I am happy to formally announce Maple T.A. 9.5! An expansion on Maple T.A. 9, this release is packed full of innovative features and new tools to assist academic institutions with a variety of different teaching and assessment tasks.

Ever have an issue on your campus where students are required to learn a new piece of technology, but you don’t know how to get them prepared for it? With Maple T.A. 9.5, we have included pre-built content to assist students in learning how to use the Maple T.A. environment, and students can take the new Readiness Test to educate themselves on how to use the system. Tasks such as enabling Java, navigating assignments, grading tests, searching for help, and much more are taught in an interactive setting, and give students the right information they need to become comfortable with Maple T.A.

We haven’t forgotten about instructors and teachers either. We have completely revamped our Instructor Examples to provide educators with a sample question of every single question type in Maple T.A. – that’s over 25 different examples! Instructors are given descriptions, feature lists, and examples for each question type. Additionally, we also created a new Sample Assignment that shows instructors what a typical assignment looks like. They can explore this assignment from both instructor and student viewpoints to test out different options and see what the experience will be like.

Essay questions have been foundational in Maple T.A. for several years now, and Maple T.A. 9.5.makes it even easier to provide feedback for students submitting essays. With the Essay Annotation feature, instructors have the ability to mark-up an essay with comments using a simple drag and drop tool. Using this new tool, your students will be able to see your comments and take note of any issues they had in their writing.

Power outages, automatic updates, computer crashes... we’ve all experienced these unpredictable events, and they can be catastrophic for students trying to meet due dates or if assignments are timed. To help with this Maple T.A. has expanded its Proctor Tools feature.  Instructors can now grant individual students with additional time or date extensions if there are ever any issues.

We’re also giving you a sneak peak at some up-and-coming technology: Gradeable Math Apps. As part of The Möbius Project, you can now embed an interactive Maple worksheet in a Maple T.A. question. Students can move sliders, push buttons, click on plot windows and much more directly inside of a Maple T.A. question. Students are then automatically graded on their interaction with the Math App – just like other question types in Maple T.A.

All these features are all for Maplesoft-hosted and self-hosted users, which also includes all the great stuff from Maple T.A. 9:

• Adaptive Testing
• New Question Repository
• Maple T.A. Cloud
• Hint Deductions
• Reworking Assignments
• MathJax Support
• Distributed Load Balancing
• Permanent User Deletion
• Customizable User Interface
• Multiple Instructors for a Class
• And much more!

At Maplesoft, we are extremely excited about Maple T.A. 9.5, and can’t wait for schools all over the world to begin using it!  And as always, we are very interested in hearing from you about your experiences with Maple T.A., as well as any suggestions you have for future releases.

Thirteen Clickable Calculus examples have been added to the Teaching Concepts with Maple section of the Maplesoft web site. The additions include examples in algebra, differential and integral calculus, lines-and-planes in multivariate calculus, and linear algebra. By my count, this means some 97 Clickable Calculus examples are now available.

In the Algebra/Precalculus section, examples of an

At any age we, being somewhat children, ask that. Here is the answer to such a question related to Maple. Let us consider the ODE

ode:=(2x^2-x-1)*y''(x)-(4x^3+x-2)*y'(x)+(4x^3+2x^2-2x+2)*y(x)=0;

and its general solution done with Maple

dsolve(ode);

y(x) = _C1*exp(x^2)+_C2*exp(x)*x.

The first thought is that Maple, mimicking the solution done by hand, finds a particular solution of the equation in the form y*(x)=exp(a*x^2+b*x). It fits...

(Presentation in Spain a month ago with a full description of the project and its current status)

Download PhysicsProjectDescri.mw

Edgardo S. Cheb-Terrab
Physics, Maplesoft

Greetings to all.

A recent post at math.stackexchange.com asked for good approximations to pi using the nine nonzero digits, the four arithmetic operations and exponentiation. The problem definition definitely suggests a computational solution, which is actually non-trivial because the search space of all legal mathematical expressions over the nine digits and with the aforementioned operations is so huge that it cannot possibly be searched exhaustively.

In a webinar on July 10, 2013, I solved the related rate problem:

Helium is pumped into a spherical balloon at the constant rate of 25 cu ft per min.
At what rate is the surface area of the balloon increasing at the moment when its radius is 8 ft?

A question in the Q&A at the end of the Webinar asked if it were possible to have an animation illustrate the expanding sphere and the rate of change in the surface area thereof. 

Voting is open for the first individual prize to be awarded as part of the Möbius App Challenge.  The winner will receive a MacBook Air! 

