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diff --git a/build/website/mathematics/calculus/derivative.pdf b/build/website/mathematics/calculus/derivative.pdf Binary files differindex 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 Binary files differnew file mode 100644 index 0000000..b74d28a --- /dev/null +++ b/build/website/mathematics/linear_algebra/source/introduction.pdf diff --git a/build/website/media/music/dusk.mp3 b/build/website/media/music/dusk.mp3 Binary files differnew file mode 100644 index 0000000..a34ff98 --- /dev/null +++ b/build/website/media/music/dusk.mp3 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 Binary files differindex fd3db0a..f56fc33 100644 --- a/website/mathematics/calculus/derivative.pdf +++ b/website/mathematics/calculus/derivative.pdf 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 Binary files differnew file mode 100644 index 0000000..b74d28a --- /dev/null +++ b/website/mathematics/linear_algebra/source/introduction.pdf diff --git a/website/media/music/dusk.mp3 b/website/media/music/dusk.mp3 Binary files differnew file mode 100644 index 0000000..a34ff98 --- /dev/null +++ b/website/media/music/dusk.mp3 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 |