Differential equations and calculus from scratch

Опубликовано: 23 Май 2023
на канале: Ten Minute Physics

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In this tutorial I start with simple algebra and derive calculus, differential equations and the most famous mathematical constants in one train of thought.

For the source html code, demo and all other tutorials see https://matthias-research.github.io/p...
There is also a discord server to discuss all videos here: / discord

Demo at: https://matthias-research.github.io/p...

Timecodes
0:00 - Intro
1:08 - The concept of change
2:16 - Rate of change
4:40 - Derivatives
8:18 - Differential equations
8:38 - The rabbit equation
10:01 - The coffee equation
11:21 - The soccer equation
13:11 - The spring equation
15:13 - How to solve differential equations mathematically
17:34 - Calculus
18:48 - Deriving the rules
23:22 - Polynomials
24:27 - Solve the soccer equation
26:18 - First attempt to solving the rabbit equation
27:22 - Exponents recap
28:50 - Finding e using the limit
32:22 - Finding e using a polynomial
39:30 - Solving the rabbit equation
40:26 - Solving the coffee equation
41:16 - First attempt to solve the spring equation
42:27 - The imaginary number i
43:20 - Juggling with i
45:15 - The complex plane
47:27 - Computing e^ix
49:38 - The polynomial quiz
52:00 - Point on a circle
54:12 - Eulers magic formula
55:45 - Solving the spring equation
56:27 - Bonus slides
56:32 - Euler in the complex plane
57:38 - Introducing pi
59:09 - The area of the unit disc
1:00:18 - i to the power of i
1:01:27 - The square game
1:02:46 - The square game in the complex plane
1:02:52 - Polar coordinates
1:03:53 - Squaring complex numbers
1:05:25 - The edge in the complex plane
1:05:55 - Introducing wind
1:06:31 - The magic program
1:07:31 - The Julia set
1:09:46 - The Mandelbrot set

The Mandelbrot zoom by Mathigon:
• Mandelbrot Zoom Sequence

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