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• I feel like Im diagonally parked in a parallel
  universe

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Math ReviewMonday June 7 2003

• Introduction
• Symbols
• Operations
• Central Tendencies
• Linear Algebra
• Correlation/Regression Analysis
• Applied Calculus

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Basic Math Review

1. System of equations

• 3x - y -7
• 5y 5 -5x
• 3x 4y 2
• 2y 4 - 3/2x

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Basic Math Review

1. Applied Calculus

Rate of change (slope) Dy/Dx or
(y2-y1)/(x2-x1) Here Dy/Dx is constant regardless
of the limit
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Basic Math Review

1. Applied Calculus

How long does it take to fill one beaker (1L)?
V(t)
t
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Basic Math Review

1. Differential equations

A differential equation is an equation in which
one or more unknowns depend on its/their rate of
change (or that of other variables included in
the equations)
Newtons principia
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Basic Math Review

1. Definition of a derivative

The derivative of a function ?(x) at a point a
is the slope of the straight line tangent to ?(x)
at a ? instantaneous rate of change! One is
pushing to limit to 0 the slope is close to
real as ?(x) approaches 0
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Basic Math Review

1. Definition of a derivative

The derivative of a function ?(x)
f(x) Important derivatives f(x) C ? f(x) 0
f(x) xn ? f(x) nxn-1 f(x) ex ? f(x)
ex f(x) lnx ? f(x) 1/x
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Basic Math Review

1. Maxima, Minima

One of the great applications of calculus
(particularly in economics) is to determine the
maxima and minima of functions. The
derivatives of the maxima and minima 0 The
function neither increase nor decreases! f(x)
x3 3x2 24x 5
f(x) 3x2 6x 24 3 (x2 2x 8) 3 (x 2)(x
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f(x) vanishes (reaches a critical point) only
when f(x) 0
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f(x) lt 0 ? maximum f(x) gt 0 ? minimum

1. Maxima, Minima

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1. Application Derivatives

Ji -? ? DS ? (?Ci /?z) DS D0 ? ?2 J Cz0
-?3 ? D0 (8 oC) ? (?Ci /?z)z0
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1. Application Derivatives

Ji -? ? DS ? (?Ci /?z) DS D0 ? ?2 J Cz0
-?3 ? D0 (8 oC) ? (?Ci /?z)z0
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A River (used to) Run Through It Part I
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Reservoirs and soil erosion
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1. Application Integral

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1. Application Integral

?(x) Polynomial (6th degree) ? ?(xn)
n(n1)/(n1) C
Integral between two limits (0 and 85 yrs) ?
?(xn)100 - ? ?(xn)0 C - C