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Algebra and Trigonometry

Algebra and Trigonometry

Sheldon Axler

ISBN: 978-0-470-47081-7

Mar 2011

784 pages


Axler Algebra & Trigonometry is written for the two semester course. The text provides students with the skill and understanding needed for their coursework and for participating as an educated citizen in a complex society. Axler Algebra & Trigonometry focuses on depth, not breadth of topics by exploring necessary topics in greater detail. Readers will benefit from the straightforward definitions and plentiful examples of complex concepts. The Student Solutions Manual is integrated at the end of every section. The proximity of the solutions encourages students to go back and read the main text as they are working through the problems and exercises. The inclusion of the manual also saves students money.

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About the Author v

Preface to the Instructor xvi

WileyPLUS xxii

Acknowledgments xxiii

Preface to the Student xxvi

1 The Real Numbers 1

1.1 The Real Line 2

1.2 Algebra of the Real Numbers 7

1.3 Inequalities, Intervals, and Absolute Value 24

2 Combining Algebra and Geometry 41

2.1 The Coordinate Plane 42

2.2 Lines 57

2.3 Quadratic Expressions and Conic Sections 75

2.4 Area 98

3 Functions and Their Graphs 117

3.1 Functions 118

3.2 Function Transformations and Graphs 142

3.3 Composition of Functions 165

3.4 Inverse Functions 180

3.5 A Graphical Approach to Inverse Functions 197

4 Polynomial and Rational Functions 213

4.1 Integer Exponents 214

4.2 Polynomials 227

4.3 Rational Functions 245

4.4 Complex Numbers 262

5 Exponents and Logarithms 279

5.1 Exponents and Exponential Functions 280

5.2 Logarithms as Inverses of Exponential Functions 293

5.3 Applications of Logarithms 310

5.4 Exponential Growth 328

6 e and the Natural Logarithm 349

6.1 Defining e and ln 350

6.2 Approximations and area with e and ln 366

6.3 Exponential Growth Revisited 376

7 Systems of Equations 387

7.1 Equations and Systems of Equations 388

7.2 Solving Systems of Linear Equations 399

7.3 Solving Systems of Linear Equations Using Matrices 411

7.4 Matrix Algebra 424

8 Sequences, Series, and Limits 447

8.1 Sequences 448

8.2 Series 463

8.3 Limits 483

9 Trigonometric Functions 497

9.1 The Unit Circle 498

9.2 Radians 514

9.3 Cosine and Sine 529

9.4 More Trigonometric Functions 542

9.5 Trigonometry in Right Triangles 555

9.6 Trigonometric Identities 566

10 Trigonometric Algebra and Geometry 583

10.1 Inverse Trigonometric Functions 584

10.2 Inverse Trigonometric Identities 599

10.3 Using Trigonometry to Compute Area 613

10.4 The Law of Sines and the Law of Cosines 628

10.5 Double-Angle and Half-Angle Formulas 644

10.6 Addition and Subtraction Formulas 658

11 Applications of Trigonometry 671

11.1 Parametric Curves 672

11.2 Transformations of Trigonometric Functions 687

11.3 Polar Coordinates 705

11.4 Vectors 718

11.5 The Complex Plane 732

Photo Credits 743

Index 745

  • Depth, Not Breadth: Topics have been carefully selected to get at the heart of algebraic weakness by narrowing down to key sets of skills which are regularly revisited from varied perspectives.
  • Unit-circle Approach: This approach is used because calculus requires the unit-circle approach and it allows for a well-motivated introduction to radian measure. Once the approach has been introduced, applications to right triangles are given.
  • Exercises and Problems: The difference between an exercise and a problem is that each exercise has a unique correct answer that is a mathematical object such as a number or a function, while the solutions to problems consist of explanations or examples. The solutions to the odd-numbered exercises appear directly behind the relevant section.
  • Variety: Exercises and problems in this book vary greatly in difficulty and purpose. Some exercises and problems are designed to hone algebraic manipulation skills; other exercises and problems are designed to push students to genuine understanding. Applications are written to reflect real scenarios, not artificial examples.
  • Integrated Student's Solutions Manual: The solutions manual encourages students to read the main text and students will save money by not having to purchase a separate solutions manual.
  • Designed to be Read: The writing style and layout are meant to induce students to read and understand the material. Explanations are more plentiful than typically found in College Algebra books, with examples of concepts making the ideas concrete whenever possible.
  • Calculator Problems: A symbol appears next to problems that require a calculator, and some exercises and problems are designed to make students realize that by understanding the material, they can overcome the limitations of calculators.