NUEN-430 Lecture 4

Operators 2 residuals operators have a domain and a

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Unformatted text preview: approximations, we must define two quantities: 1. Operators 2. Residuals Operators have a domain and a range, and map functions in the domain to functions in the range. For instance, let L denote the following differential operator: Then L applied to a function f is denoted by Lf where In general, equations can be written efficiently in operator notation. For instance, Becomes Essentially any equations can be expressed in operator form. An important property of many operators arising in nuclear engineering is the property of linearity. A linear operator, L, satisfies ( for any two functions, and ) , and any two constants, and . A residual is associated with an arbitrary function and an equation. For instance, let us denote an arbitrary equation by The residual associated with an arbitrary function ( ⃗ ) is () Note that ( ) if and...
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This note was uploaded on 10/06/2013 for the course NEUN 430 taught by Professor Morel during the Fall '10 term at Texas A&M.

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