using the mouse. Go to the plot toolbar and click on the **Scale plot axes** button (it looks like a red ball with an arrow). If you have an animation you will need to click on the word "plot" above the toolbar to switch from animation to plot toolbar. Now put the mouse in the middle of the plot and drag it. Dragging it down will zoom out, increasing the range; dragging it up will zoom in. The **Translate plot axes** button lets you 'pan' i.e. move the centre of the axis ranges without changing the range size.

My

previous blog entry was a real success.
Even though my original idea about multi-part MIME has not gotten anywhere, I do now have a concise way to package a maplet with supplemental files in a single package that can be downloaded via the WWW and automatically extracted and executed.
Most of the ideas were presented by acer.
acer first suggested that I look at the interactive interface to the InstallerBuilder. The idea here was to embed the maplet in a worksheet saved in a help database (hdb).
This did work, but was not suitable for actual use due to the overhead of the installer. In the attempt to reduce this overhead, acer then supplied some code that used march and LibraryTools.
To test the product of this interaction, download the file at the URL

http://www.math.sc.edu/~meade/TEST/SimpleTest.mla.

I got an interesting question about integration yesterday. The question was about the integral of the rather innocuous looking function f := sqrt(1+sin(x)). The inside of the square root is always non-negative so the function is continuous (and bounded!) so it must have a continuous integral.
The question I was asked, was if the following result was a bug in Maple:
Int(sqrt(1+sin(x)),x) = (2*(sin(x)-1))*sqrt(1+sin(x))/cos(x)
since the right-hand side is definitely not continuous at x=-Pi/2 + 2*n*Pi!

My apologies if this has been posted before, but a quick search didn't turn it up. I'd like to have a simple, "clickable" way, preferably in the "PlotBuilder", to shade in the region *between* two 2D curves or two 3D surfaces. I know that there are packages to do this, but I'd like my students to be able to do it without learning any new commands or loading any new packages --- it's just too useful when you are teaching calculus.
Thanks for listening!
----Josh