|
Jean-Baptiste Joseph Fourier
Jean-Baptiste Joseph Fourier (; ; 21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and vibrations. The Fourier transform and Fourier's law of conduction are also named in his honour. Fourier is also generally credited with the discovery of the greenhouse effect. Biography Fourier was born at Auxerre (now in the Yonne département of France), the son of a tailor. He was orphaned at the age of nine. Fourier was recommended to the Bishop of Auxerre and, through this introduction, he was educated by the Benedictine Order of the Convent of St. Mark. The commissions in the scientific corps of the army were reserved for those of good birth, and being thus ineligible, he accepted a military lectureship on mathematics. He took a prominent part in his own di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Auxerre
Auxerre ( , ) is the capital of the Yonne department and the fourth-largest city in Burgundy. Auxerre's population today is about 35,000; the urban area (''aire d'attraction'') comprises roughly 113,000 inhabitants. Residents of Auxerre are referred to as ''Auxerrois''. Auxerre is a commercial and industrial centre, with industries including food production, woodworking and batteries. It is also noted for its production of Burgundy wine, including Chablis. In 1995 Auxerre was named "Town of Art and History". Geography Auxerre lies on the river Yonne and the Canal du Nivernais, about 150 km southeast of Paris and 120 km northwest of Dijon. The A6 autoroute (Paris–Lyon) passes northeast of the city. Auxerre-Saint-Gervais station has rail connections to Dijon, Paris, Corbigny and Avallon. History Auxerre was a flourishing Gallo-Roman centre, then called Autissiodorum, through which passed one of the main roads of the area, the Via Agrippa (1st century AD) which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Things Named After Joseph Fourier
This is a list of things named after Joseph Fourier: Mathematics *Budan–Fourier theorem, see Budan's theorem * Fourier's theorem *Fourier–Motzkin elimination * Fourier algebra *Fourier division * Fourier method Analysis *Fourier analysis *Fourier series **Fourier–Bessel series **Fourier sine and cosine series **Generalized Fourier series **Laplace–Fourier series, see Laplace series ** Fourier–Legendre series *Fourier transform (List of Fourier-related transforms): ***Discrete-time Fourier transform (DTFT), the reverse of the Fourier series, a special case of the Z-transform around the unit circle in the complex plane ***Discrete Fourier transform (DFT), occasionally called the finite Fourier transform, the Fourier transform of a discrete periodic sequence (yielding discrete periodic frequencies), which can also be thought of as the DTFT of a finite-length sequence evaluated at discrete frequencies *** Fast Fourier transform (FFT), a fast algorithm for computing a Discr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal Conduction
Conduction is the process by which heat is transferred from the hotter end to the colder end of an object. The ability of the object to conduct heat is known as its ''thermal conductivity'', and is denoted . Heat spontaneously flows along a temperature gradient (i.e. from a hotter body to a colder body). For example, heat is conducted from the hotplate of an electric stove to the bottom of a saucepan in contact with it. In the absence of an opposing external driving energy source, within a body or between bodies, temperature differences decay over time, and thermal equilibrium is approached, temperature becoming more uniform. In conduction, the heat flow is within and through the body itself. In contrast, in heat transfer by thermal radiation, the transfer is often between bodies, which may be separated spatially. Heat can also be transferred by a combination of conduction and radiation. In solids, conduction is mediated by the combination of vibrations and collisions of molecul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vibration
Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic function, periodic, such as the motion of a pendulum—or random, such as the movement of a tire on a gravel road. Vibration can be desirable: for example, the motion of a tuning fork, the Reed (music), reed in a woodwind instrument or harmonica, a mobile phone, or the cone of a loudspeaker. In many cases, however, vibration is undesirable, wasting energy and creating unwanted sound. For example, the vibrational motions of engines, electric motors, or any Machine, mechanical device in operation are typically unwanted. Such vibrations could be caused by Engine balance, imbalances in the rotating parts, uneven friction, or the meshing of gear teeth. Careful designs usually minimize unwanted vibrations. The studies of sound and vibration are closely related. Sound, or pressure waves, are ge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heat Transfer
Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, Convection (heat transfer), thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species (mass transfer in the form of advection), either cold or hot, to achieve heat transfer. While these mechanisms have distinct characteristics, they often occur simultaneously in the same system. Heat conduction, also called diffusion, is the direct microscopic exchanges of kinetic energy of particles (such as molecules) or quasiparticles (such as lattice waves) through the boundary between two systems. When an object is at a different temperature from another body or its surroundings, heat flows so that the body and the surroundings reach the same temperature, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Analysis