Here are the finalist Apps:

• Wind Turbine Calculations
• The Cosmic Travel Planner

Technology is changing the face of education. An obvious statement, of course. Everybody from students to instructors to parents will agree. Over 40 years ago, the introduction of the pocket calculator allowed us to change the focus from menial calculations to applying our knowledge to solve problems and discover the power of mathematics. 

Since then we have seen leaps from innovation to innovation. The personal computer. Computer Algebra systems. Tablet computing....

At some point a version of the Maple Player (for the PC, rather than iPad) became available for download from its webpage.

I would like to pay attention to http://www.ams.org/samplings/feature-column/fc-2013-05 .
Comparing the Galileo's calculation 87654/53 with the capacity of Maple, the question arises:
"Are we  cleverer than Galileo Galilei?". I don't know the answer.

Introduction
The purpose of this post is the investigation of the connection between the connectivity of an undirected graph and the numbers of its vertices and edges with help of the GraphTheory package.
The reader is  referred to http://en.wikipedia.org/wiki/Graph_theory and to ?GraphTheory for info.
Let us...

It's interesting that every continuous piecewise linear function can be specified by one explicit equation with absolute values​​. The procedure JoggedLine carries out such conversion.

Formal arguments of the procedure: 

A - a list of the coordinates of the vertices of the polyline or the continuous piecewise linear expression defined on the entire real axis.

B (optional) - a point on the left "tail"...

My site of Russian Maple's Center (webmath.exponenta.ru) reached the milestone of 8000000 visits.

Year of foundation - 2000
Now - 8,000 visitors a day.
Since the Maplesoft is not interested in this project, I renamed it.
Current title: Site of Independent Work of students.
I wish you all good luck!

Mechanics of Materials toolbox for Maple: 10 (or bit more :)) free licences for Maple fans.

For students, engineers and simply creative fans of Maple.

If you are concerning mechanics of materials or structural mechanics, please feel free to

send Hardware ID code via e-mail: support@orlovsoft.com after downloading from

http://www.orlovsoft.com/download.html

and installing MM Toolbox for Maple.

(Maple 32 bit only)

Thanks to Maplesoft for analytic power

Given a figure in the plane bounded by the non-selfintersecting piecewise smooth curve. Each segment in the border defined by the list in the following format (variable names  in expressions can be arbitrary):

1) If this segment is given by an explicit equation, then  [f(x), x=x1..x2)]

2) If it is given in polar coordinates, then  [f(phi), phi=phi1..phi2, polar] , phi is polar angle

3) If the segment is given parametrically, then  [[f(t), g(t)], t=t1..t2]

4) If several consecutive segments or entire border is a broken line, then it is sufficient to set vertices the broken line [ [x1,y1], [x2,y2], .., [xn,yn]]

The first procedure symbolically finds perimeter of the figure. Global variable  Q  saves the lengths of all segments.

Perimeter := proc (L) #  L is the list of all segments of the border

local i, var, var1, var2, e, e1, e2, P;

global Q;

for i to nops(L) do if type(L[i], listlist(algebraic)) then P[i] := seq(simplify(sqrt((L[i, j, 1]-L[i, j+1, 1])^2+(L[i, j, 2]-L[i, j+1, 2])^2)), j = 1 .. nops(L[i])-1) else

var := lhs(L[i, 2]); var1 := min(lhs(rhs(L[i, 2])), rhs(rhs(L[i, 2]))); var2 := max(lhs(rhs(L[i, 2])), rhs(rhs(L[i, 2])));

if type(L[i, 1], algebraic) then e := L[i, 1]; if nops(L[i]) = 3 then P[i] := simplify(int(sqrt(e^2+(diff(e, var))^2), var = var1 .. var2)) else

P[i] := simplify(int(sqrt(1+(diff(e, var))^2), var = var1 .. var2)) end if else

e1 := L[i, 1, 1]; e2 := L[i, 1, 2]; P[i] := abs(simplify(int(sqrt((diff(e1, var))^2+(diff(e2, var))^2), var = var1 .. var2))) end if end if end do;

Q := [seq(P[i], i = 1 .. nops(L))];

add(Q[i], i = 1 .. nops(Q));

end proc:

The second procedure symbolically finds the area of the figure. For correct work of the procedure, all the segments in the list L  of border must pass sequentially in clockwise or counter-clockwise direction.

