James Clerk Maxwell was the first to obtain this relationship by his completion of Maxwell's equations with the addition of a displacement current term to Ampere's Circuital law.

In addition, James Clerk Maxwell ( 1865 ) recognized the electromagnetic nature of light and developed what are now called Maxwell's equations, but these equations were still interpreted as describing the motion of waves through an aether, whose state of motion was unknown.

The displacement current term is now seen as a crucial addition that completed Maxwell's equations and is necessary to explain many phenomena, most particularly the existence of electromagnetic waves.

The Celtics would go just 29-53 on the year, but the young Maxwell's potential, along with the promising addition of Bird and others, set the stage for what would become an NBA dynasty.

In addition, Oliver Heaviside and Hertz further developed the theory and introduced modernized versions of Maxwell's equations.

In addition, Harry Bateman and Ebenezer Cunningham ( 1910 ) showed that Maxwell's equations are invariant under a much wider group of transformation than the Lorentz-group, i. e., the so called " conformal transformations ".

The paper is based on James Clerk Maxwell's and Heinrich Rudolf Hertz's investigations and, in addition, the axioms of relativity, as Einstein states,

In addition, there are also equations of state describing solids, including the transition of solids from one crystalline state to another.

In addition to the mass, momentum, and energy conservation equations, a thermodynamical equation of state giving the pressure as a function of other thermodynamic variables for the fluid is required to completely specify the problem.

In addition, the method computes a slowly changing amplitude to satisfy other constraints of the equations or of the physical system, such as for conservation of energy in the wave.

This is inconvenient ; the list of group properties can be simplified to universally quantified equations if we add a nullary operation e and a unary operation ~ in addition to the binary operation *, then list the axioms for these three operations as follows:

In addition to the standard two-dimensional function plots, it can also produce graphs of parametric equations, polar equations, sequence plots, differential equation fields, and three-dimensional ( two independent variable ) functions.

In addition to Hawking's notable abstention from presenting equations, the book also simplifies matters by means of illustrations throughout the text, depicting complex models and diagrams.

POV-Ray, in addition to standard geometric shapes like tori, spheres and heightfields, supports mathematically defined primitives such as the isosurface ( a finite approximation of an arbitrary function ), the polynomial primitive ( an infinite object defined by a 15th order or lower polynomial ), the julia fractal ( a 3-dimensional slice of a 4-dimensional fractal ), the superquadratic ellipsoid ( intermediate between a sphere and a cube ), and the parametric primitive ( using equations that represent its surface, rather than its interior ).

With the addition of the three compatibility equations the number of independent equations is reduced to three, matching the number of unknown displacement components.

In addition, severe instabilities caused by the formation of local shock waves and the existence of both subsonic and supersonic flow ( which behave completely differently ) makes the solution of the governing equations rather difficult.

In addition to a black hole region in the future, such a solution of the Einstein field equations has a white hole region in its past.

Some textbooks refer to the elimination method as the addition method, since it involves adding equations ( or constant multiples of the said equations ) to one another, as detailed later in this article.

In addition, some methods in numerical partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be solved.

In addition to the wide range of length and time scales and the associated computational cost, the governing equations of fluid dynamics contain a non-linear convection term and a non-linear and non-local pressure gradient term.

With the addition theorems above and for a given k with 0 < k < 1 they therefore are solutions to the following nonlinear ordinary differential equations:

In addition to these works, he has written a recognised introduction to multivariate complex analysis based on his 1964 Stanford lectures, and wrote the entries on differential equations in Nationalencyklopedin.

In addition to working on mathematical topics as diverse as differential equations and the gamma function, Lindelöf actively promoted the study of the history of Finnish mathematics.

Shortly after this study ended septic conditions resulted which required the addition of sodium nitrate.

It appears that an Orthodox girl in the community disrupted plans for an outing sponsored by one of the Jewish service groups because she would not travel on Saturday and, in addition, required kosher food.

For example, if the numbers involved in a computation may be arbitrarily large, the time required by a single addition can no longer be assumed to be constant.

In addition, the carbon dioxide generated in the production and transportation of the food required by the bicyclist, per mile traveled, is less than 1 / 10 that generated by energy efficient cars.

The remaining parts of the number usually provide information required for that instruction, such as operands for an addition operation.

In addition, due to the development of body armor, support personnel required a compact weapon with more penetration than the traditional submachine gun, leading to the development of the personal defense weapon, or PDW, which uses rounds that have better ballistics than simple pistol rounds but less power and range than full rifle rounds.

The story thus symbolically reflects the way in which life is brought forth through the addition of water to the land, and once it grows, water is required to bring plants to fruit.

In addition to the between-the-legs requirement noted above, for several years after the adoption of the hand snap, a hand-to-hand snap was illegal, the ball required to be thrown instead, in Canadian football.

In addition, they are required to maintain certain books and records and have their practices examined by SEC staff.

However, in October 1549, he was again required to preach twice on Sundays and, in addition, every weekday of alternate weeks.

In addition, the planned economy of Soviet Bolshevism required the collectivization of farms and land to allow industrialization or conversion to large-scale agricultural production.

The level of formal education required varies from country to country, from a simple training certificate awarded by an employer, to a full Diploma from an Engineering College ( such as in Australia ) in addition to time spent working as an apprentice.

In addition to fixed capital, each enterprise is allocated a minimum of working capital from the state through the Central Bank and is required to meet various operating expenses with the proceeds from sales of its output.

In addition to the features required by the core API, GPU vendors may provide additional functionality in the form of extensions.

However, Principia Mathematica required, in addition to the basic axioms of type theory, three further axioms that seemed to not be true as mere matters of logic, namely the axiom of infinity, the axiom of choice, and the axiom of reducibility.

The addition of the C6 fluorine atom has since been demonstrated to not be required for the antibacterial activity of this class ( circa 1997 ).

Type I restriction enzymes possess three subunits called HsdR, HsdM, and HsdS ; HsdR is required for restriction ; HsdM is necessary for adding methyl groups to host DNA ( methyltransferase activity ) and HsdS is important for specificity of the recognition ( DNA-binding ) site in addition to both restriction ( DNA cleavage ) and modification ( DNA methyltransferase ) activity.

In addition, FEV has been shown to be required for correct maternal behaviour in mice, such that their offspring do not survive unless cross-fostered to other wild-type female mice.

Finally, the temperature gets high enough that any nucleus can be partially broken down, most commonly releasing an alpha particle ( helium nucleus ) which immediately fuses with another nucleus, so that several nuclei are effectively rearranged into a smaller number of heavier nuclei, with net release of energy because the addition of fragments to nuclei exceeds the energy required to break them off the parent nuclei.

Once the nucleosynthesis process arrives at iron-56, the continuation of this process consumes energy ( the addition of fragments to nuclei releases less energy than required to break them off the parent nuclei ).

This definition is relatively modern, generalizing the classical definition of Steiner systems which in addition required that k = t + 1.

In addition, a number of proteins including U2AF and SF1 are required for the assembly of the spliceosome.

In addition, nearly all tanks containing oil or other hazardous chemicals are required to have containment barriers set up around them to contain 100 % of the volume of the tank in the event of a catastrophic tank failure.