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CRMS Calculus May 31, 2010
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CRMS Calculus May 31, 2010
1.
The Year in
Review What the heck is Calculus?
2.
One of the
supreme creations of human thought
3.
One of the
biggest controversies in history
4.
The Culmination of
K-12 mathematics Calculus Trigonometry Elementary Functions Geometry Algebra Arithmetic
5.
6.
7.
8.
Do you Sir
Know the Foundation For All of Calculus?
9.
10.
Limits by definition
11.
Limits by
Delta - Epsilon definition
12.
Limits by graph
13.
Limits by numerical
table
14.
Limits by algebra
15.
Limits involving
16.
Intermediate Value Theorem
17.
18.
Differential Calculus The
mathematics of change Physical Meaning Instantaneous rate of change
19.
Slope of the
tangent line at a point. Graphical Meaning
20.
Do you Sir
Know the definition of The Derivative ?
21.
Derivative
22.
23.
If y
= Displacement Then y’ = Velocity And y’’ = Acceleration
24.
How’s My Deriving?
25.
Power Rule for
derivatives Function Notation: Operator Notation:
26.
27.
28.
Related Rates
29.
y = C
+ AsinB(x – D) y ‘ = ABcosB(x – D)
30.
31.
The Squeeze Theorem
32.
If y
= e x , then y’ = e x If y = b x , then y’ = b x · ln b
33.
If y =
ln x, then
34.
I PITY DA
FOO’ WHO CAN’T FIND DA DERIVATIVE !!!
35.
Integral Calculus Areas
and Volumes
36.
Counting Squares
37.
Archimedes Method of
Exhaustion
38.
Trapezoidal Rule
39.
Do you sir,
Know the difference between An indefinite integral And A definite integral?
40.
Antiderivatives of y’
= x 2 Bring the Whole Indefinite Integral Family! Indefinite Integral A Family of Curves With a given Derivative
41.
Definite Integral is
a Number
42.
43.
Solving Differential Equations
and Slope Fields
44.
45.
Sweetheart, Check out
this definition ! Definite Integral;
46.
Rolle’s Theorem The
Mean Value Theorem Is just Rolle’s Theorem Rotated
47.
48.
49.
What were those
Properties Of Integrals?
50.
Definite Integrals Allow
us to find The area between curves
51.
Naked Math Real
World
52.
53.
54.
55.
Volumes of Revolution
The Disk Method
56.
57.
An Illuminating
Volume
58.
This stuff isn’t
so hard! In fact …
59.
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