Pre-Calculus Know-It-ALL

by Gibilisco, Stan

• ISBN13: 9780071627023
• ISBN10: 0071627022
• Edition: 1st
• Format: Paperback
• Copyright: 2009-11-13
• Publisher: McGraw-Hill Education TAB

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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