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Full Description
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.
Axler Algebra & Trigonometry is available with WileyPLUS; an innovative, research-based, online environment for effective teaching and learning.
Contents
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
