Skip to main content\(\newcommand\DLGray{\color{Gray}}
\newcommand\DLO{\color{BurntOrange}}
\newcommand\DLRa{\color{WildStrawberry}}
\newcommand\DLGa{\color{Green}}
\newcommand\DLGb{\color{PineGreen}}
\newcommand\DLBa{\color{RoyalBlue}}
\newcommand\DLBb{\color{Cerulean}}
\newcommand\ds{\displaystyle}
\newcommand\ddx{\frac{d}{dx}}
\newcommand\os{\overset}
\newcommand\us{\underset}
\newcommand\ob{\overbrace}
\newcommand\obt{\overbracket}
\newcommand\ub{\underbrace}
\newcommand\ubt{\underbracket}
\newcommand\ul{\underline}
\newcommand\laplacesym{\mathscr{L}}
\newcommand\lap[1]{\laplacesym\left\{#1\right\}}
\newcommand\ilap[1]{\laplacesym^{-1}\left\{#1\right\}}
\newcommand\tikznode[3][]
{\tikz[remember picture,baseline=(#2.base)]
\node[minimum size=0pt,inner sep=0pt,#1](#2){#3};
}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\newcommand{\sfrac}[2]{{#1}/{#2}}
\)
Appendix H List of Symbols
Symbol |
Description |
Location |
- DE implies ODE
Since this text only covers ordinary differential equations, any use of
DE will always imply
ODE.
- Derivative Notation
-
We will use the following notations for derivatives:
|
Derivative Order |
|
1st |
2nd |
3rd |
4th |
\(...\) |
nth |
Prime |
\(y^\prime\) |
\(y^{\prime\prime}\) |
\(y^{\prime\prime\prime}\) |
\(y^{(4)}\) |
\(...\) |
\(y^{(n)}\) |
Leibniz |
\(\ds\frac{dy}{dx}\) |
\(\ds\frac{d^2y}{dx^2}\) |
\(\ds\frac{d^3y}{dx^3}\) |
\(\ds\frac{d^4y}{dx^4}\) |
\(...\) |
\(\ds\frac{d^ny}{dx^n}\) |