Chapter 2 Heat Conduction Equation2-106C A differential equation may involve more than one dependent or independent variable. For example, the equation ∂α221Txtxgkt(,)&+=has one dependent (T) and 2 independent variables (xand t). the equation ∂α2211xWxtxtt+has 2 dependent (T and W) and 2 independent variables (xand t). 2-107C Geometrically, the derivativeof a function y(x) at a point represents the slopeof the tangent line to the graph of the function at that point. The derivative of a function that depends on two or more independent variables with respect to one variable while holding the other variables constant is called the partial derivative. Ordinary and partial derivatives are equivalent for functions that depend on a single independent variable. 2-108C The order of a derivative represents the number of times a function is differentiated, whereas the degree of a derivative represents how many times a derivative is multiplied by itself. For example, is the third order derivative of
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This note was uploaded on 01/14/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.