Prof. E. McSquared's Calculus Primer : Expanded Intergalactic Version!

by Swann, Howard; Johnson, John

• ISBN13: 9780971462403
• ISBN10: 0971462402
• Format: Paperback
• Copyright: 2003-07-01
• Publisher: Dyers & Swann Pub

Table of Contents

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