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An Essay On The Application Of Mathematical Analysis To The Theories Of Electricity And Magnetism
''An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism'' is a fundamental publication by George Green in 1828, where he extends previous work of Siméon Denis Poisson on electricity and magnetism. The work in mathematical analysis, notably including what is now universally known as Green's theorem, is of the greatest importance in all branches of mathematical physics. It contains the first exposition of the theory of potential. In physics, Green's theorem is mostly used to solve two-dimensional flow integrals, stating that the sum of fluid outflows at any point inside a volume is equal to the total outflow summed about an enclosing area. In plane geometry, and in particular, area surveying, Green's theorem can be used to determine the area and centroid of plane figures solely by integrating over the perimeter. It is in this essay that the term ' potential function' first occurs. Herein also his remarkable theorem in pure mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potential Function (other) of amortized analysis, a function describing an investment of resources by past operations that can be used by future operations
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The term potential function may refer to: * A mathematical function whose values are a physical potential * The class of functions known as harmonic functions, which are the topic of study in potential theory * The potential function of a potential game * In the potential method In computational complexity theory, the potential method is a method used to analyze the amortized time and space complexity of a data structure, a measure of its performance over sequences of operations that smooths out the cost of infrequent but ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to Numerical methods for partial differential equations, numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematics, pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Calculus
Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3. The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration. Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields, and fluid flow. Vector calculus was developed from quaternion analysis by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century, and most of the notation and terminology was established by Gibbs and Edwin Bidwell Wilson in their 1901 book, ''Vector Analysis''. In the conventional form using cross products, vector calculus does not generalize to higher dimensions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (mathematics), series, and analytic functions. These theories are usually studied in the context of Real number, real and Complex number, complex numbers and Function (mathematics), 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 (mathematics), space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). History Ancient Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Faraday
Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic induction, diamagnetism and electrolysis. Although Faraday received little formal education, he was one of the most influential scientists in history. It was by his research on the magnetic field around a conductor carrying a direct current that Faraday established the concept of the electromagnetic field in physics. Faraday also established that magnetism could affect rays of light and that there was an underlying relationship between the two phenomena.. the 1911 Encyclopædia Britannica. He similarly discovered the principles of electromagnetic induction, diamagnetism, and the laws of electrolysis. His inventions of electromagnetic rotary devices formed the foundation of electric motor technology, and it was largely due to his efforts t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leyden Jar
A Leyden jar (or Leiden jar, or archaically, sometimes Kleistian jar) is an electrical component that stores a high-voltage electric charge (from an external source) between electrical conductors on the inside and outside of a glass jar. It typically consists of a glass jar with metal foil cemented to the inside and the outside surfaces, and a metal terminal projecting vertically through the jar lid to make contact with the inner foil. It was the original form of capacitor (also called a ''condenser''). Its invention was a discovery made independently by German cleric Ewald Georg von Kleist on 11 October 1745 and by Dutch scientist Pieter van Musschenbroek of Leiden (Leyden), Netherlands in 1745–1746. The Leyden jar was used to conduct many early experiments in electricity, and its discovery was of fundamental importance in the study of electrostatics. It was the first means of accumulating and preserving electric charge in large quantities that could be discharged at the exp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A History Of The Theories Of Aether And Electricity
''A History of the Theories of Aether and Electricity'' is any of three books written by British mathematician Sir Edmund Taylor Whittaker FRS FRSE on the history of electromagnetic theory, covering the development of classical electromagnetism, optics, and aether theories. The book's first edition, subtitled ''from the Age of Descartes to the Close of the Nineteenth Century'', was published in 1910 by Longmans, Green. The book covers the history of aether theories and the development of electromagnetic theory up to the 20th century. A second, extended and revised, edition consisting of two volumes was released in the early 1950s by Thomas Nelson, expanding the book's scope to include the first quarter of the 20th century. The first volume, subtitled ''The Classical Theories'', was published in 1951 and served as a revised and updated edition to the first book. The second volume, subtitled ''The Modern Theories (1900–1926)'', was published two years later in 1953, extended ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician, mathematical physicist and engineer born in Belfast. Professor of Natural Philosophy at the University of Glasgow for 53 years, he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging discipline of physics in its contemporary form. He received the Royal Society's Copley Medal in 1883, was its president 1890–1895, and in 1892 was the first British scientist to be elevated to the House of Lords. Absolute temperatures are stated in units of kelvin in his honour. While the existence of a coldest possible temperature ( absolute zero) was known prior to his work, Kelvin is known for determining its correct value as approximately −273.15 degrees Celsius or −459.67 degrees Fahrenheit. The Joule–Thomson effect is also named in his honour. He worked closely with mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and light as different manifestations of the same phenomenon. Maxwell's equations for electromagnetism have been called the " second great unification in physics" where the first one had been realised by Isaac Newton. With the publication of "A Dynamical Theory of the Electromagnetic Field" in 1865, Maxwell demonstrated that electric and magnetic fields travel through space as waves moving at the speed of light. He proposed that light is an undulation in the same medium that is the cause of electric and magnetic phenomena. (This article accompanied an 8 December 1864 presentation by Maxwell to the Royal Society. His statement that "light and magnetism are affections of the same substance" is at page 499.) The unification of light and electrical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lord Kelvin
William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician, Mathematical physics, mathematical physicist and engineer born in Belfast. Professor of Natural Philosophy (Glasgow), Professor of Natural Philosophy at the University of Glasgow for 53 years, he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging discipline of physics in its contemporary form. He received the Royal Society's Copley Medal in 1883, was its President of the Royal Society, president 1890–1895, and in 1892 was the first British scientist to be elevated to the House of Lords. Absolute temperatures are stated in units of kelvin in his honour. While the existence of a coldest possible temperature (absolute zero) was known prior to his work, Kelvin is known for determining its correct value as approximately −273.15 degrees Celsius or −459.67 degrees Fahrenheit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge Philosophical Society
The Cambridge Philosophical Society (CPS) is a scientific society at the University of Cambridge. It was founded in 1819. The name derives from the medieval use of the word philosophy to denote any research undertaken outside the fields of law, theology and medicine. The society was granted a royal charter by King William IV in 1832. The society is governed by an elected council of senior academics, which is chaired by the Society's President, according to a set of statutes. The society has published several scientific journals, including ''Biological Reviews'' (established 1926) and ''Mathematical Proceedings of the Cambridge Philosophical Society'' (formerly entitled ''Proceedings of the Cambridge Philosophical Society'', published since 1843). ''Transactions of the Cambridge Philosophical Society'' was published between 1821–1928, but was then discontinued. History The society was founded in 1819 by Edward Clarke, Adam Sedgwick and John Stevens Henslow, and is Cambri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
