Get Your Billy Merch: https://my-store-d2b84c.creator-spring.com/
Paper Referenced: https://arxiv.org/pdf/1006.2518.pdf
Code from the video: https://github.com/lukepolson/youtube_channel/blob/main/Python%20Metaphysics%20Series/vid38.ipynb
Discord: https://discord.gg/Ap2sf3sKqg
Instagram: https://www.instagram.com/mrpsolver/

A Fun Little Differential Equation In Python (Dark Matter)

Welcome to my four part lecture on essential math for game developers 💖 I hope you'll find this useful in your game dev journey!

This course will have assignments throughout, if you want to maximize your learning, I recommend doing them!

If you are enjoying this series, please consider supporting me on Patreon!
🧡 https://www.patreon.com/acegikmo

00:00:00 - Intro
00:07:05 - Why math?
00:12:59 - 1D vectors
00:36:13 - 2D vectors
01:09:35 - Vector normalization
01:15:23 - Direction to point
01:23:11 - Length
01:31:49 - Distance
01:44:14 - Point along direction
02:00:45 - Radial trigger
02:26:21 - Dot product
02:44:30 - Examples from my game
03:03:13 - Assignments
03:03:29 - Asgmt. 1 (Radial trigger)
03:05:49 - Asgmt. 2 (Look-at trigger)
03:10:03 - Asgmt. 3 (Space transformation)

Assignments:
https://docs.google.com/document/d/1Nou1ZAbNOkELggW9YqZ9LTRIW9Hc-isUpURbQ8gjiMM

Originally streamed as a course for students at http://futuregames.se/, who were super kind to let me both stream this live as well as upload it here! so massive thanks to the people at FutureGames!!

💖 Patreon ❱ https://www.patreon.com/acegikmo
🐦 Twitter ❱ https://twitter.com/FreyaHolmer
📺 Twitch ❱ https://www.twitch.tv/acegikmo
💬 Discord ❱ https://discord.gg/v5VWuga
🌸 Instagram ❱ https://instagram.com/freya_holmer

✫ Video Production by Higher Vision:
➥ https://twitter.com/HigherVision1
➤ Edited by Stelly: https://twitter.com/stelly47050876

Vectors & Dot Product • Math for Game Devs [Part 1]

How to translate, rotate, and scale points in 2D space, using basic algebra and trigonometry.
Part of a larger series teaching game programming and general programming. Visit http://codeschool.org

3D Transformations

🔽 Click for Timestamps & Info


This is from the improvised tutorial stream on core math concepts in game dev!
Timestamps at the bottom of the description~

Also, a little note: when drawing the curve for tan(x) I accidentally drew the sec(x) curve! Apologies for that!

Anyhow, enjoy!

💖 Patreon ❱ https://www.patreon.com/acegikmo
🐦 Twitter ❱ https://twitter.com/FreyaHolmer
📺 Twitch ❱ https://www.twitch.tv/acegikmo
💬 Discord ❱ https://discord.gg/v5VWuga
🌸 Instagram ❱ https://instagram.com/freya_holmer

00:00 - Intro
22:01 - Scaling & Ratios
46:04 - Vectors & Dot Product
1:54:45 - Trigonometry
2:30:05 - Degrees & Radians
2:52:32 - Cross Product
3:07:03 - Local vs World Space & Transformation
3:20:27 - Lerp
3:33:45 - Derivatives
3:46:35 - Framerate Independence
3:55:28 - Outro

Math for Game Dev - An Improvised Live Course

Part two! let's talk about space

If you are enjoying this series, please consider supporting me on Patreon!
🧡 https://www.patreon.com/acegikmo

00:00:00 - Quick recap
00:01:01 - Dot product recap
00:06:51 - Asgmt. 1 solution (Radial trigger)
00:18:16 - Asgmt. 2 solution (Look-at trigger)
00:35:07 - Questions
00:42:24 - Spaces
00:53:26 - Asgmt. 3 solution (Space transformation)
01:18:43 - World to local
01:34:14 - Matrices
02:15:20 - Cross product

Assignments:
Asgmt. 4 (Bouncing laser)
Asgmt. 5 (Mesh surface area)
Asgmt. 6 (The turret)
https://docs.google.com/document/d/1Nou1ZAbNOkELggW9YqZ9LTRIW9Hc-isUpURbQ8gjiMM

Originally streamed as a course for students at http://futuregames.se/, who were super kind to let me both stream this live as well as upload it here! so massive thanks to the people at FutureGames!!

