Pre-Calculus Know-It-ALL
by Gibilisco, StanEdition: 1st
Format: Paperback
Pub. Date: 2009-11-13
Publisher(s): McGraw-Hill Education TAB
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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 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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