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.
Supported in partVerified against the publisher's abstract
Fourier's 1822 abstract establishes the Fourier series for heat, the historical root of Fourier analysis, but not integral transform kernels or signal analysis.
“proposed that an infinite mathematical series may be used to analyse the conduction of heat in solids: this is now known as the 'Fourier Series'.”
- 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.
Supported in partVerified against the publisher's abstract
Publisher abstract identifies Fourier's 1822 study as the mathematical treatment of heat diffusion and the Fourier series, but says nothing about dimensional homogeneity.
“Fourier set out to study the mathematical laws governing heat diffusion and proposed that an infinite mathematical series may be used to analyse the conduction of heat in solids: this is now known as the 'Fourier Series'.”
- 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
Verification¶
Does it exist? Not checked yet. This entry carries no identifier to resolve. It was extracted from the citation as written in the article, normalized, and deduplicated against the rest of the registry.
Does it back the claim? Read against the text for 2 of 6 citations: 2 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Links previously used in the corpus¶
Before the registry existed this work was also linked 1 other way.
Registry ID ref:76b1a431a922 · see in the full table