# Assignment 4

In this assignment, you will discuss some aspects of your name function as described in Assignment 3. Your discussion will take the form of a paper typeset in LaTeX. Your paper will have four sections.

1. The first section will be titled "The <your name here> Function". Obviously you put your own surname in the place indicated. It will discuss the formulation of the function, and will include at least three equations.
1. The equation from Assignment 3 where you give the explicit definition of your function. Be sure to use the align environment, \left and \right on parentheses, and get your name in \text{}.
2. One or more equations that tell how to evaluate the integral of $$\sin(a_i\pi x+a_0)$$ over the interval from 0 to 1.
3. An equation that gives the evaluation of the integral of your name functoin over the interval from 0 to 1; e.g. ∫01 Fyourname(x) dx = 3.25. Of course, this requires you to evaluate the integral of your name function over that interval. You should discuss -how- to evaluate that integral.
2. The second section will be titled "A Plot", and discuss a plot of your name function. You should make such a plot by logging in to mathlab.math.wsu.edu using a web browser; use the menu at top left to go to "software"; then select Matlab; then insert the following code into the window provided and click "Run Matlab".
[x,y]=checkmyname('Trivium');
plot(x,y)

Of course, you will substitute -your- name for 'Trivium'. This will produce a plot rather like that in Figure 1.

Figure 1. The Trivium function
Put the plot in a figure environment with a caption and a label, and discuss its salient features briefly, including a reference using the \ref command. Note in particular that we say e.g.: "as we see in Figure 1"; we do not say: "as in the figure below." The caption will include a reference to the equation from Section 1 that defined your function.
3. The third section will be named "Turning Points". You will have noticed that when you ran the Matlab commands in the previous section, it produced a list of x and y coordinates, labeled "turningPts". Those coordinates are, in fact, approximations to the x and y coordinates of the turning points of your name function. In this section you will discuss a table of those turning points. The table should mimic that in Table 1, except it will use the information for -your- surname.
Indexxy
10.06-1.93
20.341.01
30.57-0.55
40.831.22
Only two digit accuracy
Table 1. Turning points of the Trivium function
Please note that the little gaps in the lines are artifacts of simple HTML tables. In your TeX table you will not have those gaps. Note also that the first column is centered, while the other two are right justified. Put the table in a table environment, give it a caption and label it. The text of the section will contain a brief explanation of the relationship between the number of turning points and the first few letters of your surname, and will refer to Table 1 in the process. Again, we never refer to "the table below."
4. Finally, there will be a reference section containing two items in your paper: one to Donald Knuth's TeXBook, and another to Leslie Lamport's LaTeX: A Document Preparation System. Look those references up and put them in using a thebibliography environment. If you feel strongly that you need to use BibTeX, you may.
The paper will have a title with author information - use \maketitle. It will be well written, with accurate spelling. You will proofread it. Some guidelines for mathematical writing may be found here.

The assignment is worth 50 points. You will turn it in by downloading the source from your overleaf site, and emailing the .zip file to the instructor by 9AM on Thursday, 29 September. If you do not use overleaf, you can just attach all the files (including the image) to an email message to the instructor.

The last test will take place at the final exam time, Monday 12 December, 1:30-3:30. It will be written as a one-hour in-class on-line test. As usual, you can use any resources you want. A Sample Exam is available. Note that the URL for the exam will not be emailed to all. If you need to take the exam from outside class, contact the instructor to get on the email list.

Assignment B is posted.

Most recent scores are on-line at My.math. Check the Info page. Let the instructor know if you find a discrepancy.

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