From 537cc3e9dfb47e4d84d78ba19f6b760ab5955643 Mon Sep 17 00:00:00 2001 From: Preston Pan Date: Wed, 30 Nov 2022 10:43:00 -0800 Subject: add music page --- .../linear_algebra/source/introduction.ms | 57 +++++++++++++++++++++ .../linear_algebra/source/introduction.pdf | Bin 0 -> 24790 bytes 2 files changed, 57 insertions(+) create mode 100644 website/mathematics/linear_algebra/source/introduction.ms create mode 100644 website/mathematics/linear_algebra/source/introduction.pdf (limited to 'website/mathematics/linear_algebra/source') 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 Binary files /dev/null and b/website/mathematics/linear_algebra/source/introduction.pdf differ -- cgit