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