Chapter 2
Heat Conduction Equation
2106C
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
).
2107C
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.
2108C
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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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Derivative, Mass, Heat

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