Excercise 1

1. Change the next cell from markdown to code.
2. Write a one-line program to print your name.
3. Run the cell.

Change Me

Excercise 2

1. Change the next cell from code to markdown.
2. Copy the following lines into the cell and run it.

The Lorenz Equations

    \begin{align} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{align}

A Cross-Product Formula

    \begin{equation*} \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix} \end{equation*}

The Cauchy-Schwarz Inequality

    \begin{equation*} \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \end{equation*}

Experiment with the code to modify the equations.

Examples adapted from NBViewer Examples.