The Telegrapher's Equations ( or just Telegraph Equations ) are a pair of linear differential equations which describe the voltage and current on an electrical transmission line with distance and time.

The Persian mathematician, Sharaf al-Dīn al-Tūsī ( 1135 – 1213 ), was the first to discover the derivative of cubic polynomials, an important result in differential calculus ; his Treatise on Equations developed concepts related to differential calculus, such as the derivative function and the maxima and minima of curves, in order to solve cubic equations which may not have positive solutions.

Coulomb's law of electric forces was initially also formulated as instantaneous action at a distance, but was later superseded by Maxwell's Equations of electromagnetism which obey locality.

In the classical electrodynamics, light is considered as electromagnetic wave, which is governed by the Maxwell Equations.

In part III of " A Dynamical Theory of the Electromagnetic Field ", which is entitled " General Equations of the Electromagnetic Field ", Maxwell formulated twenty equations which were to become known as Maxwell's equations, until this term became applied instead to a set of four vectorized equations selected in 1884 by Oliver Heaviside, which had all appeared in " On physical lines of force ".

Vortex rings were first mathematically analysed by the German physicist Hermann von Helmholtz, in his 1867 paper On Integrals of the Hydrodynamical Equations which Express Vortex-motion.

Equations that include operators acting at different times, which hold in the interaction picture, don't necessarily hold in the Schrödinger or the Heisenberg picture.

Equations of terms, as used in logic programming, are considered a particular form of constraints which can be simplified using unification.

As in " The Cold Equations ", various measures are proposed but the only one which will not lead to worse disaster is for the unwitting passenger to be jettisoned.

In 1950 he published a paper " On the Formulation of Rheological Equations of State " which has been described as " probably the most important single paper in theoretical rheology " as it established the basic requirements for mathematical models of rheology.

Hendrik Antoon Lorentz Lorentz ( 1892a ) set the foundations of Lorentz aether theory, by assuming the existence of electrons which he separated from the aether, and by replacing the " Maxwell-Hertz " Equations by the " Maxwell-Lorentz " Equations.

Hidden Fields Equations ( HFE ) is a public key cryptosystem which was introduced at Eurocrypt in 1996 and proposed by Jacques Patarin following the idea of the Matsumoto and Imai system.

Equations of an involute curve for a parametrically defined function ( x ( t ), y ( t ) ) are:

* Algebraic Equations at EqWorld: The World of Mathematical Equations.

* Laplace Equation ( particular solutions and boundary value problems ) at EqWorld: The World of Mathematical Equations.

* Equations of the Straight Line at cut-the-knot

* Poisson Equation at EqWorld: The World of Mathematical Equations.

* Linear Klein – Gordon Equation at EqWorld: The World of Mathematical Equations.

* Nonlinear Klein – Gordon Equation at EqWorld: The World of Mathematical Equations.

* Tables of Integral Transforms at EqWorld: The World of Mathematical Equations.

* Riccati Equation at EqWorld: The World of Mathematical Equations.

* Arieh Iserles ( born 1947 ), computational mathematician, Professor of the Numerical Analysis of Differential Equations at the University of Cambridge

* Integral Equations at EqWorld: The World of Mathematical Equations.

* Functional Equations: Exact Solutions at EqWorld: The World of Mathematical Equations.

* Functional Equations: Index at EqWorld: The World of Mathematical Equations.

* Methods of Generalized and Functional Separation of Variables at EqWorld: The World of Mathematical Equations.

* Linear Partial Differential Equations: Exact Solutions and Boundary Value Problems at EqWorld: The World of Mathematical Equations.

* Integral Equations: Exact Solutions at EqWorld: The World of Mathematical Equations.

* Integral Equations: Index at EqWorld: The World of Mathematical Equations.

Equations should be balanced according to the stoichiometry, the number of atoms of each species should be the same on both sides of the equation.

The Learning Curve model posits that for each doubling of the total quantity of items produced, costs decrease by the same proportion, as described by Equations 1 and 2.

Equations included are the real and reactive power balance equations for each Load Bus and the real power balance equation for each Generator Bus.

This speed is usually a significant fraction of the speed of light, as can be deduced from Maxwell's Equations, and is therefore many times faster than the drift velocity of the electrons.

Equations often express relationships between given quantities, the knowns, and quantities yet to be determined, the unknowns.

Equations can be classified according to the types of operations and quantities involved.

This distinction usually makes PDEs much harder to solve than Ordinary Differential Equations ( ODEs ), but here again there will be simple solutions for linear problems.

Equations of motion can therefore be grouped under these main classifiers of motion.

Since the Otto cycle is an isentropic process the isentropic equations of ideal gases and the constant pressure / volume relations can be used to yield Equations 3 & 4.

Inverted pendulums can be created in various configurations resulting in a number of Equations of Motion describing the behavior of the pendulum.

In the final steps, two equalities will be used: ( 1 ) A Vector Analysis Equality, ( 2 ) One of Maxwell's Equations.

Equations with complex roots can be handled in the same way.

Equations and analytic relations such as integrals can be manipulated to relate the desired internal properties to the transformed data.

For the fields of general charge distributions, the retarded potentials can be computed and differentiated accordingly to yield Jefimenko's Equations.

Equations or systems too complex for closed-form or analytical solutions can often be analysed by mathematical modelling and computer simulation.

In 1999, Kipnis and Shamir showed that a particular public key algorithm — known as the Hidden Field Equations scheme ( HFE )— could be reduced to an overdetermined system of quadratic equations ( more equations than unknowns ).

Equations with a fourth degree polynomial on a side of the equation are proven to be the highest degree polynomial solvable using radicals.

where the functions and are respectively defined in Equations ( 1 ) and ( 2 ) below and are equivalent to the traditional definitions of sample mean and covariance ; however, they are not meant to be statistical estimates of characteristics of a population.

Equations are something that you will constantly be using throughout your math career.

Therefore the Right Hand Sides of Equations 1 and 2 are equal, so their Left Hand Sides must also be equal:

If angles BAD and DAC are unequal, Equations 1 and 2 can be re-written as:

They can also be used to approximate a wide range of Partial Differential Equations ( PDE ) such as heat dissipation and wave propagation.