💖 Patreon ❱ https://www.patreon.com/acegikmo
🐦 Twitter ❱ https://twitter.com/FreyaHolmer
📺 Twitch ❱ https://www.twitch.tv/acegikmo
💬 Discord ❱ https://discord.gg/v5VWuga
🌸 Instagram ❱ https://instagram.com/freya_holmer

✫ Video Production by Higher Vision:
➥ https://twitter.com/HigherVision1
➤ Edited by Stelly: https://twitter.com/stelly47050876

Spaces & Cross Product • Math for Game Devs [Part 2]

This from-scratch tutorial on SciPy is designed specifically for those studying physics, mathematics, and engineering. Before watching this, you may want to brush up on numpy:

https://www.youtube.com/watch?v=DcfYgePyedM

All code can be found here:
https://github.com/lukepolson/youtube_channel/blob/main/Python%20Tutorial%20Series/scipy_essentials.ipynb

0:00 Introduction
1:47 Optimization
10:33 Interpolation
13:46 Curve Fitting
24:39 Special Functions
27:12 Differentiation
29:22 Integration
34:06 Differential Equations
48:15 Fourier Transforms
52:06 Examples
1:01:59 Linear Algebra (Basics)
1:10:18 Linear Algebra (Sparse Matrices)
1:17:50 Statistics

SciPy Tutorial (2022): For Physicists, Engineers, and Mathematicians

This from-scratch tutorial on NumPy is designed specifically for those in physics, mathematics, and engineering. In the future, I will be making tutorial videos on all the essential python packages, so subscribe for more!

All code can be found here:
https://github.com/lukepolson/youtube_channel/blob/main/Python%20Tutorial%20Series/numpy_essentials.ipynb

0:00 Introduction
3:43 Array Operations
8:28 Indexing and Slicing (1 Dimension)
15:18 Calculus and Statistics
21:28 Examples
47:18 Multi-Dimensional Arrays
52:22 Functions on Multi-Dimensional Arrays
56:26 Linear Algebra: Matrix Operations
58:33 Linear Algebra: Systems of Equations
59:53 Linear Algebra: Eigenvalue Problems
1:02:02 Examples
1:28:42 Basic Datasets

NumPy Tutorial (2022): For Physicists, Engineers, and Mathematicians

In this video, we take a look at one of the most beautiful algorithms ever created: the Fast Fourier Transform (FFT). This is a tricky algorithm to understand so we take a look at it in a context that we are all familiar with: polynomial multiplication. You will see how the core ideas of the FFT can be "discovered" through asking the right questions. The key insights that are presented in this video is that polynomial multiplication can be improved significantly by multiplying polynomials in a special value representation. The challenge that presents itself is the problem of converting a polynomial from a standard coefficient representation to value representation. 

We see that the FFT is an incredibly efficient recursive algorithm that performs this task, and we also discover that a slightly tweaked FFT (Inverse FFT) can also solve the reverse problem of interpolation. If this video doesn't blow your mind, I don't know what will. 

0:00 Introduction
2:19 Polynomial Multiplication
3:36 Polynomial Representation
6:06 Value Representation Advantages
7:07 Polynomial Multiplication Flowchart
8:04 Polynomial Evaluation
13:49 Which Evaluation Points?
16:30 Why Nth Roots of Unity?
18:28 FFT Implementation
22:47 Interpolation and Inverse FFT
26:49 Recap

Also a subtle mistake that a commenter made me aware of -- at 26:40 instead of replacing w with (1/n * e^{-2 * pi i/ n}), the actual right way to do this is by taking the final output of the IFFT at the end of the recursion and dividing by n. 

So the full change is w = e^{-2 pi i / n} 
And then somewhere outside the scope of the IFFT function ifft_result = 1/n * IFFT(values)

The treatment of the FFT in this video is inspired by several well known references, mainly Introduction to Algorithms (Cormen et al.) and Algorithms (Papadimitriou et al.).

Support: https://www.patreon.com/reducible

This video wouldn't be possible without the open source manim library created by 3blue1brown: https://github.com/3b1b/manim

Here is link to the repository that contains the code used to generate the animations in this video: https://github.com/nipunramk/Reducible

Elegant proof that the matrix used in the proof that (d + 1) points uniquely define a degree d polynomial is invertible: https://math.stackexchange.com/questions/426932/why-are-vandermonde-matrices-invertible

Music:
Lift Motif by Kevin MacLeod is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/...)
Source: http://incompetech.com/music/royalty-...
Artist: http://incompetech.com/

All other music by Aakash Gandhi

SVG Attributions:
Earth: Designed by Flat Icons from www.flaticon.com, CC BY 4.0 https://creativecommons.org/licenses/by/4.0, via Wikimedia Commons
GPS: Icons made by https://www.flaticon.com/authors/pause08 from https://www.flaticon.com/
Wireless Comms: Design inspired by https://svgsilh.com/image/297434.html