Graphical Approach to Precalculus with Limits, A

by Hornsby, John; Lial, Margaret L.; Rockswold, Gary K.

• ISBN13: 9780201735130
• ISBN10: 020173513X
• Edition: 3rd
• Format: Hardcover
• Copyright: 2003-01-01
• Publisher: Addison Wesley

Summary

This series is the culmination of many years of teaching experience with the graphing calculator. the books were written from the beginning for use with the graphing calculator. Throughout the text, the authors emphasize the power of technology but provide numerous warnings of its limitations: they stress that only through understanding the mathematical concepts can students fully appreciate the power of graphing calculators and use technology appropriately. Additionally, the authors consistently use the same four-step process when introducing the different classes of functions. This allows students to easily make connections between graphs of functions and their associated equations and inequalities.

Table of Contents

Linear Functions, Equations, and Inequalities

Real Numbers and Coordinate Systems

Introduction to Relations and Functions

Linear Functions

Equations of Lines and Linear Models

Linear Equations and Inequalities

Applications of Linear Functions

Analysis of Graphs of Functions

Graphs of Basic Functions and Relations; Symmetry

Vertical and Horizontal Shifts of Graphs

Stretching, Shrinking, and Reflecting Graphs

Absolute Value Functions: Graphs, Equations, Inequalities, and Applications

Piecewise-Defined Functions

Operations and Composition

Polynomial Functions

Complex Numbers

Quadratic Functions and Graphs

Quadratic Equations and Inequalities

Further Applications of Quadratic Functions and Models

Higher Degree Polynomial Functions and Graphs

Topics in the Theory of Polynomial Functions (I)

Topics in the Theory of Polynomial Functions (II)

Polynomial Equations and Inequalities; Further Applications and Models

Rational, Power, and Root Functions

Rational Functions and Graphs

More on Graphs of Rational Functions

Rational Equations, Inequalities, Applications, and Models

Functions Defined by Powers and Roots

Equations, Inequalities, and Applications Involving Root Functions

Inverse, Exponential, and Logarithmic Functions

Inverse Functions

Exponential Functions

Logarithms and Their Properties

Logarithmic Functions

Exponential and Logarithmic Equations and Inequalities

Applications and Modeling with Exponential and Logarithmic Functions

Analytic Geometry

Circles and Parabolas

Ellipses and Hyperbolas

Summary of the Conic Sections

Parametric Equations

Matrices and Systems of Equations and Inequalities

Systems of Equations

Solution of Linear Systems by the Echelon Method

Solution of Linear Systems by Row Transformations

Matrix Properties and Operations

Determinants and Cramer's Rule

Solution of Linear Systems by Matrix Inverses

Systems of Inequalities and Linear Programming

Partial Fractions

Trigonometric Functions and Applications

The Trigonometric (Circular) Functions

Graphs of the Sine and Cosine Functions

Graphs of the Other Circular Functions

Angles and Their Measures

Right Triangles and Functions of Angles

Evaluating Trigonometric Functions

Applications of Right Triangles

Harmonic Motion

Trigonometric Identities and Equations

Identities

Further Identities

The Inverse Circular Functions

Trigonometric Equations and Inequalities

Further Equations and Inequalities

Applications of Trigonometry; Vectors

The Law of Sines

The Law of Cosines and Area Formulas

Vectors and Their Applications

Trigonometric (Polar) Form of Complex Numbers

Powers and Roots of Complex Numbers

Polar Equations, Graphs, and Applications

More Parametric Equations

Further Topics in Algebra

Sequences and Series

Arithmetic Sequences and Series

Geometric Sequences and Series

The Binomial Theorem

Mathematical Induction

Counting Theory

Probability

An Introduction to Calculus: Limits and Derivatives

An Introduction to Limits

Techniques for Calculating Limits

One-Sided Limits; Limits Involving Infinity

Tangent Lines and Derivatives

Area Under a Curve

R. Reference: Basic Algebraic Concepts and Geometry Formulas

Review of Exponents and Polynomials

Review of Factoring

Review of Rational Expressions

Review of Negative and Rational Exponents

Review of Radicals

Review of Geometry Formulas

Vectors in Space

Polar Form of Conic Sections

Rotation of Axes

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