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Because symmetries of differential equations are essential to both physics and mathematics, the theory of special functions is closely related to the theory of Lie groups and Lie algebras, as well as certain topics in mathematical physics. Symbolic computation engines usually recognize the majority of special functions.
The h-calculus is the calculus of finite differences, which was studied by George Boole and others, and has proven useful in combinatorics and fluid mechanics. In a sense, q -calculus dates back to Leonhard Euler and Carl Gustav Jacobi , but has only recently begun to find usefulness in quantum mechanics , given its intimate connection with ...
Certain parts of mathematics that initially arose from the development of physics are not, in fact, considered parts of mathematical physics, while other closely related fields are. For example, ordinary differential equations and symplectic geometry are generally viewed as purely mathematical disciplines, whereas dynamical systems and ...
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. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.
Tensor calculus has many applications in physics, engineering and computer science including elasticity, continuum mechanics, electromagnetism (see mathematical descriptions of the electromagnetic field), general relativity (see mathematics of general relativity), quantum field theory, and machine learning.
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, . [1] 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.
C.G. Gray, G. Karl, and V. A. Novikov, "Progress in Classical and Quantum Variational Principles". 11 December 2003. physics/0312071 Classical Physics. Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 0-13-805326-X. John Venables, "The Variational Principle and some applications". Dept of Physics and ...
Discrete integral calculus is the study of the definitions, properties, and applications of the Riemann sums. The process of finding the value of a sum is called integration. In technical language, integral calculus studies a certain linear operator.