Harmonic analysis is a branch of mathematics concerned with the representation of Function (mathematics), functions or signals as the Superposition principle, superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an extended form of Fourier analysis). In the past two centuries, it has become a vast subject with applications in areas as diverse as number theory, representation theory, signal processing, quantum mechanics, tidal analysis and neuroscience. The term "harmonics" originated as the Ancient Greek word ''harmonikos'', meaning "skilled in music". In physical eigenvalue problems, it began to mean waves whose frequencies are Multiple (mathematics), integer multiples of one another, as are the frequencies of the Harmonic series (music), harmonics of music notes, but the term has been generalized beyond its original meaning. The classical Fourier transform on R''n'' is still an area of ongoing research, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Analysis
In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. For example, determining what component frequencies are present in a musical note would involve computing the Fourier transform of a sampled musical note. One could then re-synthesize the same sound by including the frequency components as revealed in the Fourier analysis. In mathematics, the term ''Fourier ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French People
The French people (french: Français) are an ethnic group and nation primarily located in Western Europe that share a common French culture, history, and language, identified with the country of France. The French people, especially the native speakers of langues d'oïl from northern and central France, are primarily the descendants of Gauls (including the Belgae) and Romans (or Gallo-Romans, western European Celtic and Italic peoples), as well as Germanic peoples such as the Franks, the Visigoths, the Suebi and the Burgundians who settled in Gaul from east of the Rhine after the fall of the Roman Empire, as well as various later waves of lower-level irregular migration that have continued to the present day. The Norse also settled in Normandy in the 10th century and contributed significantly to the ancestry of the Normans. Furthermore, regional ethnic minorities also exist within France that have distinct lineages, languages and cultures such as Bretons in Brittany, Occi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greenhouse Effect
The greenhouse effect is a process that occurs when energy from a planet's host star goes through the planet's atmosphere and heats the planet's surface, but greenhouse gases in the atmosphere prevent some of the heat from returning directly to space, resulting in a warmer planet. Earth's natural greenhouse effect makes life as we know it possible and carbon dioxide plays a significant role in providing for the relatively high temperature on Earth. The greenhouse effect is a process by which thermal radiation from a planetary atmosphere warms the planet's surface beyond the temperature it would have in the absence of its atmosphere.A concise description of the greenhouse effect is given in the ''Intergovernmental Panel on Climate Change Fourth Assessment Report,'' "What is the Greenhouse Effect?FAQ 1.3 – AR4 WGI Chapter 1: Historical Overview of Climate Change Science, IPCC Fourth Assessment Report, Chapter 1, p. 115: "To balance the absorbed incoming olarenergy, the Earth m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier–Motzkin Elimination
Fourier–Motzkin elimination, also known as the FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities. It can output real solutions. The algorithm is named after Joseph Fourier who proposed the method in 1826 and Theodore Motzkin who re-discovered it in 1936. Elimination The elimination of a set of variables, say ''V'', from a system of relations (here linear inequalities) refers to the creation of another system of the same sort, but without the variables in ''V'', such that both systems have the same solutions over the remaining variables. If all variables are eliminated from a system of linear inequalities, then one obtains a system of constant inequalities. It is then trivial to decide whether the resulting system is true or false. It is true if and only if the original system has solutions. As a consequence, elimination of all variables can be used to detect whether a system of inequalities has solutions or not. Consider a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heat Conduction
Conduction is the process by which heat is transferred from the hotter end to the colder end of an object. The ability of the object to conduct heat is known as its ''thermal conductivity'', and is denoted . Heat spontaneously flows along a temperature gradient (i.e. from a hotter body to a colder body). For example, heat is conducted from the hotplate of an electric stove to the bottom of a saucepan in contact with it. In the absence of an opposing external driving energy source, within a body or between bodies, temperature differences decay over time, and thermal equilibrium is approached, temperature becoming more uniform. In conduction, the heat flow is within and through the body itself. In contrast, in heat transfer by thermal radiation, the transfer is often between bodies, which may be separated spatially. Heat can also be transferred by a combination of conduction and radiation. In solids, conduction is mediated by the combination of vibrations and collisions of molecu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.jpg "Click for more on -> Jean-Baptiste Joseph Fourier")
.png "Click for more on -> Harmonic Analysis")
