Calculus Essentials For Dummies

( 6 )

Overview

From limits and differentiation to related rates and integration, this practical, friendly guide provides clear explanations of the core concepts you need to take your calculus skills to the next level. It's perfect for cramming, homework help, or review.

Test the limits (and continuity) - get the low-down on limits and continuity as they relate to critical concepts in calculus

Ride the slippery slope - ...

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Overview

From limits and differentiation to related rates and integration, this practical, friendly guide provides clear explanations of the core concepts you need to take your calculus skills to the next level. It's perfect for cramming, homework help, or review.

Test the limits (and continuity) - get the low-down on limits and continuity as they relate to critical concepts in calculus

Ride the slippery slope - understand how differentiation works, from finding the slope of a curve to making the rate-slope connection

Integrate yourself - discover how integration and area approximation are used to solve a bevy of calculus problems

Work it out - arm yourself with the problem-solving skills you need to crack calculus code, from using the integral to analyzing arc length, and everything in between

Product Details

• ISBN-13: 9780470618356
• Publisher: Wiley
• Publication date: 5/17/2010
• Series: For Dummies Series
• Edition number: 1
• Pages: 192
• Sales rank: 349,377
• Product dimensions: 5.50 (w) x 8.40 (h) x 0.50 (d)

Meet the Author

Mark Ryan is the owner of The Math Center in Chicago, Illinois, where he teaches students in all levels of mathematics, from pre-algebra to calculus. He is the author of Calculus For Dummies and Geometry For Dummies.

Introduction 1

Conventions Used in This Book 2

Foolish Assumptions 2

Icons Used in This Book 3

Where to Go from Here 3

Chapter 1 Calculus: No Big Deal 5

So What Is Calculus Already? 5

Real-World Examples of Calculus 7

Differentiation 8

Integration 9

Why Calculus Works 11

Limits: Math microscopes 11

What happens when you zoom in 12

Chapter 2 Limits and Continuity 15

Taking It to the Limit 15

Three functions with one limit 15

One-sided limits 17

Limits and vertical asymptotes 18

Limits and horizontal asymptotes 19

Instantaneous speed 19

Limits and Continuity 22

The hole exception 23

Chapter 3 Evaluating Limits 25

Easy Limits 25

Limits to memorize 25

Plug-and-chug limits 26

"Real" Limit Problems 26

Factoring 27

Conjugate multiplication 27

Miscellaneous algebra 28

Limits at Infinity 29

Horizontal asymptotes 30

Solving limits at infinity 31

Chapter 4 Differentiation Orientation 33

The Derivative: It's Just Slope 34

The slope of a line 35

The derivative of a line 36

The Derivative: It's Just a Rate 36

Calculus on the playground 36

The rate-slope connection 38

The Derivative of a Curve 39

The Difference Quotient 41

Average and Instantaneous Rate 47

Three Cases Where the Derivative Does Not Exist 48

Chapter 5 Differentiation Rules 49

Basic Differentiation Rules 49

The constant rule 49

The power rule 49

The constant multiple rule 50

The sum and difference rules 51

Differentiating trig functions 52

Exponential and logarithmic functions 53

Derivative Rules for Experts 53

The product and quotient rules 53

The chain rule 54

Differentiating Implicitly 59

Chapter 6 Differentiation and the Shape of Curves 61

Local Extrema 63

Finding the critical numbers 63

The First Derivative Test 65

The Second Derivative Test 66

Finding Absolute Extrema on a Closed Interval 69

Finding Absolute Extrema over a Function's Entire Domain 71

Concavity and Inflection Points 73

Graphs of Derivatives 75

The Mean Value Theorem 78

Chapter 7 Differentiation Problems 81

Optimization Problems 81

The maximum area of a corral 81

Position, Velocity, and Acceleration 83

Velocity versus speed 84

Maximum and minimum height 86

Velocity and displacement 87

Speed and distance traveled 88

Acceleration 89

Tying it all together 90

Related Rates 91

Filling up a trough 94

Linear Approximation 96

Chapter 8 Introduction to Integration 101

Finding the Area under a Curve 103

Dealing with negative area 105

Approximating Area 105

Approximating area with left sums 105

Approximating area with right sums 109

Approximating area with midpoint sums 111

Summation Notation 113

Summing up the basics 113

Writing Riemann sums with sigma notation 114

Finding Exact Area with the Definite Integral 117

Chapter 9 Integration: Backwards Differentiation 119

Antidifferentiation: Reverse Differentiation 119

The Annoying Area Function 121

The Fundamental Theorem 124

Fundamental Theorem: Take Two 126

Antiderivatives: Basic Techniques 128

Reverse rules 128

Guess and check 131

Substitution 132

Chapter 10 Integration for Experts 137

Integration by Parts 137

Tricky Trig Integrals 141

Sines and cosines 142

Secants and tangents 144

Cosecants and cotangents 147

Trigonometric Substitution 147

Case 1 Tangents 148

Case 2 Sines 150

Case 3 Secants 152

Partial Fractions 152

Case 1 The denominator contains only linear factors 152

Case 2 The denominator contains unfactorable quadratic factors 153

Case 3 The denominator contains repeated factors 155

Equating coefficients 156

Chapter 11 Using the Integral to Solve Problems 157

The Mean Value Theorem for Integrals and Average Value 158

The Area between Two Curves 160

Volumes of Weird Solids 162

The meat-slicer method 162

The disk method 164

The washer method 166

The matryoshka doll method 168

Arc Length 170

Improper Integrals 172

Improper integrals with vertical asymptotes 173

Improper integrals with infinite limits of integration 175

Chapter 12 Eight Things to Remember 177

a2 - b2 = (a - b)(a + b) 177

0/5 = 0 But 5/0 Is Undefined 177

SohCahToa 177

Trig Values to Know 178

sin2 Î¸ + cos2 Î¸ = 1 178

The Product Rule 178

The Quotient Rule 178

Index 179

Customer Reviews

Average Rating 2.5
( 6 )
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Sort by: Showing all of 6 Customer Reviews
• Anonymous

Posted January 26, 2013

Not a Good Book. Not Recommended at all.

1. Spends too much time on social relations about students to professors and other students rather than focus on the mathematics.
2. Formulas are small and difficult to see, very distracting.
3. Worst of all, e-book only goes to page 74 (attempts to turn the page and advance will not work, gives an error message that the activity reader is not responding). so the last 1/3 of the book is really not available.
4. There is some calculus value, but overall not a good book.

3 out of 3 people found this review helpful.

• Anonymous

Posted December 19, 2011

Why??!!

Jeez this is a ccaucus book

1 out of 14 people found this review helpful.

• Anonymous

Posted January 3, 2012

No text was provided for this review.

• Anonymous

Posted January 30, 2012

No text was provided for this review.

• Anonymous

Posted October 30, 2011

No text was provided for this review.

• Anonymous

Posted December 9, 2011

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