In a document block, anything written in text mode is text. To mingle math in with the text, switch to math mode for the math, and then back to text for more text. The toggle between text and math modes is function-key F5.

The equations are definitely evolution equations. The issue isn't that the system is elliptic, but that there are at least two parameters (m and e) that are not given numeric values. For the numeric option to work, Maple needs to evaluate everything in the system to a number.

q:=sin(x+Pi/4)+cos(x+Pi/3);

q1:=expand(q);

q2:=collect(q1,[sin,cos]);

simplify(convert(q2,phaseamp,x));

Without the collect step, the convert/phaseamp command returns the expanded expression back to the original.

RJL Maplesoft

There are several errors. In the first initial point, x(0) is given no value. In the last initial point, z(0) instead of x(0) appears. In the very first argument to phaseportrait, the list of equation names should be [DE,FD], not [DE,F]. Finally, the symbol "k" must be numeric. The phase portrait is drawn by solving the equations numerically, Hence, all parameters in the ODEs must be numeric. Replace k with a number.

If these changes are made, the code executes.

RJL Maplesoft

The functionalities in the student edition of Maple and in Maple itself are identical. The only difference is in the price. So, if Maple can solve the equations, then the student edition can.

RJL Maplesoft

CalcLabs with Maple: Single Variable Calculus, 4e, Yasskin, et. al.

Brooks/Cole (now Cengage)

ISBN: 978-0-495-56062-3

The copyright date is 2010, but since this volume came out, Phil Yasskin and I have revised it to highlight Maple's newer features. Unfortunately, Cengage has failed to provide a suitable contract, and the revision is still unpublished.

If you can get your hands on a copy, you'll find lots of interesting projects of the kind you describe.

RJL Maplesoft

The point of contact of the tangent line must be a point on the circle.

The slope of the tangent line is the slope of the circle at the point of contact.

Two conditions, and two equations:

x^2+y^2=4

y=-x/y*(x-4)+1

The second equation is the equation of a tangent line. The slope is obtained by implicit differentiation applied to the circle. The x and y in the expression for the slope will be the coordinates of the point of contact. The x and y used for the equation of the line must also be the coordinates of the point of contact.

Solve these two equations simultaneously, and the two points of contact will be returned. From this, it should be simple to write the equations for the two tangent lines.

RJL Maplesoft

Isn't the way to avoid reaching for the mouse while working in Maple the typing of commands in text form (1D math) in worksheet mode (as opposed to Document mode)?

Even in this mode of usage, the mouse is still needed for some selections when doing copy/paste. But a significant portion of Maple activity could be implemented strictly by typing commands. If you know them.

RJL Maplesoft

In 1(a), the value of the integral is zero because sin(Pi) is a factor in the integrand. I'm sure this is a typo, but if you take the integrand as just 1, you can get a sketch of the region of integration with the task template:

Calculus-Multivariate/Integration/Visualizing Regions of Integration/Cartesian 2-D
The help page for this template can be reached by executing the command: ?IntPlotCartesian2D

1(b) Unfortunately, I know of no algorithm by means of which the order of integration in a multiple integral can be changed. I always taught my students to draw the region, and from this sketch rebuild the integral with the alternate order.

2. The centroid is the center of mass when the mass is uniform. For this, try the task template:

Calculus-Multivariate/Integration/Center of Mass/Polar

The help page for this template can be reached by executing the command: ?CenterOfMassPlanarPolar

3. The following commands will set up and evaluate the integral in cylindrical coordinates:

q:=Int(r,[z=0..-r*sin(t),r=0..3,t=Pi..2*Pi]);

value(q);

The following task template was useful for drawing the region corresponding to the integral:

Calculus-Multivariate/Integration/Visualizing Regions of Integration/Cylindrical

The help page for this template can be reached by executing the command: ?IntPlotCylindrical

4. The following commands will set up and evaluate the integral in spherical coordinates:

q:=Int(rho^2*sin(phi),[rho=1/cos(phi)..2/cos(phi),phi=0..Pi/4,theta=0..2*Pi]);

value(q);

The following task template was useful for drawing the region corresponding to the integral:

Calculus-Multivariate/Integration/Visualizing Regions of Integration/Spherical

The help page for this templage can be reached by executing the command: ?IntPlotSpherical

The Table of Contents for the Task Templates is obtained by choosing Tasks/Browse from the Tools menu.

