Exercise 9: Use equations

Exercise 9: Use equations#

In this exercise, you will learn how to write and format mathematical equations in your TeachBook, both inline and as standalone blocks.

Tip

Using properly formatted equations makes mathematical expressions clearer and more professional. More details can be found in the JupyterBook documentation.

Writing equations#

  1. Open a new or existing Markdown file where you want to include an equation.

  2. Start with a simple block equation using double dollar signs. Try adding the following equation in your Markdown file:

$$ F_{res} = m \cdot a $$

Tip

The syntax used for creation equations is TeX, a markup language for math. It’s often part of the software-system LaTeX, which allows to create full documents in this language. There’s plenty of documentation online on how to use it, including graphical interfaces (for example this one)

  1. Now let’s add another equation with an error:

$$ E = m \ccdot c^2 $$

  1. Check whether the equations renders correctly by clicking preview if you’re making this edit in the GitHub single file editor. Make sure you already defined the file type as <title>.md to enable rendering. Note that all ill-formatted equation are indicated in red, i.e. \(\red{\text{\ccdot}}\)

  2. As an alternative you try and use the ‘math directive’. This will have the same results + adds a equation number which can be used for referencing (refer to Exercise 11: Cross-referencing content):

```{math}
v = a \cdot t
```

  1. Click on preview again. Note that these equations don’t render. That’s because these ‘directives’ is a MyST feature (an extension of markdown), which is not supported by the GitHub previewer that only support markdown.

  2. Now, add an inline equation by enclosing the equation with single dollar signs. Try this example:

The displacement can be found using the equation $s = v \cdot t$.

Formatting mathematical symbols#

  1. In this step we will experiment with different TeX symbols. Use the following table and test each example in your Markdown file:

Name

Script

Square root

\sqrt{4}

Power

^{2x}

Fraction

\frac{2}{3}

Subscript

_{gem}

Superscript

^{N}

Multiplication

\cdot

  1. Extend this exercise by trying more advanced mathematical expressions:

Name

Script

Derivative

\frac{\Delta f}{\Delta t}

Integral

\int_a^b dx

Sine function

\sin(x)

  1. Test your understanding by adding a new equation of your choice, ideally one that requires many LaTex symbols!

Adding colours to equations#

  1. The TeachBooks template includes the sphinx-named-colors extension, which lets you add colours to parts of your equations using LaTeX. Look at the CSS named colours to explore the possible colour options.

  2. It is also possible to use custom colours! Look here for documentation about the TeachBook extension which allows custom colours.

  3. Colours are added to equations using \namedcolour{...}, replacing namedcolour with the colour of choice. Test this out with the examples in the table below:

Color

\(\LaTeX\) Code

olive

\olive{\int_a^bf(x)dx}

hotpink

1.\hotpink{\mathbf{49}}

darkturquoise

\dfrac{\darkturquoise{\partial}f}{\darkturquoise{\partial}x}

  1. For colours with hyphens we use need to use the class-based command `\class{named-colour}{…}. Try this using the format shown below:

$$ \class{hyphen-color}{\sum}_{n=1}^\infty $$

  1. Test your understanding by creating a block equation where each term is a different colour!

Tip

This is especially helpful for highlighting changes between equations or focusing attention on specific terms!

  1. When you are ready, commit your changes to the repository by clicking on the green Commit changes button.

  2. Add a commit message.

  3. To see your changes, go to Actions - The most recent workflow run overview.md / the commit message of the commit you just made - Wait for it to finish - In the summary, click on the link of your book shown in the table Branches deployed and under Primary book at root (getting bored of waiting? There’ll be exercising on doing this locally which prevents you from waiting).

  4. Do you see your change? If you don’t see it click CTRL+F5/Control+F5to refresh the page.

Check your understanding

Before moving on to the next exercise, make sure you understand the following:

  • What is the difference between inline and block equations?

  • How do you use TeX formatting for different mathematical symbols?

  • What is the purpose of using single vs. double dollar signs for equations?

  • How do you troubleshoot if your equations are not rendering correctly?

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