9780495392774

Precalculus Mathematics for Calculus, Enhanced Review Edition

by ; ;
  • ISBN13:

    9780495392774

  • ISBN10:

    0495392774

  • Edition: 5th
  • Format: Hardcover
  • Copyright: 2/5/2007
  • Publisher: Cengage Learning
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Summary

This best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, so that when students finish the course, they have a solid foundation in the principles of mathematical thinking. This comprehensive, evenly paced book provides complete coverage of the function concept and integrates substantial graphing calculator materials that help students develop insight into mathematical ideas. The authors' attention to detail and clarity, as in James Stewart's market-leading Calculus text, is what makes this text the market leader.

Table of Contents

Fundamentals
Overview
Real Numbers
Exponents and Radicals
Algebraic Expressions
Discovery Project: Visualizing a Formula
Fractional Expressions
Equations
Modeling with Equations
Discovery Project: Equations through the Ages
Inequalities
Coordinate Geometry
Graphing Calculators: Solving Equations and Inequalities Graphically
Lines
Modeling Variation
Review
Test
Focus on Problem Solving: General Principles
Functions
Overview
What is a Function? Graphs of Functions
Discovery Project: Relations and Functions
Increasing and Decreasing Functions: Average Rate of Change
Transformations of Functions
Quadratic Functions: Maxima and Minima
Modeling with Functions
Combining Functions
Discovery
Project: Iteration and Chaos
One-to-One Functions and Their Inverses Review
Test
Focus on Modeling: Fitting Lines to Data
Polynomial and Rational Functions
Overview
Polynomial Functions and Their Graphs
Dividing Polynomials
Real Zeros of Polynomials
Discovery Project: Zeroing in on a Zero
Complex Numbers
Complex Zeros and the Fundamental Theorem of Algebra
Rational Functions
Review
Test
Focus on Modeling: Fitting Polynomials to Data
Exponential and Logarithmic Functions
Overview
Exponential Functions
Discovery Project: Exponential Explosion
Logarithmic Functions
Laws of Logarithms
Exponential and Logarithmic Equations
Modeling with Exponential and Logarithmic Functions
Review
Test
Focus on Modeling: Fitting Exponential and Power Curves to Data
Trigonometric Functions of Real Numbers
Overview
The Unit Circle
Trigonometric Functions of Real Numbers
Trigonometric Graphs
Discovery Project: Predator-Prey Models
More Trigonometric Graphs
Modeling Harmonic Motion
Review
Test
Focus on Modeling: Fitting Sinusoidal Curves to Data
Trigonometric Functions of Angles
Overview
Angle Measure
Trigonometry of Right Triangles
Discovery Project: Similarity
Trigonometric Functions of Angles
The Law of Sines
The Law of Cosines
Review
Test
Focus on Modeling:Surveying
Analytic Trigonometry
Overview
Trigonometric Identities
Addition and Subtraction Formulas
Double-Angle, Half-Angle, and Sum-Product Identities
Inverse Trigonometric Functions
Discovery Project: Where to Sit at the Movies
Trigonometric Equations
Review
Test
Focus on Modeling: Traveling and Standing Waves
Polar Coordinates and Vectors
Overview
Polar Coordinates
Graphs of Polar Equations
Polar Form of Complex Numbers
DeMoivre's Theorem
Discovery Project: Fractals
Vectors
The Dot Product
Discovery Project: Sailing Against the Wind
Review
Test
Focus on Modeling: Mapping the World
Systems of Equations and Inequalities
Overview
Systems of Equations
Systems of Linear Equations in Two Variables
Systems of Linear Equations in Several Variables
Discovery Project: Best Fit versus Exact Fit
Systems of Linear Equations: Matrices
The Algebra of Matrices
Discovery Project: Will the Species Survive? Inverses of Matrices and Matrix Equations
Discovery Project: Computer Graphics
I Determinants and Cramer's Rule
Partial Fractions
Systems of Inequalities
Review
Test
Focus on Modeling: Linear Programming
Analytic Geometry
Overview
Parabolas
Ellipses
Hyperbolas
Discovery Project: Conics in Architecture Shifted Conics
Rotation of Axes
Discovery Project: Computer Graphics II
Polar Equations of Conics
Plane Curves and Parametric Equations
Review
Test
Focus on Modeling: The Path of a Projectile
Sequences and Series
Overview
Sequences and Summation Notation
Arithmetic Sequences
Geometric Sequences
Discovery Project: Finding Patterns
Mathematical Finance
Mathematical Induction
The Binomial Theorem
Review
Test
Focus on Modeling: Modeling with Recursive Sequences
Limits: A Preview of Calculus
Overview
Finding Limits Numerically and Graphically
Finding Limits Algebraically
Tangent Lines and Derivatives
Discovery Project: Designing a Roller Coaster
Limits at
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