Precalculus

by Larson, Ron; Hostetler, Robert P.

• ISBN13: 9780618643448
• ISBN10: 0618643443
• Edition: 7th
• Format: Hardcover
• Copyright: 2006-01-26
• Publisher: Cengage High School

Summary

This market-leading text continues to provide both students and instructors with sound, consistently structured explanations of the mathematical concepts. Designed for a one- or two-term course that prepares students to study calculus, the new Seventh Edition retains the features that have made Precalculus a complete solution for both students and instructors: interesting applications, cutting-edge design, and innovative technology combined with an abundance of carefully written exercises. New! Side-by-side Example Solutions for select examples include multiple problem solving approaches--such as algebraic, graphical, and numerical--to appeal to a variety of teaching and learning styles. New! Checkpoints after each Example/Solution refer students to similar drills in the Section Exercises, allowing students to practice and reinforce the concepts they just learned. Answers to Checkpoints are included at the back of the book. New! Vocabulary Checks open every set of Section Exercises. This review of mathematical terms, formulas, and theorems provides regular assessment and reinforcement of students' understanding of algebraic language and concepts. Exercise Sets have been carefully analyzed and revised to improve the categorization of problems from basic skill-building to challenging; improve the pairing of similar odd- and even-numbered exercises; update all real data; and add real-life and real-data applications. New! Make a Decision applications--presented throughout the text at the end of selected exercise sets--are based on large sets of real data. These extended modeling applications give students the opportunity to use all the mathematical concepts and techniques they've learned and apply them to large sets of real date--analyzing it, graphing it, and making conjectures about its behavior. These applications are featured in Eduspace and the Online Learning Center in an interactive format. Eduspace, powered by Blackboard, Houghton Mifflin's online learning environment, brings your students quality online homework, tutorials, multimedia, and testing that correspond to the College Algebra text. This content is paired with the recognized course management tools of Blackboard. For copyright 2007, two titles have been added to the Precalculus Series: Precalculus with Limits and Precalculus: A Concise Course. These titles enhance the scope of the series, making it even more flexible and adaptable to a variety of learning and teaching styles.

Table of Contents

Note: Each chapter concludes with a Chapter Summary, Review Exercises, a Chapter Test, Proofs in Mathematics, and P.S. Problem Solving

Functions and Their Graphs

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions: Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Polynomial and Rational Functions

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential and Logarithmic Functions

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models Cumulative Test: Chapters 1–3

Trigonometry

Radian and Degree Measure

Trigonometric Functions: The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Analytic Trigonometry

Using Fundamental Identities

Verifying Trigonometric Identities

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple-Angle and Product-to-Sum Formulas

Additional Topics in Trigonometery

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number Cumulative Test: Chapters 4–6

Systems of Equations and Inequalities

Linear and Nonlinear Systems of Equations

Two-Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Determinants

Matrices and Systems of Equations

Operations with Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences, Series, and Probability

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability Cumulative Test: Chapters 7–9

Topics in Analytic Geometry

Lines

Introduction to Conics: Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

Polar Coordinates

Graphs of Polar Equations

Polar Equations of Conics

Analytic Geometry in Three Dimensions

The Three-Dimensional Coordinate System

Vectors in Space

The Cross Product of Two Vectors

Lines and Planes in Space

Limits and an Introduction to Calculus

Introduction to Limits

Techniques for Evaluating Limits

The Tangent Line Problem

Limits at Infinity and Limits of Sequences

The Area Problem Cumulative Test: Chapters 10–12

Appendix

Review of Fundamental Concepts of Algebra

Real Numbers and Their Properties

Exponents and Radicals

Polynomials and Factoring

Rational Expressions

Solving Equations

Linear Inequalities in One Variable

Errors and the Algebra of Calculus

Appendix

Concepts in Statistics (web)

Representing Data

Measures of Central Tendency and Dispersion

Least Squares Regression

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