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Bernoulli's equation; Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy of equations; Bessel's differential equation; Boltzmann equation; Borda–Carnot equation; Burgers' equation; Darcy–Weisbach equation; Dirac equation. Dirac equation in the algebra of physical space; Dirac–Kähler equation; Doppler equations; Drake equation (aka ...
This equation states that , representing the square of the length of the side that is the hypotenuse, the side opposite the right angle, is equal to the sum (addition) of the squares of the other two sides whose lengths are represented by a and b. An equation is the claim that two expressions have the same value and are equal.
An example of using Newton–Raphson method to solve numerically the equation f(x) = 0. In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign.
A functional equation is an equation in which the unknowns are functions rather than simple quantities Equations involving derivatives, integrals and finite differences: A differential equation is a functional equation involving derivatives of the unknown functions, where the function and its derivatives are evaluated at the same point, such as ...
A square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes. From Gulley (2010).The n th coloured region shows n squares of dimension n by n (the rectangle is 1 evenly divided square), hence the area of the n th region is n times n × n.
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
Septic equations solvable by radicals have a Galois group which is either the cyclic group of order 7, or the dihedral group of order 14, or a metacyclic group of order 21 or 42. [1] The L(3, 2) Galois group (of order 168) is formed by the permutations of the 7 vertex labels which preserve the 7 "lines" in the Fano plane. [1]
Language equations with concatenation and Boolean operations were first studied by Parikh, Chandra, Halpern and Meyer [9] who proved that the satisfiability problem for a given equation is undecidable, and that if a system of language equations has a unique solution, then that solution is recursive.
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