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-rw-r--r--build/website/mathematics/calculus/derivative.pdfbin33707 -> 33704 bytes
-rw-r--r--build/website/mathematics/calculus/source/derivative.ms4
-rw-r--r--build/website/mathematics/differential_equations/index.html19
-rw-r--r--build/website/mathematics/linear_algebra/source/introduction.ms57
-rw-r--r--build/website/mathematics/linear_algebra/source/introduction.pdfbin0 -> 24790 bytes
-rw-r--r--build/website/media/music/dusk.mp3bin0 -> 2719045 bytes
-rw-r--r--build/website/music/index.html46
-rw-r--r--website/mathematics/calculus/derivative.pdfbin33707 -> 33704 bytes
-rw-r--r--website/mathematics/calculus/source/derivative.ms4
-rw-r--r--website/mathematics/differential_equations/index.html19
-rw-r--r--website/mathematics/linear_algebra/source/introduction.ms57
-rw-r--r--website/mathematics/linear_algebra/source/introduction.pdfbin0 -> 24790 bytes
-rw-r--r--website/media/music/dusk.mp3bin0 -> 2719045 bytes
-rw-r--r--website/music/index.html24
14 files changed, 202 insertions, 28 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
Binary files differ
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
Binary files differ
diff --git a/build/website/media/music/dusk.mp3 b/build/website/media/music/dusk.mp3
new file mode 100644
index 0000000..a34ff98
--- /dev/null
+++ b/build/website/media/music/dusk.mp3
Binary files differ
diff --git a/build/website/music/index.html b/build/website/music/index.html
new file mode 100644
index 0000000..6fe2f74
--- /dev/null
+++ b/build/website/music/index.html
@@ -0,0 +1,46 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+ <meta charset="UTF-8">
+ <meta http-equiv="X-UA-Compatible" content="IE=edge" />
+ <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+ <meta name="description" content="My personal website.">
+ <meta name="author" content="Preston Pan">
+ <link rel="stylesheet" type="text/css" href="/css/style.css" />
+
+ <link rel="icon" type="image/png" href="/img/favicon.png">
+ <title>
+Music
+ </title>
+</head>
+<body>
+ <div class="nav" class="justcenter">
+ <a href="/index.html" class="justleft">Home</a> |
+ <a href="/about/" class="justleft">About</a> |
+ <a href="/about/contact.html" class="justleft">Contact</a>
+ | <a href="../index.html">Back</a>
+ <hr>
+ </div>
+
+ <div class="content">
+<h1>Music</h1>
+
+<p>
+ Here you will find some of the music that I've made.
+ Note that I am not a professional at singing, but I think
+ I'm pretty good at piano.
+</p>
+
+<h2>Songs</h2>
+<ul>
+ <li><a href="/media/music/superposition.mp3">Superposition</a> -- my first single.</li>
+</ul>
+
+<h2>Improvisation</h2>
+<ul>
+ <li><a href="/media/music/dusk.mp3">dusk</a> -- dark yet hopeful.</li>
+</ul>
+
+ </div>
+</body>
+</html>
diff --git a/website/mathematics/calculus/derivative.pdf b/website/mathematics/calculus/derivative.pdf
index fd3db0a..f56fc33 100644
--- a/website/mathematics/calculus/derivative.pdf
+++ b/website/mathematics/calculus/derivative.pdf
Binary files differ
diff --git a/website/mathematics/calculus/source/derivative.ms b/website/mathematics/calculus/source/derivative.ms
index 9e4196f..681e019 100644
--- a/website/mathematics/calculus/source/derivative.ms
+++ b/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/website/mathematics/differential_equations/index.html b/website/mathematics/differential_equations/index.html
index 1c414b4..209a363 100644
--- a/website/mathematics/differential_equations/index.html
+++ b/website/mathematics/differential_equations/index.html
@@ -3,22 +3,17 @@ Mathematics
$$END TITLE
$$START 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>
$$END CONTENT
diff --git a/website/mathematics/linear_algebra/source/introduction.ms b/website/mathematics/linear_algebra/source/introduction.ms
new file mode 100644
index 0000000..106ffec
--- /dev/null
+++ b/website/mathematics/linear_algebra/source/introduction.ms
@@ -0,0 +1,57 @@
+.EQ
+delim $$
+.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/website/mathematics/linear_algebra/source/introduction.pdf b/website/mathematics/linear_algebra/source/introduction.pdf
new file mode 100644
index 0000000..b74d28a
--- /dev/null
+++ b/website/mathematics/linear_algebra/source/introduction.pdf
Binary files differ
diff --git a/website/media/music/dusk.mp3 b/website/media/music/dusk.mp3
new file mode 100644
index 0000000..a34ff98
--- /dev/null
+++ b/website/media/music/dusk.mp3
Binary files differ
diff --git a/website/music/index.html b/website/music/index.html
new file mode 100644
index 0000000..f4cd5e3
--- /dev/null
+++ b/website/music/index.html
@@ -0,0 +1,24 @@
+$$START TITLE
+Music
+$$END TITLE
+
+$$START CONTENT
+<h1>Music</h1>
+
+<p>
+ Here you will find some of the music that I've made.
+ Note that I am not a professional at singing, but I think
+ I'm pretty good at piano.
+</p>
+
+<h2>Songs</h2>
+<ul>
+ <li><a href="/media/music/superposition.mp3">Superposition</a> -- my first single.</li>
+</ul>
+
+<h2>Improvisation</h2>
+<ul>
+ <li><a href="/media/music/dusk.mp3">dusk</a> -- dark yet hopeful.</li>
+</ul>
+
+$$END CONTENT