Formulas that appear in Doing Math with Python

Tags:Python,Math,SciPy,NumPy
I started reading the introduction to mathematics starting with Python, so a memorandum. Practice writing formulas with MathJax.

Math English

Both math and English are amateurs. During study. This Math Vocabulary I'm going to be indebted to you. Also, refer to $ \ LaTeX $ and MathJax.

Cahpter 1 Working with Numbers Converting Unit Fahrenheit-> Celsius $ C = (F - 32) \times \frac{5}{9} $ Celsius-> Fahrenheit $ F = ( C \times \frac{9}{5}) + 32 $

C Celsius (℃)
F Fahrenheit (Fahrenheit ℉)

Quadratic Equation ~ Quadratic Equation ~

Nostalgic

$ y = ax^2 + bx + c $

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

Cahpter 2 Visualizing Data with Graphs

Newton's law of universal Gravitation ~ Newton's law of universal Gravitation ~

$ F= \frac{Gm_1m_2}{r^2} $

F force
G Gravitational constant: $ 6.674 \ times 10 ^ {-11} Nm ^ 2kg $
m1 m2 Mass of two objects
r Distance between two objects

Projectile Motion ~ Projectile Motion ~ (wiki)

image from http://formulas.tutorvista.com/physics/projectile-motion-formula.html

$ x $ Since the axial direction is constant v_{x} = u \cos\theta
$ y $ Axial direction is pulled by gravity over time ($ t $) $v_{y} = u \sin\theta - gt $
Therefore, the travel distance ($ S $) over time is as follows.
- S{x} = u (\cos\theta)t
- S{y} = u (\sin\theta)t - \frac{1}{2}gt^2
More importantly, find the time from launch to landing. On the $ y $ axis, the point where the velocity becomes 0 (the top of the parabolic mountain) can be regarded as half the travel time.
When the speed becomes 0,
- v_{y} = 0
- u\sin\theta - gt = 0
- t_{peak} = \frac{u\sin\theta}{g}
Double the total travel time
- t_{total} = 2\frac{u\sin\theta}{g}

Cahpter 3 Discribing Data with Statistics Basic Statistics - variance and standard deviation $ variance= \frac{\sum(x_i - x_m)^2}{n} $ $v_{y} = u\sin\theta - gt $

$ \ sum (x_i --x_m) ^ 2 : Sum of the squares of each value minus the mean ( x_m $ is the mean)
Divide it by the number of $ n $ values

$ standard\hspace{3pt}deviation = \sqrt{variance} $

Correlation Coefficient Correlation coefficient

$ Correlation = \frac{n\sum xy - \sum x \sum y}{\sqrt{\bigl(n\sum x^2 - (\sum x)^2\bigl)\bigl(n\sum y^2 - (\sum y)^2 \bigl)}}$

\sum xy : Sum of the products of the indivisual elements of the two sets of numbers, x and y
\sum x : Sum of the numbers in set x
\sum y : Sum of the numbers in set y
(\sum x)^2 : Square of the sum of the numbers in set x
(\sum y)^2 : Square of the sum of the numbers in set y
\sum x^2 : Sum of the squares of the numbers in set x
\sum y^2 : Sum of the squares of the numbers in set y

Chapter 4 Algebra and Symbolic Math with Sympy The SymPy that appears in this chapter is quite interesting, so I will summarize it separately.

Series (wiki)

$ x + \frac{x^2}{2} + \frac{x^3}{3} + \frac{x^4}{4} + \cdots + \frac{x^n}{n}$

This example seems to be Convergent (divergent is Divergent) For example, if $ n = 5 $ and $ x = 1.2 $ is substituted (Substitute), It becomes $ \ small {3.51206400000000} \ $. It's strange that this can be solved programmatically using Sympy.

equation of motion $ s = ut + \frac{1}{2}at^2 $ a constant acceleration u initial velocity

t time

Solving t ... $ t = \frac{-u + \sqrt{2.0as + u^2}}{a} $ $ t = \frac{-(u + \sqrt{2.0as + u^2})}{a} $

Chapter 5 Playing with Sets and Productivity

Cartesian Product

For two sets $ A B $

$ A \times B = \{ (a,b) \mid a \in A \land b \in B \}$

Simple Pendulum (pendulum movement)

$ T = 2 \pi \sqrt{ \frac{L}{g}} $

$ T = $ pendulum period
the amount of time it takes for the pendulum to complete one full swing

$ g = $ gravitational acceleration ($ 9.8 m/s^2 $)

$ L = $ Length of the pendulum

A=\left(
\begin{matrix}
1 & 2 \\
3 & 4 
\end{matrix}
\right)