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Department of Economics
University of California, Berkeley
ECON 100A
Spring 2010

Section 1
GSI: Antonio Rosato
1 A very Short Math Review
1.1 Systems of Linear Equations
Solve the following system of two equations for the values of the two unknowns,
x
and
y
:
y
= 3
x
+ 6
y
=

6
x
+ 24
Graph the two equations on the (
x, y
) plane:
A very common application is supply and demand analysis. Solve the following for
the price and quantity in market equilibrium:
Q
D
= 100

2
P
Q
S
=

10 + 2
P
1
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View Full Document Department of Economics
University of California, Berkeley
1.2 The natural logarithm and the exponential function
ln(
x
) is called the
natural logarithm
of
x
. It is the power to which one must raise the
number
e
to get
x
. The number
e
is 2.7182.
..
e
y
is called the
exponential function
, and
is sometimes written as exp(
y
). These numbers are often used in ﬁnance and economics.
The relationship between the two is:
ln(
x
) =
y
⇔
e
y
=
x
1.3 Polynomials
Polynomials are functions made of the sum of variables raised to diﬀerent powers. The
highest power to which a variable is raised in a polynomial gives the polynomial its name.
f
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This note was uploaded on 03/18/2010 for the course ECON 100A taught by Professor Woroch during the Spring '08 term at University of California, Berkeley.
 Spring '08
 Woroch
 Economics

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