# Glossari Aquest glossari és una mostra dels camps més representatius en què Jean Baptiste Joseph Fourier va treballar. Les definicions han estat extretes dels recursos següents:

#### Diffusion equation

The diffusion equation is a partial differential equation. In physics, it describes the behavior of the collective motion of micro-particles in a material resulting from the random movement of each micro-particle. In mathematics, it is applicable in common to a subject relevant to the Markov process as well as in various other fields, such as the materials sciences, information science, life science, social science, and so on. These subjects described by the diffusion equation are generally called Brown problems.

Citació: "Diffusion equation" A: Wikipedia. Wikimedia Foundation, 2011. [en línia]. [Consulta: 26 setembre 2019]. Disponible a: <https://en.wikipedia.org/wiki/Diffusion_equation>

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#### Digital image processing

In computer science, digital image processing is the use of computer algorithms to perform image processing on digital images. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing. It allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the build-up of noise and signal distortion during processing. Since images are defined over two dimensions (perhaps more) digital image processing may be modeled in the form of multidimensional systems.

Citació: "Digital image processing" A: Wikipedia. Wikimedia Foundation, 2011. [en línia]. [Consulta: 26 setembre 2019]. Disponible a: <https://en.wikipedia.org/wiki/Digital_image_processing>

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#### Fourier series

In mathematics, a Fourier series is a periodic function composed of harmonically related sinusoids, combined by a weighted summation. With appropriate weights, one cycle (or period) of the summation can be made to approximate an arbitrary function in that interval (or the entire function if it too is periodic). As such, the summation is a synthesis of another function. The discrete-time Fourier transform is an example of Fourier series. The process of deriving the weights that describe a given function is a form of Fourier analysis. For functions on unbounded intervals, the analysis and synthesis analogies are Fourier transform and inverse transform.

Citació: "Fourier series" A: Wikipedia. Wikimedia Foundation, 2011. [en línia]. [Consulta: 26 setembre 2019]. Disponible a: <https://en.wikipedia.org/wiki/Fourier_series>

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#### Fourier transform

The Fourier transform (FT) decomposes a function of time (a signal) into its constituent frequencies. This is similar to the way a musical chord can be expressed in terms of the volumes and frequencies of its constituent notes. The term Fourier transform refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of time. The Fourier transform of a function of time is itself a complex-valued function of frequency, whose magnitude (modulus) represents the amount of that frequency present in the original function, and whose argument is the phase offset of the basic sinusoid in that frequency. The Fourier transform is not limited to functions of time, but the domain of the original function is commonly referred to as the time domain. There is also an inverse Fourier transform that mathematically synthesizes the original function from its frequency domain representation.

Citació: "Fourier transform" A: Wikipedia. Wikimedia Foundation, 2011. [en línia]. [Consulta: 26 setembre 2019]. Disponible a: <https://en.wikipedia.org/wiki/Fourier_transform>

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#### Fourier's law

The law of heat conduction, also known as Fourier's law, states that the rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows. We can state this law in two equivalent forms: the integral form, in which we look at the amount of energy flowing into or out of a body as a whole, and the differential form, in which we look at the flow rates or fluxes of energy locally.

Newton's law of cooling is a discrete analogue of Fourier's law, while Ohm's law is the electrical analogue of Fourier's law.

Citació: "Thermal conduction. Fourier's law." A: Wikipedia. Wikimedia Foundation, 2011. [en línia]. [Consulta: 26 setembre 2019]. Disponible a: <https://en.wikipedia.org/wiki/Thermal_conduction#Fourier's_law>

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#### Greenhouse effect

The greenhouse effect is the process by which radiation from a planet's atmosphere warms the planet's surface to a temperature above what it would be without this atmosphere.

Radiatively active gases (i.e., greenhouse gases) in a planet's atmosphere radiate energy in all directions. Part of this radiation is directed towards the surface, warming it.The intensity of the downward radiation – that is, the strength of the greenhouse effect – will depend on the atmosphere's temperature and on the amount of greenhouse gases that the atmosphere contains.

Citació: "Greenhouse effect" A: Wikipedia. Wikimedia Foundation, 2011. [en línia]. [Consulta: 26 setembre 2019]. Disponible a: <https://en.wikipedia.org/wiki/Greenhouse_effect>

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#### Harmonic analysis or Fourier analysis

Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the 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.

Citació: "Harmonic analysis" A: Wikipedia. Wikimedia Foundation, 2011. [en línia]. [Consulta: 26 setembre 2019]. Disponible a: <https://en.wikipedia.org/wiki/Harmonic_analysis>

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#### Heat equation

In physics and mathematics, the heat equation is a partial differential equation that describes how the distribution of some quantity (such as heat) evolves over time in a solid medium, as it spontaneously flows from places where it is higher towards places where it is lower. It is a special case of the diffusion equation.

