Precalculus

by Coburn, John

• ISBN13: 9780077276508
• ISBN10: 0077276507
• Edition: 2nd
• Format: Hardcover
• Copyright: 2009-02-13
• Publisher: McGraw Hill

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

Equations and Inequalities

Linear Equations, Formulas, and Problem Solving

Linear Inequalities in One Variable

Absolute Value Equations and Inequalities

Complex Numbers

Solving Quadratic Equations

Solving Other Types of Equations

Relations, Functions and Graphs

Rectangular Coordinates; Graphing Circles and Relations

Graphs of Linear Equations

Linear Equations and Rates of Change

Functions, Notation, and Graphs of Functions

Analyzing the Graph of a Function

Toolbox Functions and Transformations

Piecewise-Defined Functions

The Algebra and Composition of Functions

Polynomial and Rational Functions

Quadratic Functions and Applications

Synthetic Division; The Remainder and Factor Theorems

The Zeroes of Polynomial Functions

Graphing Polynomial Functions

Graphing Rational Functions

Additional Insights into Rational Functions

Polynomial and Rational Inequalities

Variation: Function Models in Action

Exponential and Logarithmic Functions

One-to-One and Inverse Functions

Exponential Functions

Logarithms and Logarithmic Functions

Properties of Logarithms; Solving Exponential and Logarithmic Equations

Applications from Business, Finance, and Science

Business, Finance, and Science Applications

Introduction to Trigonometric Functions

Angle Measure, Special Triangles, and Special Angles

Unit Circles and the Trigonometry of Real Numbers

Graphs of Sine and Cosine Functions; Cosecant and Secant Functions

Graphs of Tangent and Cotangent Functions

Transformations and Applications of Trigonometric Graphs

The Trigonometry of Right Triangles

Trigonometry and the Coordinate Plane

Trigonometric Identities, Inverses, and Equations

Fundamental Identities and Families of Identities

Constructing and Verifying Identities

The Sum and Difference Identities

Double Angle, Half Angle & Product-to-Sum Identities

The Inverse Trigonometric Functions and Their Applications

Solving Basic Trigonometric Equations

General Trigonometric Equations and Applications

Applications of Trigonometry

Oblique Triangles and the Law of Sines

The Law of Cosines; Area of a Triangle

Vectors and Vector Diagrams

Vector Applications and the Dot Product

Complex Numbers in Trigonometric Form

DemoivreG++s Theorem and the Theorem on nth Roots

Systems of Equations and Inequalities

Linear Systems in Two Variables with Applications

Linear Systems in Three Variables with Applications

Partial Fraction Decomposition

Systems of Inequalities and Linear Programming

Solving Systems Using Matrices and Row Operations

The Algebra of Matrices

Solving Linear Systems Using Matrix Equations

Applications of Matrices and Determinants: Cramer's Rule, Geometry, and More

Analytical Geometry

Introduction to Analytic Geometry

The Circle and the Ellipse

The Hyperbola

The Analytic Parabola

Nonlinear Systems of Equations and Inequalities

Polar Coordinates, Equations, and Graphs

More on Conic Sections: Rotation of Axes and Polar Form

Parametric Equations and Graphs

Additional Topics in Algebra

Sequences and Series

Arithmetic Sequences

Geometric Sequences

Mathematical Induction

Counting Techniques

Introduction to Probability

The Binomial Theorem

Bridges to Calculus

An Introduction to Limits

Finding Limits Numerically and Graphically

Algebraic Methods for Finding Limits; One-Sided Limits and Continuity

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