## Maple T.A. 3.0 Announcement

by:

MAPLESOFT’S LATEST TESTING SOLUTIONS PRODUCT OFFERS MAJOR ADVANCEMENTS IN ASSESSMENT TECHNOLOGY

Maple T.A. 3.0 is the only system designed specifically for courses using mathematics

Waterloo, Canada, January 8, 2007: Maplesoft™, the leading provider of high-performance software tools for engineering, science and mathematics, today announced significant enhancements to Maple T.A.™, its Web-based testing and assessment system. The new version, Maple T.A. 3.0, features increased flexibility in content creation, an enhanced user interface, and improved grading and assessment capabilities. The product supports complex, free-form entry of mathematical equations and intelligent evaluation of responses, making it the only system designed for mathematics, science, or any course requiring mathematics.

“Maplesoft’s decades of experience in the academic market, expertise in creating dynamic technology solutions, and our collaboration with leading institutions in math education have resulted in a product that instructors can place their full trust in,” said Jim Cooper, Maplesoft CEO. “The latest release of Maple T.A. is a more intelligent and integrated product, and is the system of choice for creating content, testing, and assessment in the math education world.”

Built on the power of Maple™, Maplesoft’s software product for solving complex mathematical problems, Maple T.A. 3.0 provides new benefits that make the product more adaptable and easier to use.

## problem solving

by:
Hello! I upload my file which has a problem. I am not an expert on MAPLE v10.05. The file name is "mapleprime-2". I try to get a solution of four equations with the symmetric assumption for time variables. Anyone could change the assumption to get a result. Or, anyone could add just two more time variables: t[6] with minus sign amplitude and t[7] with plus sign amplitude. So, the entire number of time variables are still odd number which can not be changed. The current code is following as: restart: eq1:=expand(sum((-1)^(i+1)*cos(w*t[i]),i=1..5)=0): eq2:=expand(sum((-1)^(i+1)*sin(w*t[i]),i=1..5)=0):

## how to print a matrix...

I would like to know how to print a matrix using the TextBox command from Maplets, because always print a message "Matrix(3, 3, [ [ 1,1,1],[1,1,1],[1,1,1 ] ], datatype = anything, storage = rectangular, order = Fortran_order, shape = [])", for example. Another doubt is if it's possible to print text and equations using the MAthMLViewer without erasing the previous print in the Maplets (to each program output a line is added in the MathViewer). I would be grateful for any hint. Adriene Pfeifer restart:with(LinearAlgebra):with( Maplets[Elements] ): test:=proc() local M; M:=Matrix(3,3,1);

## solve a problem

by:
hello? I wrote the following equations to be solved. restart; eq1:=expand(sum((-1)^(i+1)*cos(omega*t[i]),i=1..5)=0): eq2:=expand(sum((-1)^(i+1)*sin(omega*t[i]),i=1..5)=0): eq3:=expand(sum((-1)^(i+1)*cos(r*omega*t[i]),i=1..5)=0): eq4:=expand(sum((-1)^(i+1)*sin(r*omega*t[i]),i=1..5)=0): t[1]=0;t[4]:=2*t[3]-t[2];t[5]:=2*t[3]; _EnvAllSolutions:=true: _EnvExplicit:=true: s1:=solve({eq1,eq2,eq3,eq4},{t[2],t[3],r}); Do I have to specify t[3]>t[2], t[2]>0 in the code? where t[1] to t[5] are time variables starting from t[1]=0 and omega and r are constants. How can I get the solutions for t[2] and t[3]?

## coupled differential equations...

how do i solve a set of coupled differential equations like these for x(t) and y(t) eqn1 := (D,2)(x)(t) = -a*sqrt(D(x)(t)^2+D(y)(t)^2)*D(x)(t), eqn2 := (D,2)(y)(t) = g-a*sqrt(D(x)(t)^2+D(y)(t)^2)*D(y)(t)

## Coupled differential equations

by:
i'm trying to solve a set of coupled differential equations and need help eqn1 := (D,2)(x)(t) = -a*sqrt(D(x)(t)^2+D(y)(t)^2)*D(x)(t), eqn2 := (D,2)(y)(t) = g-a*sqrt(D(x)(t)^2+D(y)(t)^2)*D(y)(t)