This equation was first developed and solved by Joseph Fourier in 1822 to describe heat flow. However, it is of fundamental importance in diverse scientific fields. In probability theory, the heat equation is connected with the study of random walks and Brownian motion, via the Fokker–Planck equation. In financial mathematics it is used to solve the Black–Scholes partial differential equation. A variant was also instrumental in the solution of the longstanding Poincaré conjecture of topology.

Citació: "Heat equation" A: Wikipedia. Wikimedia Foundation, 2011. [en línia]. [Consulta: 26 setembre 2019]. Disponible a: <https://en.wikipedia.org/wiki/Heat_equation>

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#### Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space).

Citació: "Mathematical analysis" A: Wikipedia. Wikimedia Foundation, 2011. [en línia]. [Consulta: 26 setembre 2019]. Disponible a: <https://en.wikipedia.org/wiki/Mathematical_analysis>

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#### Musical acoustics

Musical acoustics or music acoustics is a branch of acoustics concerned with researching and describing the physics of music – how sounds are employed to make music. Examples of areas of study are the function of musical instruments, the human voice (the physics of speech and singing), computer analysis of melody, and in the clinical use of music in music therapy.

Citació: "Musical acoustics" A: Wikipedia. Wikimedia Foundation, 2011. [en línia]. [Consulta: 26 setembre 2019]. Disponible a: <https://en.wikipedia.org/wiki/Musical_acoustics>

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#### Seismology

Seismology; from Ancient Greek σεισμός (seismós) meaning "earthquake" and -λογία (-logía) meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other planet-like bodies. The field also includes studies of earthquake environmental effects such as tsunamis as well as diverse seismic sources such as volcanic, tectonic, oceanic, atmospheric, and artificial processes such as explosions. A related field that uses geology to infer information regarding past earthquakes is paleoseismology. A recording of earth motion as a function of time is called a seismogram. A seismologist is a scientist who does research in seismology.

Citació: "Seismology" A: Wikipedia. Wikimedia Foundation, 2011. [en línia]. [Consulta: 26 setembre 2019]. Disponible a: <https://en.wikipedia.org/wiki/Seismology>

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#### Signal processing

Signal processing is an electrical engineering subfield that focuses on analysing, modifying and synthesizing signals such as sound, images and biological measurements. Signal processing techniques can be used to improve transmission, storage efficiency and subjective quality and to also emphasize or detect components of interest in a measured signal.

Citació: "Signal processing" A: Wikipedia. Wikimedia Foundation, 2011. [en línia]. [Consulta: 26 setembre 2019]. Disponible a: <https://en.wikipedia.org/wiki/Signal_processing>

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#### Thermal conduction

Thermal conduction is the transfer of heat internal energy by microscopic collisions of particles and movement of electrons within a body. The microscopically colliding particles, that include molecules, atoms and electrons, transfer disorganized microscopic kinetic and potential energy, jointly known as internal energy. Conduction takes place in all phases of including solids, liquids, gases and waves. The rate at which energy is conducted as heat between two bodies is a function of the temperature difference temperature gradient between the two bodies and the properties of the conductive interface through which the heat is transferred.

Heat spontaneously flows from a hotter 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 external driving energy source to the contrary, within a body or between bodies, temperature differences decay over time, and thermal equilibrium is approached, temperature becoming more uniform.

Citació: "Thermal conduction" A: Wikipedia. Wikimedia Foundation, 2011. [en línia]. [Consulta: 26 setembre 2019]. Disponible a: <https://en.wikipedia.org/wiki/Thermal_conduction>

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#### 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, 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 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 mechanical device in operation are typically unwanted. Such vibrations could be caused by imbalances in the rotating parts, uneven friction, or the meshing of gear teeth. Careful designs usually minimize unwanted vibrations.

Citació: "Vibration" A: Wikipedia. Wikimedia Foundation, 2011. [en línia]. [Consulta: 26 setembre 2019]. Disponible a: <https://en.wikipedia.org/wiki/Vibration>

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#### Wave equation

The wave equation is an important second-order linear partial differential equation for the description of waves—as they occur in classical physics—such as mechanical waves (e.g. water waves, sound waves and seismic waves) or light waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics.

Historically, the problem of a vibrating string such as that of a musical instrument was studied by Jean le Rond d'Alembert, Leonhard Euler, Daniel Bernoulli, and Joseph-Louis Lagrange. In 1746, d’Alembert discovered the one-dimensional wave equation, and within ten years Euler discovered the three-dimensional wave equation.

Citació: "Wave equation" A: Wikipedia. Wikimedia Foundation, 2011. [en línia]. [Consulta: 26 setembre 2019]. Disponible a: <https://en.wikipedia.org/wiki/Wave_equation>

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