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LEARNING CALCULUS JUST GOT A LOT EASIER!
Here’s an innovative shortcut to gaining a more intuitive understanding of both differential and integral calculus. In Calculus Demystified an experienced teacher and author of more than 30 books puts all the math background you need inside and uses practical examples, real data, and a totally different approach to mastering calculus.
With Calculus Demystified you ease into the subject one simple step at a time — at your own speed. A user-friendly, accessible style incorporating frequent reviews, assessments, and the actual application of ideas helps you to understand and retain all the important concepts.
THIS ONE-OF-A-KIND SELF-TEACHING TEXT OFFERS:
If you’ve been looking for a painless way to learn calculus, refresh your skills, or improve your classroom performance, your search ends here.
| Preface | xi | |
| Chapter 1 | Basics | 1 |
| 1.0 | Introductory Remarks | 1 |
| 1.1 | Number Systems | 1 |
| 1.2 | Coordinates in One Dimension | 3 |
| 1.3 | Coordinates in Two Dimensions | 5 |
| 1.4 | The Slope of a Line in the Plane | 8 |
| 1.5 | The Equation of a Line | 13 |
| 1.6 | Loci in the Plane | 15 |
| 1.7 | Trigonometry | 19 |
| 1.8 | Sets and Functions | 30 |
| 1.8.1 | Examples of Functions of a Real Variable | 31 |
| 1.8.2 | Graphs of Functions | 33 |
| 1.8.3 | Plotting the Graph of a Function | 35 |
| 1.8.4 | Composition of Functions | 40 |
| 1.8.5 | The Inverse of a Function | 42 |
| 1.9 | A Few Words About Logarithms and Exponentials | 49 |
| Chapter 2 | Foundations of Calculus | 57 |
| 2.1 | Limits | 57 |
| 2.1.1 | One-Sided Limits | 60 |
| 2.2 | Properties of Limits | 61 |
| 2.3 | Continuity | 64 |
| 2.4 | The Derivative | 66 |
| 2.5 | Rules for Calculating Derivatives | 71 |
| 2.5.1 | The Derivative of an Inverse | 76 |
| 2.6 | The Derivative as a Rate of Change | 76 |
| Chapter 3 | Applications of the Derivative | 81 |
| 3.1 | Graphing of Functions | 81 |
| 3.2 | Maximum/Minimum Problems | 86 |
| 3.3 | Related Rates | 91 |
| 3.4 | Falling Bodies | 94 |
| Chapter 4 | The Integral | 99 |
| 4.0 | Introduction | 99 |
| 4.1 | Antiderivatives and Indefinite Integrals | 99 |
| 4.1.1 | The Concept of Antiderivative | 99 |
| 4.1.2 | The Indefinite Integral | 100 |
| 4.2 | Area | 103 |
| 4.3 | Signed Area | 111 |
| 4.4 | The Area Between Two Curves | 116 |
| 4.5 | Rules of Integration | 120 |
| 4.5.1 | Linear Properties | 120 |
| 4.5.2 | Additivity | 120 |
| Chapter 5 | Indeterminate Forms | 123 |
| 5.1 | l'Hopital's Rule | 123 |
| 5.1.1 | Introduction | 123 |
| 5.1.2 | l'Hopital's Rule | 124 |
| 5.2 | Other Indeterminate Forms | 128 |
| 5.2.1 | Introduction | 128 |
| 5.2.2 | Writing a Product as a Quotient | 128 |
| 5.2.3 | The Use of the Logarithm | 128 |
| 5.2.4 | Putting Terms Over a Common Denominator | 130 |
| 5.2.5 | Other Algebraic Manipulations | 131 |
| 5.3 | Improper Integrals: A First Look | 132 |
| 5.3.1 | Introduction | 132 |
| 5.3.2 | Integrals with Infinite Integrands | 133 |
| 5.3.3 | An Application to Area | 139 |
| 5.4 | More on Improper Integrals | 140 |
| 5.4.1 | Introduction | 140 |
| 5.4.2 | The Integral on an Infinite Interval | 141 |
| 5.4.3 | Some Applications | 143 |
| Chapter 6 | Transcendental Functions | 147 |
| 6.0 | Introductory Remarks | 147 |
| 6.1 | Logarithm Basics | 147 |
| 6.1.1 | A New Approach to Logarithms | 148 |
| 6.1.2 | The Logarithm Function and the Derivative | 150 |
| 6.2 | Exponential Basics | 154 |
| 6.2.1 | Facts About the Exponential Function | 155 |
| 6.2.2 | Calculus Properties of the Exponential | 156 |
| 6.2.3 | The Number e | 158 |
| 6.3 | Exponentials with Arbitrary Bases | 160 |
| 6.3.1 | Arbitrary Powers | 160 |
| 6.3.2 | Logarithms with Arbitrary Bases | 163 |
| 6.4 | Calculus with Logs and Exponentials to Arbitrary Bases | 166 |
| 6.4.1 | Differentiation and Integration of log[subscript a] x and a[superscript x] | 166 |
| 6.4.2 | Graphing of Logarithmic and Exponential Functions | 168 |
| 6.4.3 | Logarithmic Differentiation | 170 |
