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Tables of Contents for Prof. E. McSquared's Calculus Primer
Chapter/Section Title
Page #
Page Count
Introduction giving the itinerary of the calculus trip
6
4
Functions
10
66
Set theory --- unions and intersections
11
5
Venn diagrams
13
3
Sets of numbers featuring { | }, [ , ], ( , ) and `x'
16
12
Multiplying sets of numbers by constants. Stretching, shrinking and flipping
19
5
Absolute values
24
1
Describing number intervals using absolute values
25
3
Functions
28
18
Rules for functions
29
1
Function machines
30
3
Better rules for functions
33
2
Constructing graphs for functions
35
3
Labeling points
38
4
Formulas for functions
42
2
Popular straight line functions
44
2
Straight lines
46
15
Slopes
48
4
The general point-slope formula
52
4
Finding the slope of a line if you know two points on the line
56
5
Further function formulas featuring parabolas and cubics
61
15
Parabolas
62
3
Cubics
65
4
Extra Exercises and Excursions
69
7
Limits
76
111
The smoothness problem
77
3
Limit machines
80
15
e's and δ's
95
11
Proving that a function's graph is smooth
98
4
Definition of continuity
102
4
Secret computations How to figure a formula for δ(.).
106
8
More secret computations for parabolas
114
14
Functions that are not continuous
128
5
On being continuous in an interval
133
3
What happens when a point is missing from a graph. A genuine theorem is proved
136
3
Statement of theorem II.I.
139
12
The definition of a general limit point
151
7
Two limit theorems
158
29
Extra exercises and excursions
170
4
More limit theorems
174
6
Recess
180
7
Derivatives
187
50
Tangent hunting functions
188
10
Definition of a derivative
194
4
Two derivative theorems; the easy way out
198
8
Differentiating polynomials and finding maxima and minima
206
6
Velocities and derivatives
212
25
Extra exercises and excursions
220
1
More derivative theorems
221
8
More on Maxima and Minima
229
8
An Intergalactic Epilogue
237
11
Answers!
248
12
Selected solutions and answers for the extra exercises and excursions
260