Pre-calculus know-it-all

Contents......Page 8
Preface......Page 12
Acknowledgments......Page 14
Part 1 Coordinates and Vectors......Page 18
How It’s Assembled......Page 20
Distance of a Point from Origin......Page 25
Distance between Any Two Points......Page 29
Finding the Midpoint......Page 32
Practice Exercises......Page 35
Circles in the Cartesian Plane......Page 38
Primary Circular Functions......Page 40
Secondary Circular Functions......Page 47
Pythagorean Extras......Page 50
Practice Exercises......Page 53
The Variables......Page 54
Three Basic Graphs......Page 57
Coordinate Transformations......Page 62
Practice Exercises......Page 69
The “Cartesian Way”......Page 72
The “Polar Way”......Page 79
Practice Exercises......Page 88
Product of Scalar and Vector......Page 90
Dot Product of Two Vectors......Page 96
Cross Product of Two Vectors......Page 99
Practice Exercises......Page 105
Numbers with Two Parts......Page 107
How Complex Numbers Behave......Page 112
Complex Vectors......Page 118
Practice Exercises......Page 126
How It’s Assembled......Page 128
Distance of Point from Origin......Page 133
Distance between Any Two Points......Page 137
Finding the Midpoint......Page 139
Practice Exercises......Page 143
How They’re Defined......Page 145
Sum and Difference......Page 151
Some Basic Properties......Page 155
Dot Product......Page 158
Cross Product......Page 161
Some More Vector Laws......Page 163
Practice Exercises......Page 167
Cylindrical Coordinates......Page 169
Cylindrical Conversions......Page 173
Spherical Coordinates......Page 176
Spherical Conversions......Page 181
Practice Exercises......Page 188
10 Review Questions and Answers......Page 189
Part 2 Analytic Geometry......Page 226
What’s a Two-Space Relation?......Page 228
What’s a Two-Space Function?......Page 233
Algebra with Functions......Page 239
Practice Exercises......Page 244
Finding an Inverse Relation......Page 246
Finding an Inverse Function......Page 255
Practice Exercises......Page 264
Geometry......Page 266
Basic Parameters......Page 270
Standard Equations......Page 275
Practice Exercises......Page 280
Graphs Involving Exponential Functions......Page 283
Graphs Involving Logarithmic Functions......Page 290
Logarithmic Coordinate Planes......Page 296
Practice Exercises......Page 300
Graphs Involving the Sine and Cosine......Page 302
Graphs Involving the Secant and Cosecant......Page 307
Graphs Involving the Tangent and Cotangent......Page 313
Practice Exercises......Page 319
What’s a Parameter?......Page 321
From Equations to Graph......Page 325
From Graph to Equations......Page 331
Practice Exercises......Page 335
Planes......Page 337
Spheres......Page 341
Distorted Spheres......Page 345
Other Surfaces......Page 354
Practice Exercises......Page 360
Straight Lines......Page 362
Parabolas......Page 367
Circles......Page 374
Circular Helixes......Page 380
Practice Exercises......Page 387
Repeated Addition......Page 390
Repeated Multiplication......Page 395
Limit of a Sequence......Page 399
Summation “Shorthand”......Page 402
Limit of a Series......Page 405
Limits of Functions......Page 407
Memorable Limits of Series......Page 411
Practice Exercises......Page 413
20 Review Questions and Answers......Page 416
Final Exam......Page 453
Appendix A: Worked-Out Solutions to Exercises: Chapter 1-9......Page 483
Appendix B: Worked-Out Solutions to Exercises: Chapter 11-19......Page 531
Appendix C: Answers to Final Exam Questions......Page 595
Appendix D: Special Characters in Order of Appearance......Page 596
Suggested Additional Reading......Page 598
C......Page 600
D......Page 601
H......Page 602
P......Page 603
R......Page 604
VW......Page 605
XYZ......Page 606