Latex + Matlab + Jupyter Notebook + Google Colab + Markdown

Latex

Where to edit — Can be accessed online through the “Overleaf” website.

File format — .tex

\documentclass[]{article}    --> Use \documentclass{...} to choose class
\begin{document}                 use exam or beemer (for slides) instead of article
.....                            
\end{document}

use [] for Optional arguments -> eg- font size: [12pt]
For title -> use \title{title_name} and Close title using \maketitle

Packages — load them right after \documentclass:
- \usepackage{amsmath} — for equations
- \usepackage{graphicx} — to insert figures

Equations & figures

Use \begin{equation} ... \end{equation} inside body

Figure skeleton:

\begin{figure}
  \centering
  \includegraphics[width=\textwidth]{image_name}
  \caption{...}
\end{figure}

Paragraphs — start new paragraph by leaving an empty line
Graphic adjustments
- \includegraphics[width=\textwidth]{image_name} — scale to text width
- \includegraphics[scale=1.2, angle=45]{image_name} — scale and rotate (45° anticlockwise)
- \caption{...} — figure caption
- \hspace{1cm} — horizontal space; \vspace{...} — vertical space

#1, #2 placeholders — in custom macros:
#1 is the first argument passed to the function, #2 the second, etc.
Text formatting commands:
\textbf{...} — bold \textit{...} — italic
& in tables — used to separate columns (left from right).
Common font-size chart (smallest → biggest):
\tiny → \scriptsize → \footnotesize → \small → \normalsize → \large → \Large
→ \LARGE → \huge → \Huge

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Matlab (Matrix Laboratory)

If use ; at end --> does not print output
Commands in terminal -> clc - clear console       clear all - clears everything
disp(...) ---> to display output
Use % for comment
Use elseif (without space in between)
Use ~= for unequal to (just like != in c++)

To take input with prompt (Prompt must be given)

n = input('Enter a number');  -> Prompt is "Enter a number"
n = input('...', 's') -> for string input MUST give 's' as additional argument
                         -> accepts string as input without requiring quotes

To create function -

function [sum, sub] = Sum(x,y)
    sum = x+y;
    sub = x-y;
end           ---> make function call as [a, b] = Sum(2,3)

File name must be same as function name (Sum)
Can use this function in any other file (except Function file)

square = @(x) x.^2; ---> inline fxn created without any separate file
B = arrayfun(func, A1) ---> apply func to each element of multiple arrays

Eg - A = [1 2 3]; B = [4 5 6];
C = arrayfun(@(x,y) x*y, A, B) ---> C = [4 10 18]
D = arrayfun(@(x) x^2, A) ---> D = [1 4 9]

A = [1 2 3; 4 5 6] ---> 2x3 matrix ---> to access => A(2, 3) [1-based indexing]
B = 0:2:20 ---> array from 0 to 20 in increments of 2
rand, zeros, ones, size, eye, linspace ---> same as python for matrices
Matrix multiplication --> use * => C = A*B
A.*B --> element-wise multiplication of A and B
Transpose ---> use ' => C = A'

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Jupyter Notebook

Runs locally + manually install any libraries + No free GPU + needs manual setup
If type variable in last line → print it using display() [by default, present in Jupyter]

renders dataframe and plots in visually more appealing format (better than print)

When add new file → jupyter may not recognize it → better to restart whole thing

from google.colab import files -> files.upload() and files.download('file_path')

pip install pandas → runs directly within Python environment (like script/shell)
!pip install pandas → ! tells environment to run it as shell command

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Google Colab

Cloud-based + pre-installed libraries + Free GPU/TPU + save notebooks to G-Drive

Can switch to GPU/TPU from "change runtime type"
GPU (Graphics Processing Unit) - speeds computing jobs for ML, scientific computing, and 3D visualization → better on smaller batches
TPUs (Tensor Processing Unit) - accelerate operations on Tensorflow Graph

optimized for large batch size + has highest training throughput

from google.colab import files -> files.upload() and files.download('file_path')

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Markdown

It is a way to write content for web (with .md or .markdown extension)

Use * => 1 time - italic, 2 times - bold, 3 times - bold + italic
For links use [text for link](link) but if don't want to change name => use <link>
Extended markdown only valid in selected platforms
Use ~ => 1 time for subscript like H₂O and 2 times for strikethrough
can use <mark> to highlight </mark>
<sup> for superscript like x² </sup>
<sub> for subscript like H₂O </sub>
For table at least 3 dash are must
If press enter => hard break
                  if use double space => soft break (like shift + enter in blog)