Did you know the same equation is used to predict the heat dispersion in a material and predict a financial stock's value in the future?
Why? Because the movement of particles and the human mind can be treated mathematically identically.
Watch the video to see why.
I hope you learn something new and enjoy it! =]
The video was made using Canva Video Editor, and all images, icons, and designs are either mine or those of Canva Stock Footage. The same applies to sound effects.
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References for information:
Cochrane, R. (2016). The Secret Life of Equations. Hachette UK, pp.70-73, 80-83.
Chasnov, J.R. (2021). 9.1: Derivation of the Diffusion Equation. [online] Mathematics LibreTexts. Available at: math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_(Chasnov)/09%3A_Partial_Differential_Equations/9.01%3A_Derivation_of_the_Diffusion_Equation [Accessed 7 Jun. 2024].
Joyner, C. (2016). Black-Scholes Equation and Heat Equation. [online] Georgia Southern University. Available at: digitalcommons.georgiasouthern.edu/cgi/viewcontent.cgi?article=1247&context=honors-theses [Accessed 12 Jun. 2024].
Lecture #26, 27: Solving the Black-Scholes Partial Differential Equation. (n.d.). Available at: uregina.ca/~kozdron/Teaching/Regina/441Fall14/Notes/L26-27-Nov5.pdf [Accessed 16 Jun. 2024].
olaker ♦. (2011). Transformation from the Black-Scholes differential equation to the diffusion equation - and back. [online] Quantitative Finance Stack Exchange. Available at: quant.stackexchange.com/questions/84/transformation-from-the-black-scholes-differential-equation-to-the-diffusion-equ [Accessed 22 Jun. 2024].
quantpie (2019). Diffusion Equation - Derivation and Explanation using Brownian. [online] TH-cam. Available at: th-cam.com/video/P9qar8mv3Tk/w-d-xo.html [Accessed 7 Jun. 2024].
quantpie (2019). Transformation of Black Scholes PDE to Heat Equation. TH-cam. Available at: th-cam.com/video/IgMoOcO095U/w-d-xo.html [Accessed 16 Jun. 2024].
StudySmarter UK (n.d.). Diffusion Equation: Meaning & Application | StudySmarter. [online] StudySmarter UK. Available at: www.studysmarter.co.uk/explanations/engineering/engineering-thermodynamics/diffusion-equation/#:~:text=The%20diffusion%20equation%20plays%20a [Accessed 7 Jun. 2024].
The Diffusion Equation. (n.d.). Available at: www.uni-muenster.de/imperia/md/content/physik_tp/lectures/ws2016-2017/num_methods_i/heat.pdf [Accessed 7 Jun. 2024].
Veritasium (2024). The Trillion Dollar Equation. TH-cam. Available at: th-cam.com/video/A5w-dEgIU1M/w-d-xo.html [Accessed 12 Jun. 2024].
Yun, T. (2011). Instant Diffusion Equation of Price Changing and Time-Space Exchanging Description. Technology and Investment, 02(02), pp.124-128. doi:doi.org/10.4236/ti.2011.22012 [Accessed 12 Jun. 2024].