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For a given arbitrary stencil points of length with the order of derivatives <, the finite difference coefficients can be obtained by solving the linear equations ( s 1 0 ⋯ s N 0 ⋮ ⋱ ⋮ s 1 N − 1 ⋯ s N N − 1 ) ( a 1 ⋮ a N ) = d !
Integrals are also used in thermodynamics, where thermodynamic integration is used to calculate the difference in free energy between two given states. Computation Analytical. The most basic technique for computing definite integrals of one real variable is based on the fundamental theorem of calculus.
Arithmetic (from Ancient Greek ἀριθμός (arithmós) 'number', and τική  (tikḗ [tékhnē]) 'art, craft') is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
The exponential function is a mathematical function denoted by () = or (where the argument x is written as an exponent).Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
Basal metabolic rate (BMR) is the rate of energy expenditure per unit time by endothermic animals at rest. It is reported in energy units per unit time ranging from watt (joule/second) to ml O 2 /min or joule per hour per kg body mass J/(h·kg).
The derivative of () = for any (nonvanishing) function f is: ′ = ′ (()) wherever f is non-zero. In Leibniz's notation, this is written (/) =.The reciprocal rule can be derived either from the quotient rule, or from the combination of power rule and chain rule.
A finite difference is a mathematical expression of the form f (x + b) − f (x + a).If a finite difference is divided by b − a, one gets a difference quotient.The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems.
In particular, the numerator and denominator of the difference quotient are not even in the same vector space: The numerator lies in the codomain R m while the denominator lies in the domain R n. Furthermore, the derivative is a linear transformation, a different type of object from both the numerator and denominator.