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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.
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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