Algebra and Trigonometry

Sheldon Axler is well-known within the mathematics community. He has an Ivy League education, having received his AB in mathematics from Princeton in 1971, and his PhD in mathematics from UC Berkeley in 1975. Currently, Sheldon is the Dean of the College of Science and Engineering at SFSU. Previously, he held teaching positions at Michigan State, UC Berkeley, Indiana University, and MIT. He has received numerous grants, awards, and fellowships throughout his career. He regularly speaks at conferences and conventions and has done extensive writing in his discipline. Notably, he is the author of a successful textbook for the second course in linear Algebra, published with Springer and has held several editorial positions for mathematics journals and is currently a series editor for Springer.As the author for Wiley's Precalculus: A Prelude to Calculus, Sheldon has shown himself an able and willing promoter of his title, garnering the interest of his colleagues nationwide and proving himself a valuable and responsive resource for our sales force.

• About the Author vPreface to the Instructor xviWileyPLUS xxiiAcknowledgments xxiiiPreface to the Student xxvi1 The Real Numbers 11.1 The Real Line 21.2 Algebra of the Real Numbers 71.3 Inequalities, Intervals, and Absolute Value 242 Combining Algebra and Geometry 412.1 The Coordinate Plane 422.2 Lines 572.3 Quadratic Expressions and Conic Sections 752.4 Area 983 Functions and Their Graphs 1173.1 Functions 1183.2 Function Transformations and Graphs 1423.3 Composition of Functions 1653.4 Inverse Functions 1803.5 A Graphical Approach to Inverse Functions 1974 Polynomial and Rational Functions 2134.1 Integer Exponents 2144.2 Polynomials 2274.3 Rational Functions 2454.4 Complex Numbers 2625 Exponents and Logarithms 2795.1 Exponents and Exponential Functions 2805.2 Logarithms as Inverses of Exponential Functions 2935.3 Applications of Logarithms 3105.4 Exponential Growth 3286 e and the Natural Logarithm 3496.1 Defining e and ln 3506.2 Approximations and area with e and ln 3666.3 Exponential Growth Revisited 3767 Systems of Equations 3877.1 Equations and Systems of Equations 3887.2 Solving Systems of Linear Equations 3997.3 Solving Systems of Linear Equations Using Matrices 4117.4 Matrix Algebra 4248 Sequences, Series, and Limits 4478.1 Sequences 4488.2 Series 4638.3 Limits 4839 Trigonometric Functions 4979.1 The Unit Circle 4989.2 Radians 5149.3 Cosine and Sine 5299.4 More Trigonometric Functions 5429.5 Trigonometry in Right Triangles 5559.6 Trigonometric Identities 56610 Trigonometric Algebra and Geometry 58310.1 Inverse Trigonometric Functions 58410.2 Inverse Trigonometric Identities 59910.3 Using Trigonometry to Compute Area 61310.4 The Law of Sines and the Law of Cosines 62810.5 Double-Angle and Half-Angle Formulas 64410.6 Addition and Subtraction Formulas 65811 Applications of Trigonometry 67111.1 Parametric Curves 67211.2 Transformations of Trigonometric Functions 68711.3 Polar Coordinates 70511.4 Vectors 71811.5 The Complex Plane 732Photo Credits 743Index 745