Engineering at Alberta Courses

Mathematica Lab Tutorials: Lab 1

This lab covers Variables, Matrices, Built-in Functions, and Plotting:

Consider the relationship
$y=\sin{\frac{\pi x}{6}}$

Find $y'$ and $y''$ . Evaluate $y$ , $y'$ , and $y''$ at $x_0=1$ . Then, plot the relationships $y$ , $y'$ , and $y''$ for the domain $x\in[-5,5]$ . Label your plot and plot legend appropriately.
Consider the sequence whose terms are $a_n=\frac{1}{3^n}$ . Evaluate the sum of the first twenty terms. Then, evaluate the infinite sum
$\sum_{n=1}^\infty a_n$

Use the ListPlot command to plot the first ten terms of the ordered pairs $(i,\sum_{n=1}^ia_n)$ . Label the plot appropriately and use the option “Joined->True”.
Consider the matrix
$M=\left(\begin{matrix}1 & x\\ x & 1\end{matrix}\right)$

Plot the relationship between the determinant of $M$ and $x$ for $x\in[-5,5]$ . Label the plot appropriately. From the plot, can you identify the values of $x$ for which the determinant is equal to zero?