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diff --git a/mindmap/differential equation.org b/mindmap/differential equation.org new file mode 100644 index 0000000..8229587 --- /dev/null +++ b/mindmap/differential equation.org @@ -0,0 +1,26 @@ +:PROPERTIES: +:ID: 4be41e2e-52b9-4cd1-ac4c-7ecb57106692 +:END: +#+title: differential equation +#+author: Preston Pan +#+html_head: <link rel="stylesheet" type="text/css" href="../style.css" /> +#+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> +#+options: broken-links:t +* Introduction +A differential equation is an equation whose solutions are functions and which incorporate derivatives of the function +you're solving for. Differential equations often have a family of infinite solutions, where a general solution for +a differential equation incorporates many particular solutions. Particular solutions to differential equations are specific +functions, corresponding to a single choice of an initial value problem. Therefore, general solutions tell you how to solve +initial value problems. + +Differential equations are often used to model real world systems, and are the main tool in numerical simulations of said +systems. +** ODE +An ODE is a differential equation involving single variable function solution classes and their derivatives. +** PDE +A PDE is a differential equation involving multivariable function solution classes and generally involve partial derivatives +of the unknown function. +** initial value problem +An initial value problem is a problem where one is given a differential equation and particular values of the unknown function +and particular values of its derivatives, and the result is a particular solution. |