RJL Maplesoft

Just asked Customer Services for the details on how to answer this question. Yes, a new purchase code is needed, but it can be obtained from the page at the end of the following link.

http://www.maplesoft.com/productupdates/

There are two reasons why the Maple 14 versions of AEM won't work in Maple 16. The first has to do with the way in which the worksheets are encoded and installed. I, as author of the AEM ebook, and a Maplesoft employee, am also at the mercy of this encoding. But I do have access to the original files, so can update them as needed.

The second reason is the update process. Each new release of Maple is tested against the calculations in AEM, and either Maple is changed or AEM is changed. If Maple has a new bug in it, then the bug gets fixed. If a change in Maple makes something in AEM break, or even improve, then I modify AEM to be compatible with the new version of Maple.

If someone with a valid copy of AEM for, say, Maple 14 updates to Maple 16, there's an automatic process on the website for obtaining not only a new purchase code, but also a download of AEM that works in Maple 16.

Good luck! If you have problems with this process, please contact Customer Services for help.

RJL Maplesoft

http://www.maplesoft.com/applications/view.aspx?SID=4848

http://www.maplesoft.com/applications/view.aspx?SID=4876

http://www.maplesoft.com/applications/view.aspx?SID=4885

http://www.maplesoft.com/applications/view.aspx?SID=4898

All of these are Maple worksheets in Maple's Application Center.

RJL Maplesoft

plots:-interactiveparams(plot,[x(a,t),y(a,t),t=t1..t2],view=[x1..x2,y1..y2]],a=a1..a2);

This will create a graph with a slider controlling the value of the parameter a. The same graph can be generated interactively with the Plot Builder, but with the Plot Builder,  you can't add the view option. Without the view option, the scale of the axes changes. The movement of the curve in the plane is thereby masked.

RJL Maplesoft

The given syntax for the system matrix contains a list with 21 entries. It should be only 20. After the first a, there are six 1s. Make that 5, s in

Matrix(4, 5, [a, 1, 1, 1, 1, 1, -1, -1, 1, -a, 0, 1, 1, -a, b, 1, -1, b, 1, -2*a]);

Put the system matrix into reduced row-echelon form. From this, and from the determinant of the non-augmented matrix, the conditions for the three cases can be deduced. I believe these conditions are

a=0, b=-1 => infinite number of solutions

a not zero, b=-1 => no solution

all other cases result in a unique solution

Use the commands from the LinearAlgebra package, or work interactively via the Context Menu after loading the package. The GenerateMatrix command (also available in the Context Menu) will extract the system matrix from a list of equations. This is what I used to correct the error in the given code.

RJL Maplesoft

There are 21 elements in the list of entries for the matrix. There should be only 20. The system matrix is correctly entered with

Matrix(4,5,[a,1,1,1,1,1,-1,-1,1,-a,0,1,1,-a,b,1,-1,b,1,-2a]): (After the a, there were 6 1s where there should have been only 5.)

Once this has been entered, put it into reduced row-echelon form. The conditions for the three cases can be deduced from this, and from the determinant of the non-augmented matrix.

I believe the conditions are

a=0, b=-1 => infinite number of solutions

a not=0, b=-1 => no solution

all other cases have a unique solution

The row-reduction and calculation of the determinant can be done with commands from the Linear Algebra package, or interactively by means of the Context Menu.

The augmented matrix can be obtained by entering the 4 equations, and applying the GenerateMatrix command, which is what I did to correct the error in the given syntax. This command is also available in the Context Menu after loading the LinearAlgebra package.

RJL Maplesoft

Unfortunately, Maple does not have a numeric solver for elliptic PDEs. Its numeric solver only handles evolution equations (parabolic and hyperbolic), and these, in only one statial variable.

This is the meaning of the first statement in the Parameters section from the help page for pdsolve/numeric:

"...single or set or list of time-dependent partial differential equations in two independent variables"

The two independent variables would be a time and a space variable. The "time-dependent" problems are evolution equations, typically the heat and wave equations.

RJL Maplesoft