1
To differentiate logarithmic functions with bases other than e, use
1
To differentiate logarithmic functions with bases other than e, use
ln m
logb m =
ln b
1
To differentiate logarithmic functions with bases other than e, use
ln m
logb m =
ln b
Example
8.10 Garbage Collection and Method finalize
Every class in Java has the methods of class Object (package java.lang), one of which is the finalize
method. This method is rarely used because it can cause performance problems and theres some
uncertainty as t
Derivatives Involving Absolute Value
Calculating derivatives of functions containing absolute values can be confusing at first, but is
actually relatively easy once we know the formula.
Suppose we want to find the derivative of u . Recall that u = u 2 . S
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c 2012 Math Medics LLC. All rights reserved.
TRIGONOMETRIC IDENTITIES
Reciprocal identities
1
1
sin u =
cos u =
csc u
sec u
1
1
tan u =
cot u =
cot u
tan u
1
1
csc u =
sec u =
sin u
cos u
Pythagorean Identities
Power-Reducing/Half Angle Formulas
1 cos(
Correlated and Uncorrelated Signals
Problem: we have two signals x[n] and y[n] . How close are they to each other?
Example: in a radar (or sonar) we transmit a pulse and we expect a return
1
0.8
0.6
Transmit
0.4
0.2
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12 14