▼ IMPORTANT ▼
In this video, in collaboration with @Math Rocks, we will talk about the Calor equation and who Jean-Baptiste Joseph Fourier was. We will talk about the space of integrable square functions, and how a function can be expressed as an infinite linear combination of sines and cosines (Fourier series), and we will even briefly mention other types of series (Bessel, Hermite, Legendre, Chebyshev, Laguerre , ...), we will solve the partial differential equation for heat in one dimension by means of a series of sines, in a half interval, and we will also mention other cases in which the heat equation can be solved (inhomogeneous conditions, isolated extremes, extreme radiating, inhomogeneous equation with heat source, two-dimensional equation, etc). Everything explained step by step.
Complete, step-by-step explanation of Fourier series, Fourier method, space of functions, internal product (point, interior) of functions, space of integrable square functions, etc.
#Fourier #EDP #Heat
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** BIBLIOGRAPHY **
- Advanced Mathematics for Engineering, by Peter V. O'Neil
- Introduction to Partial Differential Equations, by Peter J. Olver
- Equations in Partial Derivatives, by Richard Haberman
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