Calculus Essentials For Dummies

__Calculus Essentials For Dummies__ (9781119591207) was previously published as __Calculus Essentials For Dummies__ (9780470618356). While this version features a new __Dummies__ cover and design, the content is the same as the prior release and should not be considered a new or updated product. Many colleges and universities require students to take at least one math course, and Calculus I is often the chosen option. __Calculus Essentials For Dummies__ provides explanations of key concepts for students who may have taken calculus in high school and want to review the most important concepts as they gear up for a faster-paced college course. Free of review and ramp-up material, __Calculus Essentials For Dummies__ sticks to the point with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical two-semester high school calculus class or a college level Calculus I course, from limits and differentiation to integration and infinite series. This guide is also a perfect reference for parents who need to review critical calculus concepts as they help high school students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts. Title Page......Page 3 Copyright Page......Page 4 Table of Contents ......Page 7 About This Book......Page 11 Foolish Assumptions......Page 12 Where to Go from Here......Page 13 So What Is Calculus Already?......Page 15 Real-World Examples of Calculus......Page 17 Differentiation......Page 18 Integration......Page 19 Limits: Math microscopes......Page 21 What happens when you zoom in......Page 22 Three functions with one limit......Page 25 One-sided limits......Page 27 Limits and horizontal asymptotes......Page 28 Instantaneous speed......Page 29 Limits and Continuity......Page 31 The hole exception......Page 32 Limits to memorize......Page 35 “Real” Limit Problems......Page 36 Conjugate multiplication......Page 37 Miscellaneous algebra......Page 38 Limits at Infinity......Page 39 Horizontal asymptotes......Page 40 Solving limits at infinity......Page 41 Chapter 4 Differentiation Orientation......Page 43 The Derivative: It’s Just Slope......Page 44 The slope of a line......Page 45 Calculus on the playground......Page 46 The rate-slope connection......Page 48 The Derivative of a Curve......Page 49 The Difference Quotient......Page 50 Average and Instantaneous Rate......Page 56 Three Cases Where the Derivative Does Not Exist......Page 57 The power rule......Page 59 The constant multiple rule......Page 60 The sum and difference rules......Page 61 Exponential and logarithmic functions......Page 62 The product and quotient rules......Page 63 The chain rule......Page 64 Differentiating Implicitly......Page 69 A Calculus Road Trip......Page 71 Finding the critical numbers......Page 73 The First Derivative Test......Page 75 The Second Derivative Test......Page 76 Finding Absolute Extrema on a Closed Interval......Page 79 Finding Absolute Extrema over a Function’s Entire Domain......Page 81 Concavity and Inflection Points......Page 83 Graphs of Derivatives......Page 85 The Mean Value Theorem......Page 88 The maximum area of a corral......Page 91 Position, Velocity, and Acceleration......Page 93 Velocity versus speed......Page 94 Maximum and minimum height......Page 96 Total displacement......Page 97 Total distance traveled......Page 98 Acceleration......Page 99 Tying it all together......Page 100 A calculus crossroads......Page 101 Filling up a trough......Page 104 Linear Approximation......Page 107 Integration: Just Fancy Addition......Page 111 Finding the Area under a Curve......Page 113 Approximating area with left sums......Page 115 Approximating area with right sums......Page 118 Approximating area with midpoint sums......Page 120 Summing up the basics......Page 122 Writing Riemann sums with sigma notation......Page 123 Finding Exact Area with the Definite Integral......Page 126 Antidifferentiation: Reverse Differentiation......Page 129 The Annoying Area Function......Page 131 The Fundamental Theorem......Page 134 Fundamental Theorem: Take Two......Page 136 Reverse rules......Page 138 Guess and check......Page 140 Substitution......Page 142 Integration by Parts......Page 147 Picking your u......Page 149 Sines and cosines......Page 151 Secants and tangents......Page 154 Trigonometric Substitution......Page 157 Case 1: Tangents......Page 158 Case 2: Sines......Page 160 Case 3: Secants......Page 161 Case 1: The denominator contains only linear factors......Page 162 Case 2: The denominator contains unfactorable quadratic factors......Page 163 Equating coefficients......Page 165 Chapter 11 Using the Integral to Solve Problems......Page 167 The Mean Value Theorem for Integrals and Average Value......Page 168 The Area between Two Curves......Page 170 The meat-slicer method......Page 172 The disk method......Page 173 The washer method......Page 175 The matryoshka doll method......Page 176 Arc Length......Page 178 Improper integrals with vertical asymptotes......Page 181 Improper integrals with infinite limits of integration......Page 183 SohCahToa......Page 185 Your Sunglasses......Page 186 Index......Page 187 EULA......Page 195

Calculus Essentials For Dummies (9781119591207) was previously published as Calculus Essentials For Dummies (9780470618356). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.

 

Many colleges and universities require students to take at least one math course, and Calculus I is often the chosen option. Calculus Essentials For Dummies provides explanations of key concepts for students who may have taken calculus in high school and want to review the most important concepts as they gear up for a faster-paced college course. Free of review and ramp-up material, Calculus Essentials For Dummies sticks to the point with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical two-semester high school calculus class or a college level Calculus I course, from limits and differentiation to integration and infinite series. This guide is also a perfect reference for parents who need to review critical calculus concepts as they help high school students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts.

The Essentials For Dummies Series
Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.

Calculus Essentials For Dummies (9781119591207) was previously published as Calculus Essentials For Dummies (9780470618356). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Many colleges and universities require students to take at least one math course, and Calculus I is often the chosen option. Calculus Essentials For Dummies provides explanations of key concepts for students who may have taken calculus in high school and want to review the most important concepts as they gear up for a faster-paced college course. Free of review and ramp-up material, Calculus Essentials For Dummies sticks to the point with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical two-semester high school calculus class or a college level Calculus I course, from limits and differentiation to integration and infinite series. This guide is also a perfect reference for parents who need to review critical calculus concepts as they help high school students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts. The Essentials For Dummies Series Dummies is proud to present our new series, The Essentials For Dummies . Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject. The key concepts for crushing calculusThis practical, friendly guide provides clear explanations of the core concepts you need to take your calculus skills to the next level. Understand how differentiation works, from finding the slope of a curve to finding the minimum and maximum values of a function. Discover how integration and area approximation are used to solve calculus problems. Get the lowdown on limits and continuity. And more! This book is perfect for cramming, homework help, or review.Inside...• Differentiation rules• Integration techniques• Optimization problems• The fundamental theorem• How to calculate volumes of unusual solids• Tips for working with linear approximation• Real-world examplesMark 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.