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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 ...
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 ...
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.
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 ...
Surface integrals have applications in physics, particularly in the classical theories of electromagnetism and fluid mechanics. An illustration of a single surface element. These elements are made infinitesimally small, by the limiting process, so as to approximate the surface.
An example of a solenoidal vector field, (,) = (,) In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field) is a vector field v with divergence zero at all points in the field: =