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### Summary

### Summary

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:

Questions at the end of each chapter and section to reinforce learning and pinpoint weaknesses A 100-question final exam for self-assessment Detailed examples and solutions Numerous "Math Notes" and "You Try It" items to gauge progress and make learning more enjoyable An easy-to-absorb style -- perfect for those without a mathematics backgroundIf you've been looking for a painless way to learn calculus, refresh your skills, or improve your classroom performance, your search ends here.

### Table of Contents

Preface | p. xi |

Chapter 1 Basics | p. 1 |

1.0 Introductory Remarks | p. 1 |

1.1 Number Systems | p. 1 |

1.2 Coordinates in One Dimension | p. 3 |

1.3 Coordinates in Two Dimensions | p. 5 |

1.4 The Slope of a Line in the Plane | p. 8 |

1.5 The Equation of a Line | p. 13 |

1.6 Loci in the Plane | p. 15 |

1.7 Trigonometry | p. 19 |

1.8 Sets and Functions | p. 30 |

1.8.1 Examples of Functions of a Real Variable | p. 31 |

1.8.2 Graphs of Functions | p. 33 |

1.8.3 Plotting the Graph of a Function | p. 35 |

1.8.4 Composition of Functions | p. 40 |

1.8.5 The Inverse of a Function | p. 42 |

1.9 A Few Words About Logarithms and Exponentials | p. 49 |

Chapter 2 Foundations of Calculus | p. 57 |

2.1 Limits | p. 57 |

2.1.1 One-Sided Limits | p. 60 |

2.2 Properties of Limits | p. 61 |

2.3 Continuity | p. 64 |

2.4 The Derivative | p. 66 |

2.5 Rules for Calculating Derivatives | p. 71 |

2.5.1 The Derivative of an Inverse | p. 76 |

2.6 The Derivative as a Rate of Change | p. 76 |

Chapter 3 Applications of the Derivative | p. 81 |

3.1 Graphing of Functions | p. 81 |

3.2 Maximum/Minimum Problems | p. 86 |

3.3 Related Rates | p. 91 |

3.4 Falling Bodies | p. 94 |

Chapter 4 The Integral | p. 99 |

4.0 Introduction | p. 99 |

4.1 Antiderivatives and Indefinite Integrals | p. 99 |

4.1.1 The Concept of Antiderivative | p. 99 |

4.1.2 The Indefinite Integral | p. 100 |

4.2 Area | p. 103 |

4.3 Signed Area | p. 111 |

4.4 The Area Between Two Curves | p. 116 |

4.5 Rules of Integration | p. 120 |

4.5.1 Linear Properties | p. 120 |

4.5.2 Additivity | p. 120 |

Chapter 5 Indeterminate Forms | p. 123 |

5.1 l'Hopital's Rule | p. 123 |

5.1.1 Introduction | p. 123 |

5.1.2 l'Hopital's Rule | p. 124 |

5.2 Other Indeterminate Forms | p. 128 |

5.2.1 Introduction | p. 128 |

5.2.2 Writing a Product as a Quotient | p. 128 |

5.2.3 The Use of the Logarithm | p. 128 |

5.2.4 Putting Terms Over a Common Denominator | p. 130 |

5.2.5 Other Algebraic Manipulations | p. 131 |

5.3 Improper Integrals: A First Look | p. 132 |

5.3.1 Introduction | p. 132 |

5.3.2 Integrals with Infinite Integrands | p. 133 |

5.3.3 An Application to Area | p. 139 |

5.4 More on Improper Integrals | p. 140 |

5.4.1 Introduction | p. 140 |

5.4.2 The Integral on an Infinite Interval | p. 141 |

5.4.3 Some Applications | p. 143 |

Chapter 6 Transcendental Functions | p. 147 |

6.0 Introductory Remarks | p. 147 |

6.1 Logarithm Basics | p. 147 |

6.1.1 A New Approach to Logarithms | p. 148 |

6.1.2 The Logarithm Function and the Derivative | p. 150 |

6.2 Exponential Basics | p. 154 |

6.2.1 Facts About the Exponential Function | p. 155 |

6.2.2 Calculus Properties of the Exponential | p. 156 |

6.2.3 The Number e | p. 158 |

6.3 Exponentials with Arbitrary Bases | p. 160 |

6.3.1 Arbitrary Powers | p. 160 |

6.3.2 Logarithms with Arbitrary Bases | p. 163 |

6.4 Calculus with Logs and Exponentials to Arbitrary Bases | p. 166 |

6.4.1 Differentiation and Integration of log[subscript a] x and a[superscript x] | p. 166 |

6.4.2 Graphing of Logarithmic and Exponential Functions | p. 168 |

6.4.3 Logarithmic Differentiation | p. 170 |

6.5 Exponential Growth and Decay | p. 172 |

6.5.1 A Differential Equation | p. 173 |

6.5.2 Bacterial Growth | p. 174 |

6.5.3 Radioactive Decay | p. 176 |

6.5.4 Compound Interest | p. 178 |

6.6 Inverse Trigonometric Functions | p. 180 |

6.6.1 Introductory Remarks | p. 180 |

6.6.2 Inverse Sine and Cosine | p. 180 |

6.6.3 The Inverse Tangent Function | p. 185 |

6.6.4 Integrals in Which Inverse Trigonometric Functions Arise | p. 187 |

6.6.5 Other Inverse Trigonometric Functions | p. 189 |

6.6.6 An Example Involving Inverse Trigonometric Functions | p. 193 |

Chapter 7 Methods of Integration | p. 197 |

7.1 Integration by Parts | p. 197 |

7.2 Partial Fractions | p. 202 |

7.2.1 Introductory Remarks | p. 202 |

7.2.2 Products of Linear Factors | p. 203 |

7.2.3 Quadratic Factors | p. 206 |

7.3 Substitution | p. 207 |

7.4 Integrals of Trigonometric Expressions | p. 210 |

Chapter 8 Applications of the Integral | p. 217 |

8.1 Volumes by Slicing | p. 217 |

8.1.0 Introduction | p. 217 |

8.1.1 The Basic Strategy | p. 217 |

8.1.2 Examples | p. 219 |

8.2 Volumes of Solids of Revolution | p. 224 |

8.2.0 Introduction | p. 224 |

8.2.1 The Method of Washers | p. 225 |

8.2.2 The Method of Cylindrical Shells | p. 228 |

8.2.3 Different Axes | p. 231 |

8.3 Work | p. 233 |

8.4 Averages | p. 237 |

8.5 Arc Length and Surface Area | p. 240 |

8.5.1 Arc Length | p. 240 |

8.5.2 Surface Area | p. 243 |

8.6 Hydrostatic Pressure | p. 247 |

8.7 Numerical Methods of Integration | p. 252 |

8.7.1 The Trapezoid Rule | p. 253 |

8.7.2 Simpson's Rule | p. 256 |

Bibliography | p. 263 |

Solutions to Exercises | p. 265 |

Final Exam | p. 313 |

Index | p. 339 |