Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering.
The number e is a mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function. It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted . Alternatively, e can be called Napier's constant after John Napier. The Swiss mathematician Jacob Bernoulli discovered the constant while studying compound interest.
Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions.
In astrophysics, the Eddington number, NEdd, is the number of protons in the observable universe. Eddington originally calculated it as about 1.57×1079; current estimates make it approximately 1080.
Sir Edmund Taylor Whittaker was a British mathematician, physicist, and historian of science. Whittaker was a leading mathematical scholar of the early 20th century who contributed widely to applied mathematics and was renowned for his research in mathematical physics and numerical analysis, including the theory of special functions, along with his contributions to astronomy, celestial mechanics, the history of physics, and digital signal processing.
George Neville Watson was an English mathematician, who applied complex analysis to the theory of special functions. His collaboration on the 1915 second edition of E. T. Whittaker's A Course of Modern Analysis (1902) produced the classic "Whittaker and Watson" text. In 1918 he proved a significant result known as Watson's lemma, that has many applications in the theory on the asymptotic behaviour of exponential integrals.
Abramowitz and Stegun (AS) is the informal name of a 1964 mathematical reference work edited by Milton Abramowitz and Irene Stegun of the United States National Bureau of Standards (NBS), now the National Institute of Standards and Technology (NIST). Its full title is Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. A digital successor to the Handbook was released as the "Digital Library of Mathematical Functions" (DLMF) on 11 May 2010, along with a printed version, the NIST Handbook of Mathematical Functions, published by Cambridge University Press.
In mathematical analysis, a domain or region is a non-empty, connected, and open set in a topological space. In particular, it is any non-empty connected open subset of the real coordinate space Rn or the complex coordinate space Cn. A connected open subset of coordinate space is frequently used for the domain of a function.
Alan Baker was an English mathematician, known for his work on effective methods in number theory, in particular those arising from transcendental number theory.
Mathematical diagrams, such as charts and graphs, are mainly designed to convey mathematical relationships—for example, comparisons over time.
Introductio in analysin infinitorum is a two-volume work by Leonhard Euler which lays the foundations of mathematical analysis. Written in Latin and published in 1748, the Introductio contains 18 chapters in the first part and 22 chapters in the second. It has Eneström numbers E101 and E102.
Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications.
John Charles Burkill was an English mathematician who worked on analysis and introduced the Burkill integral.
Adrian William Moore is a British philosopher and broadcaster. He is Professor of Philosophy at the University of Oxford and tutorial fellow of St Hugh's College, Oxford. His main areas of interest are Kant, Wittgenstein, history of philosophy, metaphysics, philosophy of mathematics, philosophy of logic and language, ethics and philosophy of religion.
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 this work covering the years 1900 to 1926. Notwithstanding a notorious controversy on Whittaker's views on the history of special relativity, covered in volume two of the second edition, the books are considered authoritative references on the history of electricity and magnetism as well as classics in the history of physics.
A Treatise on the Analytical Dynamics of Particles and Rigid Bodies is a treatise and textbook on analytical dynamics by British mathematician Sir Edmund Taylor Whittaker. Initially published in 1904 by the Cambridge University Press, the book focuses heavily on the three-body problem and has since gone through four editions and has been translated to German and Russian. Considered a landmark book in English mathematics and physics, the treatise presented what was the state-of-the-art at the time of publication and, remaining in print for more than a hundred years, it is considered a classic textbook in the subject. In addition to the original editions published in 1904, 1917, 1927, and 1937, a reprint of the fourth edition was released in 1989 with a new foreword by William Hunter McCrea.
Sir Edmund Taylor Whittaker was a British mathematician, physicist, historian of science, and philosopher who authored three titles that remain in circulation over a century after their initial publications. His bibliography includes several books and over one hundred published papers on a variety of subjects, including mathematics, astronomy, mathematical physics, theoretical physics, philosophy, and theism. Whittaker's bibliography in the Biographical Memoirs of Fellows of the Royal Society categorises his publications into three categories: books and monographs, maths and physics articles, and biographical articles; the bibliography excludes works published in popular magazines like Scientific American. The bibliography includes eleven total books and monographs, fifty-six maths and physics articles, thirty-five philosophy and history articles, and twenty-one biographical articles. In the bibliography compiled by William Hunter McCrea in 1957, there are thirteen books and monographs and the same journal articles; McCrea counts all three volumes of A History of the Theories of Aether and Electricity as separate books and excludes the same papers. Whittaker's contributions to Scientific American include two book reviews and a popular article on mathematics.
Douglas Arthur Quadling (1926–2015) was an English mathematician, school master and educationalist who was one of the four drivers behind the School Mathematics Project (SMP) in the 1960s and 70s.
Victor Hugo Moll is a Chilean American mathematician specializing in calculus.
