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In mathematics, the method of dominant balance approximates the solution to an equation by solving a simplified form of the equation containing 2 or more of the equation's terms that most influence (dominate) the solution and excluding terms contributing only small modifications to this approximate solution.
Harmonic balance is a method used to calculate the steady-state response of nonlinear differential equations, [1] and is mostly applied to nonlinear electrical circuits. [2] [3] [4] It is a frequency domain method for calculating the steady state, as opposed to the various time-domain steady-state methods. The name "harmonic balance" is ...
The barycenter is the point between two objects where they balance each other; it is the center of mass where two or more celestial bodies orbit each other. When a moon orbits a planet, or a planet orbits a star, both bodies are actually orbiting a point that lies away from the center of the primary (larger) body. [25]
The concept is the same as for a large mass balance, but it is performed in the context of a limiting system (for example, one can consider the limiting case in time or, more commonly, volume). A differential mass balance is used to generate differential equations that can provide an effective tool for modelling and understanding the target system.
y-cruncher is a computer program for the calculation of some mathematical constant with theoretical accuracy (limited only by computing time and available storage space). It was originally developed to calculate the Euler-Mascheroni constant γ {\displaystyle \gamma } ; the y is derived from it in the name.
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Sverdrup balance may be thought of as a consistency relationship for flow which is dominated by the Earth's rotation. Such flow will be characterized by weak rates of spin compared to that of the earth. Any parcel at rest with respect to the surface of the earth must match the spin of the earth underneath it.
In physics and engineering contexts, especially in the context of diffusion through a medium, it is more common to fix a Cartesian coordinate system and then to consider the specific case of a function u(x, y, z, t) of three spatial variables (x, y, z) and time variable t. One then says that u is a solution of the heat equation if