Pre-Calculus Know-It-ALL

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  • Edition: 1st
  • Format: Paperback
  • Copyright: 11/13/2009
  • Publisher: McGraw-Hill Education TAB
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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

Prefacep. xi
Acknowledgmentsp. xiii
Coordinates and Vectorsp. 1
Cartesian Two-Spacep. 3
How It's Assembledp. 3
Distance of a Point from Originp. 8
Distance between Any Two Pointsp. 12
Finding the Midpointp. 15
Practice Exercisesp. 18
A Fresh Look at Trigonometryp. 21
Circles in the Cartesian Planep. 21
Primary Circular Functionsp. 23
Secondary Circular Functionsp. 30
Pythagorean Extrasp. 33
Practice Exercisesp. 36
Polar Two-Spacep. 37
The Variablesp. 37
Three Basic Graphsp. 40
Coordinate Transformationsp. 45
Practice Exercisesp. 52
Vector Basicsp. 55
The "Cartesian Way"p. 55
The "Mar Way"p. 62
Practice Exercisesp. 71
Vector Multiplicationp. 73
Product of Scalar and Vectorp. 73
Dot Product of Two Vectorsp. 79
Cross Product of Two Vectorsp. 82
Practice Exercisesp. 88
Complex Numbers and Vectorsp. 90
Numbers with Two Partsp. 90
How Complex Numbers Behavep. 95
Complex Vectorsp. 101
Practice Exercisesp. 109
Cartesian Three-Spacep. 111
How It's Assembledp. 111
Distance of Point from Originp. 116
Distance between Any Two Pointsp. 120
Finding the Midpointp. 122
Practice Exercisesp. 126
Vectors in Cartesian Three-Spacep. 128
How They're Definedp. 128
Sum and Differencep. 134
Some Basic Propertiesp. 138
Dot Productp. 141
Cross Productp. 144
Some More Vector Lawsp. 146
Practice Exercisesp. 150
Alternative Three-Spacep. 152
Cylindrical Coordinatesp. 152
Cylindrical Conversionsp. 156
Spherical Coordinatesp. 159
Spherical Conversionsp. 164
Practice Exercisesp. 171
Review Questions and Answersp. 172
Analytic Geometryp. 209
Relations in Two-Spacep. 211
"What's aTwo-Space Relation?p. 211
What's aTwo-Space Function?p. 216
Algebra with Functionsp. 222
Practice Exercisesp. 227
Inverse Relations in Two-Spacep. 229
Finding an Inverse Relationp. 229
Finding an Inverse Functionp. 238
Practice Exercisesp. 247
Conic Sectionsp. 249
Geometryp. 249
Basic Parametersp. 253
Standard Equationsp. 258
Practice Exercisesp. 263
Exponential and Logarithmic Curvesp. 266
Graphs Involving Exponential Functionsp. 266
Graphs Involving Logarithmic Functionsp. 273
Logarithmic Coordinate Planesp. 279
Practice Exercisesp. 283
Trigonometric Curvesp. 285
Graphs Involving the Sine and Cosinep. 285
Graphs Involving the Secant and Cosecantp. 290
Graphs Involving the Tangent and Cotangentp. 296
Practice Exercisesp. 302
Parametric Equations in Two-Spacep. 304
What's a Parameter?p. 304
From Equations to Graphp. 308
From Graph to Equationsp. 314
Practice Exercisesp. 318
Surfaces in Three-Spacep. 320
Planesp. 320
Spheresp. 324
Distorted Spheresp. 328
Other Surfacesp. 337
Practice Exercisesp. 343
Lines and Curves in Three-Spacep. 345
Straight Linesp. 345
Parabolasp. 350
Circlesp. 357
Circular Helixesp. 363
Practice Exercisesp. 370
Sequences, Series, and Limitsp. 373
Repeated Additionp. 373
Repeated Multiplicationp. 378
Limit of a Sequencep. 382
Summation "Shorthand"p. 385
Limit of a Seriesp. 388
Limits of Functionsp. 390
Memorable Limits of Seriesp. 394
Practice Exercisesp. 396
Review Questions and Answersp. 399
Final Examp. 436
Worked-Out Solutions to Exercises: Chapter 1-9p. 466
Worked-Out Solutions to Exercises: Chapter 11-19p. 514
Answers to Final Exam Questionsp. 578
Special Characters in Order of Appearancep. 579
Suggested Additional Readingp. 581
Indexp. 583
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