Precalculus

About our authors Marvin Bittinger has been teaching math at the university level for more than 38 years. Since 1968, he has been employed at Indiana University - Purdue University Indianapolis (IUPUI) and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. His hobbies include hiking in Utah, baseball, golf and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has 2 grown and married sons, Lowell and Chris, and 4 granddaughters. Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University - Purdue University Indianapolis (IUPUI). In addition to her career in textbook publishing, she enjoys traveling, spending time with her grandchildren and promoting charity projects for a children's camp. Judy Penna received her undergraduate degree in mathematics from Kansas State University and her graduate degree in mathematics from the University of Illinois. Since then, she has taught at Indiana University - Purdue University Indianapolis (IUPUI) and at Butler University, and continues to focus on writing quality textbooks for undergraduate mathematics students. In her free time she likes to travel, read, knit and spend time with her children.

1. Graphs, Functions, and Models 1.1 Introduction to Graphing 1.2 Functions and Graphs 1.3 Linear Functions, Slope, and Applications 1.4 Equations of Lines and Modeling 1.5 Linear Equations, Functions, Zeros, and Applications 1.6 Solving Linear Inequalities 2. More on Functions 2.1 Increasing, Decreasing, and Piecewise Functions; Applications 2.2 The Algebra of Functions 2.3 The Composition of Functions 2.4 Symmetry 2.5 Transformations 2.6 Variation and Applications 3. Quadratic Functions and Equations; Inequalities 3.1 The Complex Numbers 3.2 Quadratic Equations, Functions, Zeros, and Models 3.3 Analyzing Graphs of Quadratic Functions 3.4 Solving Rational Equations and Radical Equations 3.5 Solving Equations and Inequalities with Absolute Value 4. Polynomial Functions and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions 4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem 4.4 Theorems about Zeros of Polynomial Functions 4.5 Rational Functions 4.6 Polynomial Inequalities and Rational Inequalities 5. Exponential Functions and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions and Graphs 5.3 Logarithmic Functions and Graphs 5.4 Properties of Logarithmic Functions 5.5 Solving Exponential Equations and Logarithmic Equations 5.6 Applications and Models: Growth and Decay; Compound Interest 6. The Trigonometric Functions 6.1 Trigonometric Functions of Acute Angles 6.2 Applications of Right Triangles 6.3 Trigonometric Functions of Any Angle 6.4 Radians, Arc Length, and Angular Speed 6.5 Circular Functions: Graphs and Properties 6.6 Graphs of Transformed Sine and Cosine Functions 7. Trigonometric Identities, Inverse Functions, and Equations 7.1 Identities: Pythagorean and Sum and Difference 7.2 Identities: Cofunction, Double-Angle, and Half-Angle 7.3 Proving Trigonometric Identities 7.4 Inverses of the Trigonometric Functions 7.5 Solving Trigonometric Equations 8. Applications of Trigonometry 8.1 The Law of Sines 8.2 The Law of Cosines 8.3 Complex Numbers: Trigonometric Notation 8.4 Polar Coordinates and Graphs 8.5 Vectors and Applications 8.6 Vector Operations 9. Systems of Equations and Matrices 9.1 Systems of Equations in Two Variables 9.2 Systems of Equations in Three Variables 9.3 Matrices and Systems of Equations 9.4 Matrix Operations 9.5 Inverses of Matrices 9.6 Determinants and Cramer's Rule 9.7 Systems of Inequalities and Linear Programming 9.8 Partial Fractions 10. Conic Sections 10.1 The Parabola 10.2 The Circle and the Ellipse 10.3 The Hyperbola 10.4 Nonlinear Systems of Equations and Inequalities 10.5 Rotation of Axes 10.6 Polar Equations of Conics 10.7 Parametric Equations 11. Sequences, Series, and Combinatorics 11.1 Sequences and Series 11.2 Arithmetic Sequences and Series 11.3 Geometric Sequences and Series 11.4 Mathematical Induction 11.5 Combinatorics: Permutations 11.6 Combinatorics: Combinations 11.7 The Binomial Theorem 11.8 Probability