5 files changed, 66 insertions, 14 deletions
diff --git a/build/website/mathematics/calculus/derivative.pdf b/build/website/mathematics/calculus/derivative.pdf
index fd3db0a..f56fc33 100644
--- a/build/website/mathematics/calculus/derivative.pdf
+++ b/build/website/mathematics/calculus/derivative.pdf
diff --git a/build/website/mathematics/calculus/source/derivative.ms b/build/website/mathematics/calculus/source/derivative.ms
index 9e4196f..681e019 100644
--- a/build/website/mathematics/calculus/source/derivative.ms
+++ b/build/website/mathematics/calculus/source/derivative.ms
@@ -205,10 +205,10 @@ d sub initial = f(t sub {initial})
 d sub final = f(t sub {final})
 .EN
 .EQ
-\[*D]t = f(t sub initial + \[*D]t) - d sub initial
+\[*D]d = f(t sub initial + \[*D]t) - d sub initial
 .EN
 .EQ
-\[*D]t = f(t sub initial + \[*D]t) - f(t sub {initial})
+\[*D]d = f(t sub initial + \[*D]t) - f(t sub {initial})
 .EN
 .EQ
 f'(t) = {f(t sub initial + \[*D]t) - f(t sub {initial})} over \[*D]t
diff --git a/build/website/mathematics/differential_equations/index.html b/build/website/mathematics/differential_equations/index.html
index a28e97a..ab9dd91 100644
--- a/build/website/mathematics/differential_equations/index.html
+++ b/build/website/mathematics/differential_equations/index.html
@@ -23,24 +23,19 @@ Mathematics
 	</div>
 
 	<div class="content">
-<h1>Mathematics</h1>
+<h1>Differential Equations</h1>
 <p>
-	Mathematics is the basis for the analysis of things that we
-	believe to adhere to our logical system.
+	Differential equations describe how things in our universe change. They come up
+	as fundamental equations in all models of our universe, and they also describe
+	change on more macro levels as well. Understanding differential equations gives
+	you one of the most powerful tools in mathematics.
 </p>
 
-<h2>Topics</h2>
+<h2>Ordinary Differential Equations</h2>
 <ul>
-	<li><a href="./linear_algebra/">Linear Algebra</a> -- the study multidimensional linear quantities.</li>
-	<li><a href="./calculus/">Calculus</a> -- The age-old study of infinitesimal ratios.</li>
-	<li><a href="./differential_equations/">Differential Equations</a> -- The math underlying our physical world.</li>
+	<li><a href="./introduction.pdf">Introduction</a> -- Why we study differential equations, and explaining the simplest case.</li>
 </ul>
 
-<p>
-	These are all the topics I have learned about so far. I will learn more in the future and add new topics.
-	All of these topics I know a lot about but writing the articles takes an extreme amount of time, so stay
-	tuned!
-</p>
 	</div>
 </body>
 </html>
diff --git a/build/website/mathematics/linear_algebra/source/introduction.ms b/build/website/mathematics/linear_algebra/source/introduction.ms
new file mode 100644
index 0000000..106ffec
--- /dev/null
+++ b/build/website/mathematics/linear_algebra/source/introduction.ms
@@ -0,0 +1,57 @@
+.EQ
+delim $$
+.EN
+.TL
+Linear Algebra Introduction
+.AU
+Preston Pan
+.AI
+Pacific School of Science and Inquiry
+
+.PP
+Linear algebra is a subject that is worthy of studying if you are looking
+to analyze data in any systematic way, or if you are attempting to represent
+multidimensional (or multivariable) quantities in a structured way.
+Therefore, everyone in STEM and even in the social sciences should know about
+linear algebra and a little bit of the mathematical theory behind it.
+
+.PP
+I will be introducing subjects regarding linear algebra from the perspective
+of physics, though you do not need to know much physics in order to understand
+most of my explanations.
+
+.PP
+You might know that in high school physics, all the equations are introduced
+as one dimensional equations (that is to say, most equations that are introduced
+only work if the object or objects in question only move forwards and backwards,
+or any other singluar direction). Of course, in real life, there are at least
+three spatial dimensions, so one dimensional equations just won't model real
+life well. In these scenarios, it is useful to consider linear algebra as a
+systematic way to represent direction and motion in three dimensions. With
+this motivation, we start investigating.
+
+.PP
+One way we can represent two dimensional space is with a coordinate system. For
+example, we can have a point $(3, 2)$ which represents a single point three
+units right and two units up in a coordinate system.
+
+.G1
+coord x 0, 11 y 0, 11
+3 2
+"(3, 2)" above at 3,2
+.G2
+
+.PP
+Now, let's imagine that this point $(3, 2)$ represents a force in a certain direction.
+For example, we can draw a line from the origin to this point and the resulting force's
+magnitude will be represented by the length of the line in question (which can be obtained
+via the pythagorean theorem).
+
+.G1
+draw solid
+coord x 0, 11 y 0, 11
+0 0
+3 2
+"(3, 2)" above at 3,2
+"$sqrt {3 sup 2 + 2 sup 2}$" above at 1,2
+.G2
diff --git a/build/website/mathematics/linear_algebra/source/introduction.pdf b/build/website/mathematics/linear_algebra/source/introduction.pdf
new file mode 100644
index 0000000..b74d28a
--- /dev/null
+++ b/build/website/mathematics/linear_algebra/source/introduction.pdf