For the past decade Doug Meade, at the University of South Carolina, has created and maintained a two-page document with essential Maple commands. The first version was created for Maple V, Release 4, in January 1998. n update has been created for each version of Maple (except Maple 10) as it was released. The document has become pretty stable - hence the omission for Maple 10. Here are links to the complete set of documents he has created

• Maple 12 (Nov 2008)
• Maple 11 (Jan 2008)
• Maple 9 (Mar 2004)
• Maple 8 (Oct 2002)
• Maple 7 (Jan 2002)
• Maple 6 (Dec 2000)
• Maple V, Release 5 (Apr 1998)
• Maple V, Release 4 (Jan 1998)

Comments, corrections, and suggestions for improvement are welcomed. Please contact the author by e-mail.

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.

To those who are interested: New version of FourierTrigSeries package was released. This release fixes a bug in ExploreFourierSeriesCoefficients procedure. FourierTrigSeries package provides new data structure for the representation of trigonometric series and also several procedures to manipulate with trigonometric series and to compute Fourier series. Visit the homepage and see some examples. Try also the online Fourier series calculator.

This isn't specifically Maple-related; but mathematics-related; related to Linear Algebra and Modern Algebra. While reviewing Linear Algebra; I ran across the concept of "Similar Matrices"; which are defined as: if A,B are nxn matrices and there exists invertible nxn matrix P such that P^(-1)*A*P = B then A is similar to B The payoff was: if A, B are similar then they "have the same eigenvalues" (the characteristic equation is same for both A and B). (Here we are talking about the group of invertible nxn matrices, with operation matrix multiplication) --

It seems to me that I found a tip (I am a beginning user) In running these three commands in Maple 10, one gets: > sum(1/(n^4+1), n = -infinity .. infinity) sum(1/(n^4+1), n = -infinity .. infinity) > sum(1/(n^4+1), n = 0 .. infinity) 1/4*(Sum(_alpha*Psi(-_alpha), _alpha = RootOf(_Z^4+1))) > sum(1/(n^4+1), n = -infinity .. infinity) 0 The last answer is obviously wrong. In other similar experiments, Maple gives the answer -infinity to the last expression, which is also wrong. Could somebody comment on this phenomenon? Many thanks in advance.

We are pleased to announce the winners of the monthly Maple Mentors Awards for October and November. The winner for October is Douglas Meade and Georgios Kokovidis has won for November. Douglas Meade and Georgios Kokovidis will receive a prize of their choice to thank them for their involvement with the MaplePrimes community. We have received many emails nominating these individuals. One member had this comment concerning the help given by Douglas Meade:

I would like to see solutions to Exercise 7 at the end of Chapter 6 in the 2007 edition of the Maple 11 Introductory Programming Guide. It's on page 255. The exercise reads as follows: “Demonstrate that the BinarySearch procedure always terminates.” “Hint: Suppose the dictionary has n entries. How many words in the dictionary D does BinarySearch look at in the worst case?” My solution (I’m a Maple novice and I’m reading the book.) is: View 4937_Chapter6Exercise7.mw on MapleNet or Download 4937_Chapter6Exercise7.mw
View file details

I would like to see a solution to Exercise 5 at the end of Chapter 6 in the 2007 edition of the Maple 11 Introductory Programming Guide. It's on page 255. My humble attempt is: View 4937_Chapter6Exercise5.mw on MapleNet or Download 4937_Chapter6Exercise5.mw
View file details I am asking this question because in the past the answers have been way cool, magic happens!

In my work developing Maplets for Calculus, there are many instances when I want to determine that a function is monotone (decreasing or increasing or non-decreasing or non-increasing) on an interval. If I can do one of these, I can do them all. So, let's focus on decreasing. I have no problem assuming f is continuous and differentiable on the interval. The interval could be unbounded, and I am not terribly concerned about endpoints (at least now). Given a function f, how would you use Maple to determine that f is decreasing on an interval (possibly unbounded)?

Origami and thales theorem See this.

As a math phobic, I took a class this semester at UConn Math102Q. The instructor is pretty good but now at mid-semester there are a lot of "do more problems" answers. I hoped at the beginning this would help with my math phobia. The course is fairly new and uses the PSSSP model and the book is written by DeFranco and Vinsonhaler.

We are pleased to announce the first winners of the monthly Maple Mentors Awards. Jacques Carette and Robert Israel will receive a prize of their choice to thank them for their involvement with the MaplePrimes community. Jacques has consistently been a valuable member of MaplePrimes, posting clear and insightful information on advanced topics. Robert in particular has been active in the Student Forums on MaplePrimes since their inception and we would like to recognize this. One member had these comments on the two:

As new features are being built into upcoming releases of Maple, here is one request that would be very helpful for those of us who use Maple to teach lower-level (Calculus) students. Maple can work nicely with functions, but students are not always so comfortable with this language. Here's a current example. Suppose you want to find the tangent line to a function. We might work as follows.

> f := x -> sqrt(4-x^2);
                                      /     2\
                             x -> sqrt\4 - x /
> df := D( f );           # typed, or from context-menu
                                         x      
                            x -> - ------------
                                       /     2\
                                   sqrt\4 - x /
> TL := f(1)+df(1)*(x-1); # tangent line at (1,sqrt(3))
                           (1/2)   1  (1/2)        
                          3      - - 3      (x - 1)
                                   3               

This works nicely and looks fine. Now change the function.

f := x -> sin(x);
                                 x -> sin(x)
df := D( f );           # typed, or from context-menu
                                     cos
TL := f(1)+df(1)*(x-1); # tangent line at (1,sin(1))
                           sin(1) + cos(1) (x - 1)

This works fine, but does not LOOK good. The problem is that Maple is TOO SMART. It knows that the derivative function (x->cos(x)) is simply the cosine FUNCTION. Instead of the abbreviation (cos) I want to be able to tell Maple to show this result as (x->cos(x)).

Find the equation to a line that contains the point (-4, -3) and is perpendicular to the line x^2+y^2=25.

I recently posted to the Applications Center a set of class notes and a solutions manual for the exercises to accomany a course in Multivariable Calculus. These notes are a result of teaching this course for the last number of years to Engineering students at NSAC and they have found them to be benificial. I am interested in any comments and/or suggestions on how they could be improved for later editions. Link to Application on Maplesoft App Center