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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.