Area := proc (L)

local i, var, e, e1, e2, P;

for i to nops(L) do

if type(L[i], listlist(algebraic)) then P[i] := (1/2)*add(L[i, j, 1]*L[i, j+1, 2]-L[i, j, 2]*L[i, j+1, 1], j = 1 .. nops(L[i])-1) else

var := lhs(L[i, 2]);

if type(L[i, 1], algebraic) then e := L[i, 1];

if nops(L[i]) = 3 then P[i] := (1/2)*(int(e^2, L[i, 2])) else

P[i] := (1/2)*simplify(int(var*(diff(e, var))-e, L[i, 2])) end if else

e1 := L[i, 1, 1]; e2 := L[i, 1, 2]; P[i] := (1/2)*simplify(int(e1*(diff(e2, var))-e2*(diff(e1, var)), L[i, 2])) end if end if

end do;

abs(add(P[i], i = 1 .. nops(L)));

end proc:

The third procedure shows this figure. To paint the interior of the boundary polyline approximation is used. Required parameters: L - a list of all segments of the border and C - the color of the interior of the figure in the format color = color of the figure. Optional parameters: N - the number of parts for the approximation of each segment (default N = 100) and Boundary is defined by a list for special design of the figure's border (the default border is drawed by a thin black line). The border of the figure can be drawn separately without filling the interior by the global variable Border.

Picture := proc (L, C, N::posint := 100, Boundary::list := [linestyle = 1])

local i, var, var1, var2, e, e1, e2, P, Q, h;

global Border;

for i to nops(L) do

if type(L[i], listlist(algebraic)) then P[i] := op(L[i]) else

var := lhs(L[i, 2]); var1 := lhs(rhs(L[i, 2])); var2 := rhs(rhs(L[i, 2])); h := (var2-var1)/N;

if type(L[i, 1], algebraic) then e := L[i, 1];

if nops(L[i]) = 3 then P[i] := seq(subs(var = var1+h*i, [e*cos(var), e*sin(var)]), i = 0 .. N) else

P[i] := seq([var1+h*i, subs(var = var1+h*i, e)], i = 0 .. N) end if else

e1 := L[i, 1, 1]; e2 := L[i, 1, 2]; P[i] := seq(subs(var = var1+h*i, [e1, e2]), i = 0 .. N) end if end if

end do;

Q := [seq(P[i], i = 1 .. nops(L))];

Border := plottools[curve]([op(Q), Q[1]], op(Boundary));

[plottools[polygon](Q, C), Border];

end proc:

Examples of works:

Example 1.

L := [[sqrt(-x), x = -1 .. 0], [2*cos(t), t = -(1/2)*Pi .. (1/4)*Pi, polar], [[1, 1], [1/2, 0], [0, 3/2]], [[-1+cos(t), 3/2+(1/2)*sin(t)], t = 0 .. -(1/2)*Pi]];

Perimeter(L); Q; evalf(`%%`); evalf(`%%`); Area(L); 

plots[display](Picture(L, color = grey, [color = "DarkGreen", thickness = 4]), scaling = constrained);

plots[display](Border, scaling = constrained);

Example 2.

The easiest way to use this  procedures for polygons.

 L := [[[3, -1], [-2, 2], [5, 6], [2, 3/2], [3, -1]]];

Perimeter(L), Q;

Area(L);

plots[display](Picture(L, color = pink, [color = red, thickness = 3]));

Example 3 (more complicated )

3 circles on the plane C1, C2 and C3 defined by the parametric equations  of their borders. We want to find the perimeter, area, and paint the figure  C3 minus (C1 union C2) . For details see attached file. 

C1 := {x = -sqrt(7)+4*cos(t), y = 4*sin(t)};

C2 := {x = 3*cos(s), y = 3+3*sin(s)};

C3 := {x = 4+5*cos(u), y = 5*sin(u)};

L := [[[-sqrt(7)+4*cos(t), 4*sin(t)], t = -arccos((1/4)*(7+4*sqrt(7))/(sqrt(7)+4)) .. -arctan((3*(-23+sqrt(7)*sqrt(55)))/(23*sqrt(7)+9*sqrt(55)))], [[3*cos(s), 3+3*sin(s)], s = -arctan((1/3)*(9+sqrt(7)*sqrt(55))/(-sqrt(7)+sqrt(55))) .. arctan((1/3)*(-9+4*sqrt(91))/(4+sqrt(91)))], [[4+5*cos(u), 5*sin(u)], u = arctan((3*(41+4*sqrt(91)))/(-164+9*sqrt(91)))+Pi .. arctan(3/4)-Pi]];

Perimeter(L), Q; evalf(%);

Area(L); evalf(%)

 A := plot([[rhs(C1[1]), rhs(C1[2]), t = 0 .. 2*Pi], [rhs(C2[1]), rhs(C2[2]), s = 0 .. 2*Pi], [rhs(C3[1]), rhs(C3[2]), u = 0 .. 2*Pi]], color = black);

B := Picture(L, color = green, [color = black, thickness = 4]);

plots[display](A, B, scaling = constrained);

More examples and all codes see in attached file

Plane_figure.mw