## Surface Coloring...

Hi, Im using the display command to plot 3d surefaces/projections (which the also overlap on different occasions)on the same graph coming from different equations. My question is how can i colour the surfaces with a command (its too hard to do it onthe graph)so i know to which equation each surface corresponds to? Is there an additional way offered from maple to distinuish the graphs from each other. Finaly, I use the command labels=[x,y,z] to call my axis "Time of Fault Clearance,s" , "Magnitude of Fault Current" , "Parametr".How do i syntax a string? Thanks for your time

## fsolve fails to give numurical solution...

Hi, I am trying to solve these 6 equations with 6 unknowns. Unfortunately, "fsolve" does not give numerical results. Please let me know if there are other commands that I can use. I am using Maple 10.06 (Build ID 255401). restart; C := 2; TY := .9; Y := Vector(1 .. C, TY/C); TM := 1; DL := 5; eq1 := X1 = (Y[1]+Z2)/TM; eq2 := X2 = (Y[2]-Z2)/M2; TX := X1+X2; eq3 := M2 = (1-X1)*TM+X1/(1/TM+W1); W0 := Y[1]/TM^2+Y[2]/M2^2; EF := W0/(1-TX); eq4 := W2 = EF+X1*min(W2, DL); eq5 := W1 = (TX*EF-X2*W2)/X1; eq6 := Z2 = Y[2]*max(0, W2-DL)/W2; fsolve({eq2, eq5, eq1, eq3, eq6, eq4}, {M2, X1, X2, Z2, W1, W2});

## Solving parameteric equation....

I have these equations.

## Solving system of nonlinear equations...

Hi, I've solved a system of nonlinear equations by hand, but I'm not sure if my answer is correct. I would like to verify my results with maple's output. However, I am having some trouble using maple: Here's my code: > eq1:=2*(x*r) + 2*(y*s) + 2*(z*t)-(t^2) + (r^2)=0: > eq2:=3*(x*(r^2)) + 3*(y*(s^2)) + 3*(z*(t^2))-(t^3)+(r^3) =0: > eq3:=4*(x*(r^3)) + 4*(y*(s^3)) + 4*(z*(t^3))-(t^4)+(r^4)=0: > fsolve({eq1, eq2, eq3}); Error, (in fsolve) number of equations, 3, does not match number of variables, 6 where r, s, and t are coefficients/constants and x, y, and z are variables.

## Questions about dsolve(...,numeric), odeplot and D...

Hello all, I'm looking into visualizing/solving the Lotka-Volterra equations in Maple 10. In doing so I've run into a few problems: 1) When executing the following commands ``` > odeqs:= {diff(N(t),t) = a*N(t) - b*N(t)*P(t), diff(P(t),t)=c*N(t)*P(t) - d*P(t)}: > # Growth rate of prey > a:= 3; > # Predatation rate > b:= 2; > # Growth of predators as a consequence of predation > c:= 1; > # Mortality rate of predators > d:= 1/2; > # Initial Conditions > initConds:=[N(0)=(5/3),P(0)=(10/9)]]; > > # Display number of prey as a function of time > DEplot(odeqs, [N(t),P(t)], t=0..100, N=0..7, P=0..7, initConds, ```

## Project a 3D surface on the XY plane?...

Hi, I would like to project the 3D surface generated from the following equation to the xy plane (2D): Itouch50 := -0.4058074876e13*sqrt(1.+h)/(sqrt(ts)*(-500000000.0*ln((625.+125.*h+25.*h^2+5.*h^3)/h)*sqrt(1.+h)+587311661.7)) where x=Itouch50 y= ts and z= h Moreover, if possible, I would like to calculate the equation of the projection or the equations giving the upper and lower side of the projection. Finally, if I had multiple equations as the initial one, would it be possible to create their accumulated projections on the same plane. I know that Im asking for too much, but any help would be extremely appreciated.

## I've been dissed by MAPLE!

by: Maple
p >Hello. I'm still kind of new to the practice of using a computer program to manipulate equations. I knew that one way to define an ellipse is as the locus of points P such that for 2 fixed points F1 and F2 the sum PF1 + PF2 is constant. I also know that in Cartesian coordinates, we get a formula of the form Ax2 + By2 = 1. If we set up our coordinate system such that F1 and F2 are on the x axis each a distance c from the origin and the maximum width of the ellipse is 2a, let's try to figure out A and B using MAPLE.

>