CoCalc Shared FilesPersonal / peter_francis_tools / peter_francis_tools.sty
Author: Peter Francis
Views : 27
1%%% UPDATED 3/3/2019
2
3\usepackage{hyperref, amsmath, amsthm, latexsym, amsfonts, graphicx, enumerate, float, bm}
4
5% quick set of natural numbers
6\newcommand{\N}{\mathbb{N}}
7
8% quick set integers
9\newcommand{\Z}{\mathbb{Z}}
10
11% quick set of real numbers
12\newcommand{\R}{\mathbb{R}}
13
14% quick set of rational numbers
15\newcommand{\Q}{\mathbb{Q}}
16
17% quick set of complex numbers
18\newcommand{\C}{\mathbb{C}}
19
20% partial derivative symbol
21\newcommand{\dabba}{\partial}
22
23% epsilon
24\newcommand{\e}{\epsilon}
25
26% blacksquare
27\newcommand{\bs}{\blacksquare}
28
29% Capital Psi
30\newcommand{\IU}{\Psi}
31
32% Lowercase psi
33\newcommand{\U}{\psi}
34
35% nth differentiation of one variable
36\newcommand{\dv}[2][]{\frac{d^{#1}}{d{#2}^{#1}}}
37
38% Variable of integration
39\newcommand{\d}[2][]{\text{d}^{#1}#2}
40
41% bold Nabla
42\newcommand{\Na}{\bm{\nabla}}
43
44% Nabla vector
45\newcommand{\Nav}{\begin{bmatrix}\frac{\dabba}{\dabba x}\\ \frac{\dabba}{\dabba y}\\ \frac{\dabba}{\dabba z}\end{bmatrix}}
46
47%sherical Nabla
48\newcommand{\NaSph}{\hat{e}_r\pt{r}+\hat{e}_\theta\frac{1}{r}\pt{\theta}+\hat{e}_\phi\frac{1}{r\sin(\theta)}\pt{\phi}}
49
50
51% Scalar-vector product
52\newcommand{\scalVec}[4]{\begin{bmatrix}(#1)(#2)\\(#1)(#3)\\ (#1)(#4)\end{bmatrix}}
53
55\newcommand{\gradient}[1]{\begin{bmatrix}\frac{\dabba}{\dabba x}\left[#1\right]\\ \frac{\dabba}{\dabba y}\left[#1\right]\\ \frac{\dabba}{\dabba z}\left[#1\right]\end{bmatrix}}
56
57% Partial with given variable
58\newcommand{\pt}[2][]{\frac{\dabba^{#1}}{\dabba #2^{#1}}}
59
60% Divergence
61\newcommand{\divergence}[3]{\pt{x}\left[#1\right]+\pt{y}\left[#2\right]+\pt{z}\left[#3\right]}
62
63% Cross product 6 arguents
64\newcommand{\cross}[6]{\begin{bmatrix}#2 #6-#3 #5\\ #3 #4-#1 #6\\ #1 #5-#2 #4\end{bmatrix}}
65
66% Curl
67\newcommand{\curl}[3]{\begin{bmatrix}\pt{y}\left[#3\right]-\pt{z}\left[#2\right]\\ \pt{z}\left[#1\right]-\pt{x}\left[#3\right]\\ \pt{x}\left[#2\right]-\pt{y}\left[#1\right]\end{bmatrix}}
68
69% infinite integral
70\newcommand{\inint}{\int_{-\infty}^{\infty}}
71
72% expectation Value
73\newcommand{\xpctn}[1]{\left\langle#1\right\rangle}
74
75% script L
76\newcommand{\sL}{\mathcal{L}}
77
78\newtheorem{theorem}{Theorem}
79\newtheorem{lemma}[theorem]{Lemma}
80\newtheorem{definition}[theorem]{Definition}
81\newtheorem{corollary}[theorem]{Corollary}
82\newtheorem{remark}[theorem]{Remark}
83
84\newtheorem*{theorem*}{Theorem}
85\newtheorem*{lemma*}{Lemma}
86\newtheorem*{definition*}{Definition}
87\newtheorem*{corollary*}{Corollary}
88\newtheorem*{remark*}{Remark}
89
90\endinput