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Thermodynamics HW Solutions 141

# Thermodynamics HW Solutions 141 - Chapter 2 Heat Conduction...

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Chapter 2 Heat Conduction Equation 2-106C A differential equation may involve more than one dependent or independent variable. For example, the equation α 2 2 1 Txt x g k t (,) & += has one dependent ( T ) and 2 independent variables ( x and t ). the equation ∂α 2 2 11 x Wxt x t t + has 2 dependent ( T and W ) and 2 independent variables ( x and t ). 2-107C Geometrically, the derivative of a function y ( x ) at a point represents the slope of 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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