Theorie analytique de la chaleur¶
Fourier, J. J. (1822). Theorie analytique de la chaleur.
Cited by¶
6 citations across 6 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Conjugate Variables
- or an integral transform kernel (e.g., Fourier pairing) in signal analysis
This sourceIntroduces Fourier series/integral decomposition of arbitrary functions into harmonic components; the foundational source for the time↔frequency (Fourier-conjugate) pairing invoked for signal analysis.
- or an integral transform kernel (e.g., Fourier pairing) in signal analysis
- Dimensional Analysis
- The practice traces to Fourier's systematic application of homogeneity to heat conduction equations
This sourceIntroduces the concept of dimensional homogeneity (an equation is correct only if dimensions match on both sides) alongside the heat equation; supports the claim that the practice of dimensional homogeneity traces to Fourier's heat-conduction work.
- The practice traces to Fourier's systematic application of homogeneity to heat conduction equations
- Duality
- … logical operations in one vocabulary (∧, ∀) translate mechanically to the other (∨, ∃) via De Morgan's laws, topological and algebraic categories (Boolean algebras ↔ Stone spaces, locally-compact groups ↔ character groups) pair up so that problems in one setting resolve via the other, and physics dualities (Fourier
This sourceIntroduces Fourier series and the decomposition of arbitrary functions into harmonic components; foundational for wave analysis and heat-diffusion theory; enables exact solution of linear PDEs via mode separation.
- … logical operations in one vocabulary (∧, ∀) translate mechanically to the other (∨, ∃) via De Morgan's laws, topological and algebraic categories (Boolean algebras ↔ Stone spaces, locally-compact groups ↔ character groups) pair up so that problems in one setting resolve via the other, and physics dualities (Fourier
- Gradient
- Integrability or flow relation (often): in physical systems, the gradient drives a flow of the associated conserved quantity down the gradient (Fourier's law for heat
This sourceIntroduces Fourier series and the decomposition of arbitrary functions into harmonic components; foundational for wave analysis and heat-diffusion theory; enables exact solution of linear PDEs via mode separation.
- Integrability or flow relation (often): in physical systems, the gradient drives a flow of the associated conserved quantity down the gradient (Fourier's law for heat
- Periodicity
- The toolkit includes Fourier decomposition (Fourier 1822
This sourceIntroduces Fourier series and the decomposition of arbitrary functions into harmonic components; foundational for wave analysis and heat-diffusion theory; enables exact solution of linear PDEs via mode separation.
- The toolkit includes Fourier decomposition (Fourier 1822
- Wave
- In the electromagnetic case, the disturbance is the transverse oscillation of
This sourceIntroduces Fourier series and the decomposition of arbitrary functions into harmonic components; foundational for wave analysis and heat-diffusion theory; enables exact solution of linear PDEs via mode separation.
- In the electromagnetic case, the disturbance is the transverse oscillation of
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Links previously used in the corpus¶
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