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Summary
Three components contribute to a theme sustained throughout the Coburn Series: that of laying a firm foundation, building a solid framework, and providing strong connections. Not only does Coburn present a sound problem-solving process to teach students to recognize a problem, organize a procedure, and formulate a solution, the text encourages students to see beyond procedures in an effort to gain a greater understanding of the big ideas behind mathematical concepts. Written in a readable, yet mathematically mature manner appropriate for college algebra level students, Coburn's Precalculus uses narrative, extensive examples, and a range of exercises to connect seemingly disparate mathematical topics into a cohesive whole. Coburn's hallmark applications are born out of the author's extensive experiences in and outside the classroom, and appeal to the vast diversity of students and teaching methods in this course area. Benefiting from the feedback of hundreds of instructors and students across the country, Precalculus second edition, continues to emphasize connections in order to improve the level of student engagement in mathematics and increase their chances of success in college algebra.
Table of Contents
Chapter 1: Equations and Inequalities
1-1 Linear Equations, Formulas, and Problem Solving
1-2 Linear Inequalities in One Variable
1-3 Absolute Value Equations and Inequalities
1-4 Complex Numbers
1-5 Solving Quadratic Equations
1-6 Solving Other Types of Equations
Chapter 2: Relations, Functions and Graphs
2-1 Rectangular Coordinates; Graphing Circles and Relations
2-2 Graphs of Linear Equations
2-3 Linear Equations and Rates of Change
2-4 Functions, Notation, and Graphs of Functions
2-5 Analyzing the Graph of a Function
2-6 Toolbox Functions and Transformations
2-7 Piecewise-Defined Functions
2-8 The Algebra and Composition of Functions
Chapter 3: Polynomial and Rational Functions
3-1 Quadratic Functions and Applications
3-2 Synthetic Division; The Remainder and Factor Theorems
3-3 The Zeroes of Polynomial Functions
3-4 Graphing Polynomial Functions
3-5 Graphing Rational Functions
3-6 Additional Insights into Rational Functions
3-7 Polynomial and Rational Inequalities
3-8 Variation: Function Models in Action
Chapter 4: Exponential and Logarithmic Functions
4-1 One-to-One and Inverse Functions
4-2 Exponential Functions
4-3 Logarithms and Logarithmic Functions
4-4 Properties of Logarithms; Solving Exponential and Logarithmic Equations
4-5 Applications from Business, Finance, and Science
Chapter 5: Introduction to Trigonometric Functions
5-1 Angle Measure, Special Triangles, and Special Angles
5-2 Unit Circles and the Trigonometry of Real Numbers
5-3 Graphs of Sine and Cosine Functions; Cosecant and Secant Functions
5-4 Graphs of Tangent and Cotangent Functions
5-5 Transformations and Applications of Trigonometric Graphs
5-6 The Trigonometry of Right Triangles
5-7 Trigonometry and the Coordinate Plane
Chapter 6: Trigonometric Identities, Inverses, and Equations
6-1 Fundamental Identities and Families of Identities