Preliminary draft only: please check for final version
ARE211, Fall 2007
LECTURE #16: TUE, OCT 23, 2007
PRINT DATE: AUGUST 21, 2007
(CALCULUS1)
Contents
4.
Univariate and Multivariate Differentiation
1
4.1.
The fundamental idea: linear approximations to nonlinear functions
2
4.2.
Univariate Calculus
3
4.
Univariate and Multivariate Differentiation
Assume you all know how to calculate the derivative of a single variable function, i.e., given
f
,
calculate
d
f
(
·
)
d
x
, denoted also
f
prime
(
·
).
Important to know the difference between
f
prime
(
·
), which is a
function and
f
prime
(
x
), which is a number, the function evaluated at a point.
I’ll try to be careful to use this notation from now on:
g
(
·
) is a RULE, represents a function.
Since
f
prime
(
·
) is a function, like any other, it may have a derivative; if it does, call it
f
primeprime
(
·
). Do example
f
(
x
) =
x
2
.
Lots of standard kinds of functions you have to be able to differentiate in your sleep. Equivalent
of being able to spell. Brainless activity.
1
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LECTURE #16: TUE, OCT 23, 2007
PRINT DATE: AUGUST 21, 2007
(CALCULUS1)
x
f
df
dx
dx
x
*
x
*
+
dx
*
f
(
x
*
)
f
(
x
*
+
dx
*
)
df
=
f
prime
(
x
*
)
dx
f
(
x
*
) +
f
prime
(
x
*
)
dx
*
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 Fall '07
 Simon
 Calculus, Derivative, Slope, dr af

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