It's a new day, but not a new problem. Yesterday I asked about solving inequalities with abs. Today I am looking at solving an equation with abs. Try the following:

restart;
q :=  sin(x)/x - 1:
test4 := y -> [ y,
                solve( q=y, x ),
                [solve( abs(q)=y, x )],
                fsolve( q=y, x ),
                fsolve( abs(q)=y, x ) ]:
test4(  0  );
test4( 0.1 );
test4( 0.5 );
test4( 1/2 );
test4(  1  );

[                         /sin(x)           \                -13]
[ 0,   0, [0],      fsolve|------ - 1 = 0, x|, 1.869896012 10   ]
[                         \  x              /                   ]

Quick, what numbers x satisfy:

abs( x-2 ) < 1

How does Maple answer this?

solve( abs( x-2 ) < 1, x );
                         RealRange(Open(0), Open(2))

Now, change the RHS to 1. (floating-point 1):

solve( abs(x-1) < 1., x );
           RealRange(1., Open(2.)), RealRange(Open(0.), Open(1.))

Of course, these two intervals can be combined to the one interval. Maple 10 did not have this problem. (I will explain what Maple 11 is doing later, I want the next paragraph to appear in the truncated version of this post.) This issue is important for those of us trying to use Maple in the classroom. While it's not difficult to explain what is going on, the point is that this is not the mathematics I am trying to teach and these issues are a distraction.

I need help with a problem. There are 24 square tables, but the tables must be formed as rectangles. i.e. two together. How many combinations can be made with the 24 tables. What is the maximim number of people to sit at the tables using what combination What is the least number of people to sit at the tables using what combination.

The latest edition of TUGboat (vol. 28 no. 2, 2007), the journal of the TeX users group, contains an article by Edward Reingold, Writing numbers in words in TeX, which, as its title states, gives TeX macros for converting integers to names. In this case, American English names. For my amusement Sunday I wrote the equivalent procedure in Maple.

Hi How do I find the max possible volume of the following cylinder when volume given as V=pi(6r^2 -r^3). The sum of its radius and height is 6cm.

... I doubt that there has ever been a better way to learn the relationship between numbers - and even mathematics in general - than the slide-rule from days-gone-by, and the ability to plot functions using modern computer technology. For the young people here who may not have ever used a slide rule, below is a link to a virtual slide rule:     virtual slide rule

I wish, and think...

I have just released the new version of the FourierTrigSeries package. Some bugs were fixed and new procedures were added. This 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. Previous package name FourierSeries was changed to FourierTrigSeries to be distinguished from the FourierSeries package made by Wilhelm Werner.

Here are some possible bugs or limitations that I have come across while working with Tensors in the new physics package. I have done best of my efforts looking into the documentation, but it is still possible that the bugs I am listing are not bugs at all but outcome of lack of my knowledge in using Maple. My intention of creating this blog is to not to criticize but to help the Physics package development team in making updates. I appreciate their efforts for developing a much needed package for areas like fluid mechanics, continuum mechanics, theory relativity etc. Platform I am using: Maple Ver 11.01 on Mac OS X 10.4.10

Jacques posted a link to an interesting article in the New Yorker about feature creep. Perhaps we should ask whether Maple is suffering from this malady, but before doing so we really need to answer the question "what is Maple for?" So here's a place to say what you think Maple's main purpose is/should be. Here's my shot: Maple's prime purpose is to help teach math. J.Tarr

At what age do you think students should start learning and using Maple? What are your reasons?

Having looked recently at a suite of engineering software in use, I wondered whether engineers would need maths for much longer. Of course they’ll always need sufficient for business purposes, but my guess is maths will become unnecessary for engineering in much the same way as it’s unnecessary for weather forecasting. There would probably be a residual role for maths in engineering research, but not in the mainstream, and that would have huge implications for schools and universities. How do those engaged in teaching maths to budding engineers see the future?

hi, i made a markov model with 2 treshold values (k and n, n>k) and 3 maintenance activities. i write my availability equation: for a = λd / (λd + λin) P(0,0)= 1 / ( k + ((k-1) * (λin/μin)) + ((k-1) * (λin/μm)) + (a * ((1-a^(n-k))/(1-a))) + (a * ((1-a^(n-k))/(1-a)) * (λin/μin)) + (a * ((1-a^(n-k))/(1-a)) * (λin/μM)) + ((a^(n-k) * (λd/μD)) ) Availability = P(0,0)*(k + (a * (1-a^(n-k)))) i want to find the optimal λin which max. the availability.. is there any way to solve without giving any numerical values??

To put it simply - it's about the grandkids. As anyone who is a grandparent may understand, once you have grandkids you spend time reflecting back on your own life and no matter where you've been, or what you've done, you always want them to have the opportunity to do better. Having left school at 15 years of age    ( for somewhat noble reasons )   I never learned or had the opportunity to learn the math that I later always wished I had. My life has been so busy raising my family and working the kinds of jobs that many who use Maple will never have to work, that I never had the opportunity to spend the time to further my education.

Get this Quaternion Package from Maple's Application Center. Make sure you get the March 2007 version not the March 2005 version.

Overview on Hamilton Quaternions

A Hamilton Quaternion is a hypercomplex number with one real part (the scalar) and three imaginary parts (the vector).

This is an extension of the concept of numbers. We have found that a real number is a one-part number that can be represented on a number line and a complex number is a two-part number that can be represented on a plane. Extending that logic, we have also found that we can produce more numbers by adding more parts.
Quaternion --> a + b*i + c*j + d*k, where the coefficients a, b, c, d are elements of the reals

I have been teaching University Math courses and recently posted two worksheets about pendulums. The first is on the double pendulum and the latest is for a pendulum with a moving pivot. These are just two of the problems presented to my students in their introductory Differential Equations course at the NSAC. I am interested in any comments about either worksheet. View 4221_double pendulum.mw on MapleNet or Download 4221_double pendulum.mw
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