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authorPreston Pan <ret2pop@gmail.com>2025-01-03 20:22:16 -0800
committerPreston Pan <ret2pop@gmail.com>2025-01-03 20:22:16 -0800
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treed2b323e23ec12bf7851c5da3e9659cf78995cb39 /mindmap/Fourier Transform.org
parent7b6c23a672ad42103c358bcbe72d42baa6263ec7 (diff)
add blog posts and journal posts; update emacs configuration
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#+html_head: <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
#+html_head: <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
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* Introduction
The Fourier Transform is a generalization of the Fourier Series. It has applications in solving [[id:4be41e2e-52b9-4cd1-ac4c-7ecb57106692][differential equations]] and
has applications in many different fields, including [[id:136e79df-106f-4989-ab19-89705929cf91][quantum mechanics]], radio, planetary motion, and even the study
@@ -16,8 +15,8 @@ of the heat equation. In this article we will study the heat equation, the Fouri
** The Heat Equation
The heat equation is the study of how heat travels in a conductor with the unknown function in question being $f(\vec{r}, t)$,
-giving the temperature at position $\vec{r}$ at time $t$. Now we want to describe the time rate of change of this function, so we use a
-[[id:3993a45d-699b-4512-93f9-ba61f498f77f][partial derivative]]:
+giving the temperature at position $\vec{r}$ at time $t$. Now we want to describe the time rate of
+change of this function, so we use a [[id:3993a45d-699b-4512-93f9-ba61f498f77f][partial derivative]]:
\begin{align}
\label{Heat equation 1}
\partial_{t}f = ?f