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Mathematica Lab Tutorials: Lab 1

Lab questions

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

  1. 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.

  2. 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”.

  3. 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?

Video Tutorials

Variables and rules in Mathematica

Vectors and matrices in Mathematica

Some built in functions in Mathematica

Plot function in Mathematica

Brackets in Mathematica

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