Typing Equations in LaTeX
==========================

There are two types of equations in LaTeX: Inline and display. Inline equations are written within a line of text, while display equations are centered on a new line.

There are multiple ways of typing equations in LaTeX but only some of them will be shown here.

Put the inline equation between two dollar signs ``$``. For example, the code

.. code-block:: latex

    Bla bla bla $a^2 + b^2 = c^2$.

will produce the following output:

Bla bla bla :math:`a^2 + b^2 = c^2`.

To write a display equation, put the equation in ``equation`` environment as shown below:

.. code-block:: latex

    \begin{equation}
        a^2 + b^2 = c^2
    \end{equation}

This will produce the following output:

.. math::
    :label: eq1
    a^2 + b^2 = c^2

For multi-line equations, use the ``align`` environment as shown below:

.. code-block:: latex

    \begin{align}
        a^2 + b^2 &= c^2 \\
        x^2 + y^2 &= z^2
    \end{align}

This will produce the following output:

.. math::
    :label: eq2
    \begin{aligned}
        a^2 + b^2 &= c^2 \\
        x^2 + y^2 &= z^2
    \end{aligned}

To use the ``align`` environment, you need to include the ``amsmath`` package in the preamble of your LaTeX document. Here is a complete example:

.. code-block:: latex

    \documentclass{article}
    \usepackage{amsmath}

    \begin{document}

        Now we can write multi-line equations using the align environment:
        \begin{align}
            a^2 + b^2 &= c^2 \\
            x^2 + y^2 &= z^2
        \end{align}

    \end{document}

Beware not to put blank line between the paragraph and the equation/align environment. Otherwise, the equation will not be part of the paragraph and will be separated from it by a vertical space.

Display equations are numbered by default. The ``align`` environment will number each line of a multi-line equation. One of the ways to give only one equation number to a multi-line equation is to use the ``aligned`` environment inside the ``equation`` environment as shown below:

.. code-block:: latex

    \begin{equation}
        \begin{aligned}
            a^2 + b^2 &= c^2 \\
            x^2 + y^2 &= z^2
        \end{aligned}
    \end{equation}

This will produce the following output:

.. math::
    :label: eq3
    \begin{equation}
        \begin{aligned}
            a^2 + b^2 &= c^2 \\
            x^2 + y^2 &= z^2
        \end{aligned}
    \end{equation}

Un-numbered Equations
---------------------

To write an un-numbered equation, use the ``equation*`` or ``align*`` environment as shown below:

.. code-block:: latex

    \begin{equation*}
        a^2 + b^2 = c^2
    \end{equation*}

Shorter Ways of Writing Equations
---------------------------------

There are shorter ways of writing equations in LaTeX such as using double dollar signs ``$$`` for display equations. Here is an example:

.. code-block:: latex

    $$
        a^2 + b^2 = c^2
    $$

There is one more way of writing display equations using the \[ and \] symbols as shown below:

.. code-block:: latex
    \[
        a^2 + b^2 = c^2
    \]

For inline equations, you can also use the \(...\) symbols as shown below:

.. code-block:: latex

    Bla bla bla \( a^2 + b^2 = c^2 \).

Typing Some of the Math Symbols
-------------------------------

It is impossible to list all the math symbols in LaTeX but here are some of the most common ones:

Greek Letters
^^^^^^^^^^^^^

Lowercase Greek letters are written using a backslash followed by the name of the letter. For example, ``\alpha`` produces :math:`\alpha`, ``\beta`` produces :math:`\beta`, and so on. Uppercase Greek letters are written using a backslash followed by the name of the letter with the first letter capitalized. For example, ``\Gamma`` produces :math:`\Gamma`, ``\Delta`` produces :math:`\Delta`, and so on.

Subscripts and Superscripts
^^^^^^^^^^^^^^^^^^^^^^^^^^^

Use the underscore symbol ``_`` for subscripts and the caret symbol ``^`` for superscripts. For example, ``a_i`` produces :math:`a_i` and ``a^2`` produces :math:`a^2`.

Fractions
^^^^^^^^^

Use the ``\frac`` command to write fractions. The syntax is ``\frac{numerator}{denominator}``. For example, ``\frac{a}{b}`` produces :math:`\frac{a}{b}`. If you want to write a fraction in inline math mode, you can use the ``\dfrac`` command instead of ``\frac`` to make the fraction larger and more readable. For example, ``\dfrac{a}{b}`` produces :math:`\dfrac{a}{b}`.

Derivatives
^^^^^^^^^^^

The syntax for ordinary derivatives is ``\frac{dy}{dx}`` and for partial derivatives is ``\frac{\partial f}{\partial x}``. For example, ``\frac{dy}{dx}`` produces :math:`\frac{dy}{dx}` and ``\frac{\partial f}{\partial x}`` produces :math:`\frac{\partial f}{\partial x}`.

Square Roots
^^^^^^^^^^^^

Use the ``\sqrt`` command to write square roots. The syntax is ``\sqrt{expression}``. For example, ``\sqrt{a}`` produces :math:`\sqrt{a}`.

Integrals
^^^^^^^^^

Use the ``\int`` command to write integrals. The syntax is ``\int_{lower}^{upper} expression \, dx``. For example, ``\int_a^b f(x) \, dx`` produces :math:`\int_a^b f(x) \, dx`.

Summations
^^^^^^^^^^

Use the ``\sum`` command to write summations. The syntax is ``\sum_{lower}^{upper} expression``. For example, ``\sum_{i=1}^n a_i`` produces :math:`\sum_{i=1}^n a_i`.

Limits
^^^^^^

Use the ``\lim`` command to write limits. The syntax is ``\lim_{x \to value} expression``. For example, ``\lim_{x \to \infty} f(x)`` produces :math:`\lim_{x \to \infty} f(x)`.

Exponential and Logarithmic Functions
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Use the ``\exp`` command for the exponential function and the ``\log`` command for the logarithmic function. For example, ``\exp(x)`` produces :math:`\exp(x)` and ``\log(x)`` produces :math:`\log(x)`. You can also use the caret symbol ``^`` to write exponential functions. For example, ``e^x`` produces :math:`e^x`. Use the ``\ln`` command for the natural logarithm. For example, ``\ln(x)`` produces :math:`\ln(x)`.

Matrices
^^^^^^^^

Use the ``\begin{matrix}`` and ``\end{matrix}`` commands to write matrices. The syntax is as follows:

.. code-block:: latex

    \begin{matrix}
        a & b \\
        c & d
    \end{matrix}