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Precalculus: A Prelude to Calculus, 3rd Edition

Precalculus: A Prelude to Calculus, 3rd Edition

Sheldon Axler

ISBN: 978-1-119-32151-4

Nov 2016

574 pages

Select type: E-Book



Sheldon Axler's Precalculus: A Prelude to Calculus, 3rd Edition focuses only on topics that students actually need to succeed in calculus. This book is geared towards courses with intermediate algebra prerequisites and it does not assume that students remember any trigonometry. It covers topics such as inverse functions, logarithms, half-life and exponential growth, area, e, the exponential function, the natural logarithm and trigonometry.

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About the Author v

Preface to the Instructor xv

WileyPLUS xxi

Acknowledgments xxii

Preface to the Student xxiv

0 The Real Numbers 1

0.1 The Real Line 2

0.2 Algebra of the Real Numbers 7

0.3 Inequalities, Intervals, and Absolute Value 23

Chapter Summary and Chapter Review Questions 40

1 Functions and Their Graphs 41

1.1 Functions 42

1.2 The Coordinate Plane and Graphs 55

1.3 Function Transformations and Graphs 69

1.4 Composition of Functions 90

1.5 Inverse Functions 104

1.6 A Graphical Approach to Inverse Functions 119

Chapter Summary and Chapter Review Questions 129

2 Linear, Quadratic, Polynomial, and Rational Functions 133

2.1 Lines and Linear Functions 134

2.2 Quadratic Functions and Conics 150

2.3 Exponents 174

2.4 Polynomials 193

2.5 Rational Functions 208

Chapter Summary and Chapter Review Questions 223

3 Exponential Functions, Logarithms, and e 225

3.1 Logarithms as Inverses of Exponential Functions 226

3.2 Applications of the Power Rule for Logarithms 237

3.3 Applications of the Product and Quotient Rules for Logarithms 247

3.4 Exponential Growth 260

3.5 e and the Natural Logarithm 278

3.6 Approximations and area with e and ln 292

3.7 Exponential Growth Revisited 302

Chapter Summary and Chapter Review Questions 311

4 Trigonometric Functions 313

4.1 The Unit Circle 314

4.2 Radians 329

4.3 Cosine and Sine 343

4.4 More Trigonometric Functions 355

4.5 Trigonometry in Right Triangles 367

4.6 Trigonometric Identities 377

Chapter Summary and Chapter Review Questions 390

5 Trigonometric Algebra and Geometry 393

5.1 Inverse Trigonometric Functions 394

5.2 Inverse Trigonometric Identities 408

5.3 Using Trigonometry to Compute Area 417

5.4 The Law of Sines and the Law of Cosines 431

5.5 Double-Angle and Half-Angle Formulas 448

5.6 Addition and Subtraction Formulas 462

Chapter Summary and Chapter Review Questions 472

6 Applications of Trigonometry 475

6.1 Transformations of Trigonometric Functions 476

6.2 Polar Coordinates 493

6.3 Vectors 504

6.4 Complex Numbers 518

6.5 The Complex Plane 531

Chapter Summary and Chapter Review Questions 540

7 Sequences, Series, and Limits 541

7.1 Sequences 542

7.2 Series 557

7.3 Limits 576

Chapter Summary and Chapter Review Questions 589

8 Systems of Linear Equations 591

8.1 Solving Systems of Linear Equations 592

8.2 Matrices 604

Chapter Summary and Chapter Review Questions 616

Appendix A: Area 617

Circumference 617

Squares, Rectangles, and Parallelograms 618

Triangles and Trapezoids 620

Stretching 621

Circles and Ellipses 622

Exercises and Problems 625

Appendix B: Parametric Curves 629

Curves in the Coordinate Plane 629

Graphing Inverse Functions as Parametric Curves 634

Shifting, Stretching, or Flipping a Parametric Curve 635

Exercises and Problems 638

Photo Credits 640

Index 641

  • The section on transformations of trigonometric functions has been moved to Chapter 5.
  • What are now Chapters 6 and 7 were in the reverse order in the previous edition; Chapter 7 has a new title.
  • Definition boxes, result boxes, learning objectives boxes, and example label boxes have been revised.
  • Numerous improvements have been made throughout the text based upon suggestions from faculty and students who used the previous edition.
  • New exercises have been added in almost all sections. The Appendix now includes worked-out solutions to the Appendix’s exercises.
  • Manageable Size: Even with a student solutions manual included, the text is shorter and more concise than other Precalculus books. It is also cost-effective for students because they do not have to purchase a separate solutions manual.
  • Flexible and Abundant Topics: The text is not overloaded with extraneous topics.
  • Made to be Read: The writing style and layout are meant to encourage students to read and understand the material. Explanations are plentiful with descriptions of concepts making the ideas concrete whenever possible.
  • Technology Optional: To aid instructors in presenting the kind of course they want, an icon appears next to exercises and problems that require students to use a calculator. Some exercises and problems that require a calculator are intentionally designed to make students realize that by understanding the material, they can overcome the limitations of calculators.
  • Worked-Out Solutions to Odd-Numbered Exercises: These solutions are written exclusively by the author. Therefore students can expect a consistent approach to the material.