| 6.5 | Exponential Growth and Decay | 172 |
| 6.5.1 | A Differential Equation | 173 |
| 6.5.2 | Bacterial Growth | 174 |
| 6.5.3 | Radioactive Decay | 176 |
| 6.5.4 | Compound Interest | 178 |
| 6.6 | Inverse Trigonometric Functions | 180 |
| 6.6.1 | Introductory Remarks | 180 |
| 6.6.2 | Inverse Sine and Cosine | 180 |
| 6.6.3 | The Inverse Tangent Function | 185 |
| 6.6.4 | Integrals in Which Inverse Trigonometric Functions Arise | 187 |
| 6.6.5 | Other Inverse Trigonometric Functions | 189 |
| 6.6.6 | An Example Involving Inverse Trigonometric Functions | 193 |
| Chapter 7 | Methods of Integration | 197 |
| 7.1 | Integration by Parts | 197 |
| 7.2 | Partial Fractions | 202 |
| 7.2.1 | Introductory Remarks | 202 |
| 7.2.2 | Products of Linear Factors | 203 |
| 7.2.3 | Quadratic Factors | 206 |
| 7.3 | Substitution | 207 |
| 7.4 | Integrals of Trigonometric Expressions | 210 |
| Chapter 8 | Applications of the Integral | 217 |
| 8.1 | Volumes by Slicing | 217 |
| 8.1.0 | Introduction | 217 |
| 8.1.1 | The Basic Strategy | 217 |
| 8.1.2 | Examples | 219 |
| 8.2 | Volumes of Solids of Revolution | 224 |
| 8.2.0 | Introduction | 224 |
| 8.2.1 | The Method of Washers | 225 |
| 8.2.2 | The Method of Cylindrical Shells | 228 |
| 8.2.3 | Different Axes | 231 |
| 8.3 | Work | 233 |
| 8.4 | Averages | 237 |
| 8.5 | Arc Length and Surface Area | 240 |
| 8.5.1 | Arc Length | 240 |
| 8.5.2 | Surface Area | 243 |
| 8.6 | Hydrostatic Pressure | 247 |
| 8.7 | Numerical Methods of Integration | 252 |
| 8.7.1 | The Trapezoid Rule | 253 |
| 8.7.2 | Simpson's Rule | 256 |
| Bibliography | 263 | |
| Solutions to Exercises | 265 | |
| Final Exam | 313 | |
| Index | 339 |
Anonymous
Posted April 24, 2006
Calculus Demystified is not like the other math books in the Demystified series. It's much more opaque, and isn't particularly suited for filling in the gaps. The book skims over a huge chunk of derivatives in a single chapter. There are no answers to the 'you try this' exercises, which are mystifyingly complex, so (unlike Algebra Demystified, for example) you don't know if you've got it right or not. The exercises in chapter 2 assume you've read chapter 5 (!) and learned 'non-trivial' (the author's words) facts about limits. Even Finney/Thomas doesn't expect you to have mastered material from later in the book to do the exercises. Calculus Demystified would not be all that suitable for people taking calculus the first time (home school, AP, college, etc), but might be OK for people who already know it who need to review (although you'd have to remember calculus fairly well to hold your own). Wasn't this book 'beta tested' by first-time calculus students?
4 out of 4 people found this review helpful.
Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.nezbit
Posted February 22, 2011
Would have been better to use money to get sparknotes. Purchased book to help with Calculus studies. Got through the basics easily, but the REAL calculus wasn't so easy. This book lacked detailed examples for beginners or intermediates. The audience of this book was more for teachers and advanced mathmaticians. This book also lacks practice problems to help you use the material.
2 out of 2 people found this review helpful.
Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.Anonymous
Posted October 18, 2009
I'd recommend this book to anybody who needs to catch up on their calculus skills. Not the best choice for beginners. Great for references.
1 out of 1 people found this review helpful.
Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.Anonymous
Posted August 17, 2009
No text was provided for this review.
Overview
LEARNING CALCULUS JUST GOT A LOT EASIER!
Here’s an innovative shortcut to gaining a more intuitive understanding of both differential and integral calculus. In Calculus Demystified an experienced teacher and author of more than 30 books puts all the math background you need inside and uses practical examples, real data, and a totally different approach to mastering calculus.
With Calculus Demystified you ease into the subject one simple step at...