Joseph-Louis LagrangeJoseph-Louis Lagrange (born Giuseppe Luigi Lagrangia or Giuseppe Ludovico De la Grange Tournier; 25 January 1736 – 10 April 1813), also reported as Giuseppe Luigi Lagrange or Lagrangia, was an Italian and naturalized French mathematician, physicist and astronomer. He made significant contributions to the fields of analysis, number theory, and both classical and celestial mechanics.
Fourier seriesDecomposition of periodic functionsA Fourier series () is a series expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood. For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation.
Fourier analysisIn mathematics, the sciences, and engineering, Fourier analysis () is the study of the way general functions on the real line, circle, integers, finite cyclic group or general locally compact Abelian group may be represented or approximated by sums of trigonometric functions or more conveniently, complex exponentials.
Fourier transformMathematical transform that expresses a function of time as a function of frequencyThe Fourier transform applied to the waveform of a C majorpianochord (with logarithmic horizontal (frequency) axis). The first three peaks on the left correspond to the fundamental frequencies of the chord (C, E, G).
Harmonic analysisHarmonic analysis is an area of mathematical analysis that emerged from the study of harmonic functions, and especially their boundary behavior. The methods of harmonic analysis decompose functions and related objects, such as measures, into components based on symmetries, scales, spectra, or oscillation. It is also concerned with the analytic estimates for operators arising from such decompositions.
AuxerreAuxerre ( oh-SAIR, French: [osɛʁ] , Burgundian: Auchoirre) is the capital (prefecture) of the Yonne department and the fourth-largest city in the Burgundy historical region southeast of Paris. Auxerre's population today is about 35,000; the urban area (aire d'attraction) comprises roughly 111,000 inhabitants. Residents of Auxerre are referred to as Auxerrois. Auxerre is a commercial and industrial centre, with industries including food production, woodworking and batteries.
Greenhouse effectThe greenhouse effect occurs when heat-trapping gases in a planet's atmosphere prevent the planet from losing heat to space, raising its surface temperature. Surface heating can happen from an internal heat source (as in the case of Jupiter) or come from an external source, such as a host star. In the case of Earth, the Sun emits shortwave radiation (sunlight) that passes through greenhouse gases to heat the Earth's surface.
BurgundyBurgundy ( ; French: Bourgogne; Burgundian: Bregogne) is a historical region in France, broadly corresponding to the territory of the former administrative region of the same name, which existed from 1982 to 2015 before it was merged on 1 January 2016 into Bourgogne-Franche-Comté. Its capital is Dijon.
PhysicistA physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate causes of phenomena, and usually frame their understanding in mathematical terms.
Heat transferSimulation of thermal convection in the Earth's mantle. Colors span from red and green to blue with decreasing temperatures. A hot, less-dense lower boundary layer sends plumes of hot material upwards, and cold material from the top moves downwards.Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems.
VibrationIn mechanics, vibration (from Latin'to shake') is an oscillation of matter about an equilibrium point. Vibration may be deterministic if the oscillations can be characterised precisely (e.g. the periodic motion of a pendulum), or random if the oscillations can only be analysed statistically (e.g. the movement of a tire on a gravel road).
Thermal conductionIn thermodynamics, thermal conduction is the diffusion of thermal energy (heat) within one material or between materials in contact. The higher temperature object has molecules with more kinetic energy; collisions between molecules distribute this kinetic energy until an object has the same kinetic energy throughout. Thermal conductivity, represented by k, is a property that relates the rate of heat loss per unit area to its rate of change of temperature.*As an Amazon Associate I earn from qualifying purchases.