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# Pre-Calculus Know-It-ALL

**by**Gibilisco, Stan

1st

### 9780071627023

0071627022

Paperback

10/23/2009

McGraw-Hill/TAB Electronics

## Summary

When you cant get to a tutor, and your teacher and expensive textbook are not working, Pre-Calculus Know-it-ALL provides all the instruction youll need to master the topic. This is the perfect book to bridge the massive and essential topics of algebra and calculus, and to complete a fantastic third offering in the Know-it-ALL series.

## Author Biography

**Stan Gibilisco** is one of McGraw-Hilln++s most prolific authors, with more than two dozen highly successful titles to his credit, including the wildly popular *Teach Yourself Electricity and Electronics, Physics DeMYSTiFied, Algebra Know-it-ALL*, and *Calculus Know-it-ALL*.

## Table of Contents

Preface | p. xi |

Acknowledgments | p. xiii |

Coordinates and Vectors | p. 1 |

Cartesian Two-Space | p. 3 |

How It's Assembled | p. 3 |

Distance of a Point from Origin | p. 8 |

Distance between Any Two Points | p. 12 |

Finding the Midpoint | p. 15 |

Practice Exercises | p. 18 |

A Fresh Look at Trigonometry | p. 21 |

Circles in the Cartesian Plane | p. 21 |

Primary Circular Functions | p. 23 |

Secondary Circular Functions | p. 30 |

Pythagorean Extras | p. 33 |

Practice Exercises | p. 36 |

Polar Two-Space | p. 37 |

The Variables | p. 37 |

Three Basic Graphs | p. 40 |

Coordinate Transformations | p. 45 |

Practice Exercises | p. 52 |

Vector Basics | p. 55 |

The "Cartesian Way" | p. 55 |

The "Mar Way" | p. 62 |

Practice Exercises | p. 71 |

Vector Multiplication | p. 73 |

Product of Scalar and Vector | p. 73 |

Dot Product of Two Vectors | p. 79 |

Cross Product of Two Vectors | p. 82 |

Practice Exercises | p. 88 |

Complex Numbers and Vectors | p. 90 |

Numbers with Two Parts | p. 90 |

How Complex Numbers Behave | p. 95 |

Complex Vectors | p. 101 |

Practice Exercises | p. 109 |

Cartesian Three-Space | p. 111 |

How It's Assembled | p. 111 |

Distance of Point from Origin | p. 116 |

Distance between Any Two Points | p. 120 |

Finding the Midpoint | p. 122 |

Practice Exercises | p. 126 |

Vectors in Cartesian Three-Space | p. 128 |

How They're Defined | p. 128 |

Sum and Difference | p. 134 |

Some Basic Properties | p. 138 |

Dot Product | p. 141 |

Cross Product | p. 144 |

Some More Vector Laws | p. 146 |

Practice Exercises | p. 150 |

Alternative Three-Space | p. 152 |

Cylindrical Coordinates | p. 152 |

Cylindrical Conversions | p. 156 |

Spherical Coordinates | p. 159 |

Spherical Conversions | p. 164 |

Practice Exercises | p. 171 |

Review Questions and Answers | p. 172 |

Analytic Geometry | p. 209 |

Relations in Two-Space | p. 211 |

"What's aTwo-Space Relation? | p. 211 |

What's aTwo-Space Function? | p. 216 |

Algebra with Functions | p. 222 |

Practice Exercises | p. 227 |

Inverse Relations in Two-Space | p. 229 |

Finding an Inverse Relation | p. 229 |

Finding an Inverse Function | p. 238 |

Practice Exercises | p. 247 |

Conic Sections | p. 249 |

Geometry | p. 249 |

Basic Parameters | p. 253 |

Standard Equations | p. 258 |

Practice Exercises | p. 263 |

Exponential and Logarithmic Curves | p. 266 |

Graphs Involving Exponential Functions | p. 266 |

Graphs Involving Logarithmic Functions | p. 273 |

Logarithmic Coordinate Planes | p. 279 |

Practice Exercises | p. 283 |

Trigonometric Curves | p. 285 |

Graphs Involving the Sine and Cosine | p. 285 |

Graphs Involving the Secant and Cosecant | p. 290 |

Graphs Involving the Tangent and Cotangent | p. 296 |

Practice Exercises | p. 302 |

Parametric Equations in Two-Space | p. 304 |

What's a Parameter? | p. 304 |

From Equations to Graph | p. 308 |

From Graph to Equations | p. 314 |

Practice Exercises | p. 318 |

Surfaces in Three-Space | p. 320 |

Planes | p. 320 |

Spheres | p. 324 |

Distorted Spheres | p. 328 |

Other Surfaces | p. 337 |

Practice Exercises | p. 343 |

Lines and Curves in Three-Space | p. 345 |

Straight Lines | p. 345 |

Parabolas | p. 350 |

Circles | p. 357 |

Circular Helixes | p. 363 |

Practice Exercises | p. 370 |

Sequences, Series, and Limits | p. 373 |

Repeated Addition | p. 373 |

Repeated Multiplication | p. 378 |

Limit of a Sequence | p. 382 |

Summation "Shorthand" | p. 385 |

Limit of a Series | p. 388 |

Limits of Functions | p. 390 |

Memorable Limits of Series | p. 394 |

Practice Exercises | p. 396 |

Review Questions and Answers | p. 399 |

Final Exam | p. 436 |

Worked-Out Solutions to Exercises: Chapter 1-9 | p. 466 |

Worked-Out Solutions to Exercises: Chapter 11-19 | p. 514 |

Answers to Final Exam Questions | p. 578 |

Special Characters in Order of Appearance | p. 579 |

Suggested Additional Reading | p. 581 |

Index | p. 583 |

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