https://github.com/damienbod/math-docs

docs for some math equations
https://github.com/damienbod/math-docs

math mathjax tex

Last synced: about 1 month ago
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docs for some math equations

• Host: GitHub
• URL: https://github.com/damienbod/math-docs
• Owner: damienbod
• License: mit
• Created: 2022-05-28T09:10:10.000Z (almost 3 years ago)
• Default Branch: main
• Last Pushed: 2022-05-28T18:30:03.000Z (almost 3 years ago)
• Last Synced: 2025-03-04T13:46:20.076Z (about 2 months ago)
• Topics: math, mathjax, tex
• Homepage:
• Size: 57.6 KB
• Stars: 8
• Watchers: 3
• Forks: 13
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Exploring github markdown for math

## Quadratic equations

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

$(a+b)^2$

$$\eqalign{

(a+b)^2 &= (a+b)(a+b) \\

        &= a^2 + ab + ba + b^2 \\

        &= a^2 + 2ab + b^2

}$$

$(a-b)^2$

$$\eqalign{

(a-b)^2 &= (a-b)(a-b) \\

        &= a^2 - ab - ba + b^2 \\

        &= a^2 - 2ab + b^2

}$$

$(a-b)(a+b)$

$$\eqalign{

(a+b)(a-b)  &= a^2 - ab + ba - b^2 \\

        &= a^2 - b^2

}$$

## Functions

$$ f(x) = {\sqrt{5x^2+2x-1}+(x-2)^2 } $$

$$ g(x) = {\\frac{a}{1-a^2} }$$

$$ f(x) = {(x + 2) \over (2x + 1)} $$   

$$ f(x) = { \sqrt[3]{x^2} }$$

  

$$ \sqrt[5]{34}$$

  

## Trigonometry

$$ cos^2 \theta + sin^2 \theta  = 1  $$

$$ tan 2 \theta = {2tan \theta  \over 1 - tan^2 \theta}  $$

$$\eqalign{

cos 2 \theta = cos^2 \theta - sin^2 \theta \\

                       &=  2 cos^2  \theta -1 \\

                       &= 1 - 2sin^2 \theta 

}$$

Prove $ \sqrt{ 1 - cos^2 \theta \over 1- sin^2 \theta} = tan \theta $

$$ \sqrt{ 1 - cos^2 \theta \over 1- sin^2 \theta} = \sqrt{ sin^2 \theta \over cos^2 \theta} = {sin \theta \over cos \theta}  = Tan \theta $$

## Calculus

$$\eqalign{

f(x) = {3x^4} \implies {dy \over dx} = 12x^3

}$$

$$\eqalign{

f(x) = {2x^{-3/2}} \implies  {dy \over dx} = -3x^{-5/2} &= - {3 \over \sqrt{x^5}}

}$$

If $x = 2t + 1$ and $ y = t^2$ find ${dy \over dx}$ ?

$$\eqalign{

x = 2t + 1 \implies  {dx \over dt} = 2 \\

        y = t^2 \implies  {dy \over dt} = 2t \\

        {dy \over dx} = {dy \over dt} \div {dx \over dt} \\

         \implies 2t \div 2 = t

}$$

## Integration

Evaluate $\int_1^2 (x + 4)^2 dx $

$$\eqalign{

\int_1^2 (x + 4)^2 dx =  \int_1^2 (x^2 + 8x + 16) dx \\

        &= \left\lbrack {x^3 \over 3} + {8x^2 \over 2}  + 16x \right\rbrack_1^2 \\

        &= \left\lbrack {8 \over 3} + {8 * 4 \over 2}  + 16 * 2 \right\rbrack - \left\lbrack {1 \over 3} + {8 \over 2}  + 16  \right\rbrack 

}$$

## Matrix

$$ {\left\lbrack \matrix{2 & 3 \cr 4 & 5} \right\rbrack} * \left\lbrack \matrix{1 & 0 \cr 0 & 1} \right\rbrack = \left\lbrack \matrix{2 & 3 \cr 4 & 5} \right\rbrack $$

## Sum

$$\sum_{n=1}^n n = {n \over 2} (n + 1) $$

$$\sum_{n=1}^n n^2 = {n \over 6} (n + 1)(2n + 1) $$

# Links

https://github.blog/changelog/2022-05-19-render-mathematical-expressions-in-markdown/

https://www.mathjax.org/

http://docs.mathjax.org/en/latest/

https://docs.mathjax.org/en/v2.7-latest/tex.html

https://www.onemathematicalcat.org/MathJaxDocumentation/TeXSyntax.htm