Disclaimer: This blog post has been contributed by Dr. Nicola Wilkin, Head of Teaching Innovation (Science), College of Engineering and Physical Sciences and Jonathan Watkins from the University of Birmingham Maple T.A. user group*.

We all know the problem. During the course of a degree, students become experts at solving problems when they are given the sets of equations that they need to solve. As anyone will tell you, the skill they often lack is the ability to produce these sets of equations in the first place. With Maple T.A. it is a fairly trivial task to ask a student to enter the solution to a system of equations and have the system check if they have entered it correctly. I speak with many lecturers who tell me they want to be able to challenge their students, to think further about the concepts. They want them to be able to test if they can provide the governing equations and boundary conditions to a specific problem.

**With Maple T.A. we now have access to a math engine that enables us to test whether a student is able to form this system of equations for themselves as well as solve it.**

In this post we are going to explore how we can use Maple T.A. to set up this type of question. The example I have chosen is 2D Couette flow. For those of you unfamiliar with this, have a look at this wikipedia page explaining the important details.

In most cases I prefer to use the question designer to create questions. This gives a uniform interface for question design and the most flexibility over layout of the question text presented to the student.

- On the Questions tab, click New question link and then choose the question designer.
- For the question title enter "System of equations for Couette Flow".
- For the question text enter the text

The image below shows laminar flow of a viscous incompressible liquid between two parallel plates.

What is the system of equations that specifies this system. You can enter them as a comma separated list.

e.g. diff(u(y),y,y)+diff(u(y),y)=0,u(-1)=U,u(h)=0

You then want to insert a Maple graded answer box but we'll do that in a minute after we have discussed the algorithm.

When using the questions designer, you often find answers are longer than width of the answer box. One work around is to change the width of all input boxes in a question using a style tag. Click the source button on the editor and enter the following at the start of the question

` <style id="previewTextHidden" type="text/css">`

input[type="text"] {width:300px !important}

</style>

Pressing source again will show the result of this change. The input box should now be significantly wider. You may find it useful to know the default width is 186px.
- Next, we need to add the algorithm for this question. The teacher's answer for this question is the system of equations for the flow in the picture.

` $TA="diff(u(y),y,y) = 0, u(0) = 0, u(h) = U";`

$sol=maple("dsolve({$TA})");

I always set this to `$TA`

for consitency across my questions. To check there is a solution to this I use a maple call to the dsolve function in Maple, this returns the solution to the provided system of equations. Pressing refresh on next to the algorithm performs these operations and checks the teacher's answer.

The key part of this question is the grading code in the Maple graded answer box. Let's go ahead and add the answer box to the question text. I add it at the end of the text we added in step 3. Click Insert Response area and choose the Maple-graded answer box in the left hand menu. For the answer enter the `$TA`

variable that we defined in the algorithm. For the grading code enter

a:=dsolve({$RESPONSE}):

evalb({$sol}={a})

This code checks that the students system of equations produces the same solution as the teachers. Asking the question in this way allows a more open ended response for the student.

To finish off make sure the expression type is Maple syntax and Text entry only is selected.
- Press OK and then Finish on the Question designer screen.

That is the question completed. To preview a working copy of the question, have a look here at the live preview of this question. Enter the system of equations and click **How did I do?**

I have included a downloadable version of the question that contains the .xml file and image for this question. Click this link to download the file. The question can also be found on the Maple T.A. cloud under "System of equations for Couette Flow".

* Any views or opinions presented are solely those of the author(s) and do not necessarily represent those of the University of Birmingham unless explicitly stated otherwise.