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PRECALCULUS, Fourth Edition focuses on teaching the essentials of what a student needs to fulfill their PreCalculus requirement and to fully prepare them to succeed in calculus. It provides students with an integrated review of algebra and trigonometry while focusing on essential calculus concepts. Faires and DeFranza prepare students for calculus by providing a solid grounding in analysis and graphing, tools necessary to make a successful transition to calculus. This streamlined text provides all the mathematics that students need--it doesn't bog them down in review, or overwhelm them with too much, too soon. The authors are careful to keep this book, unlike many of the PreCalculus books on the market, at a length that can be covered in one term.
1. FUNCTIONS.
Introduction.
The Real Line.
Inequalities.
Intervals.
Absolute Values.
The Coordinate Plane.
Distance Between Points in the Plane.
Circles in the Plane.
Completing the Square.
Equations and Graphs.
Graphs of Equations.
Symmetry of a Graph.
Using Technology to Graph Equations.
Functions.
Applications of Functions.
Linear Functions.
Parallel and Perpendicular Lines.
Quadratic Functions.
The Standard Form of a Quadratic Equation.
The Quadratic Formula.
2. NEW FUNCTIONS FROM OLD.
Introduction.
Other Common Functions.
The Absolute Value Function.
The Square Root Function.
The Greatest Integer Function.
Arithmetic Combinations of Functions.
Composition of Functions.
Inverse Functions.
3. ALGEBRAIC FUNCTIONS.
Introduction.
Polynomial Functions.
Finding Factors and Zeros of Polynomials.
The Rational Zero Test.
Rational Functions.
Other Algebraic Functions.
Complex Roots of Polynomials.
4. TRIGONOMETRIC FUNCTIONS.
Introduction.
Measuring Angles.
Length of a Circular Arc. Area of a Circular Sector.
The Sine and Cosine Functions.
Graphs of the Sine and Cosine Functions.
Other Trigonometric Functions.
The Graph of the Tangent Function.
Trigonometric Identities.
Pythagorean Identities.
Sum and Difference Formulas.
Double Angle Formulas.
Half Angle Formulas.
Products of Sines and Cosines.
Right-Triangle Trigonometry.
Inverse Trigonometric Functions.
Applications of Trigonometric Functions.
Law of Cosines.
Law of Sines.
Simple Harmonic Motion.
Heron's Formula.
5. EXPONENTIAL AND LOGARITHM FUNCTIONS.
Introduction.
The Natural Exponential Function.
Compound Interest.
Logarithm Functions.
Exponential Growth and Decay.
6. CONIC SECTIONS, POLAR COORDINATES, AND PARAMETRIC EQUATIONS.
Introduction. Parabolas.
Ellipses.
Hyperbolas.
Polar Coordinates.
Graphs of Polar Equations.
Conic Sections in Polar Coordinates.
Parametric Equations.
J. Douglas Faires and James DeFranza
ISBN13: 978-0495012696PRECALCULUS, Fourth Edition focuses on teaching the essentials of what a student needs to fulfill their PreCalculus requirement and to fully prepare them to succeed in calculus. It provides students with an integrated review of algebra and trigonometry while focusing on essential calculus concepts. Faires and DeFranza prepare students for calculus by providing a solid grounding in analysis and graphing, tools necessary to make a successful transition to calculus. This streamlined text provides all the mathematics that students need--it doesn't bog them down in review, or overwhelm them with too much, too soon. The authors are careful to keep this book, unlike many of the PreCalculus books on the market, at a length that can be covered in one term.
Table of Contents
1. FUNCTIONS.
Introduction.
The Real Line.
Inequalities.
Intervals.
Absolute Values.
The Coordinate Plane.
Distance Between Points in the Plane.
Circles in the Plane.
Completing the Square.
Equations and Graphs.
Graphs of Equations.
Symmetry of a Graph.
Using Technology to Graph Equations.
Functions.
Applications of Functions.
Linear Functions.
Parallel and Perpendicular Lines.
Quadratic Functions.
The Standard Form of a Quadratic Equation.
The Quadratic Formula.
2. NEW FUNCTIONS FROM OLD.
Introduction.
Other Common Functions.
The Absolute Value Function.
The Square Root Function.
The Greatest Integer Function.
Arithmetic Combinations of Functions.
Composition of Functions.
Inverse Functions.
3. ALGEBRAIC FUNCTIONS.
Introduction.
Polynomial Functions.
Finding Factors and Zeros of Polynomials.
The Rational Zero Test.
Rational Functions.
Other Algebraic Functions.
Complex Roots of Polynomials.
4. TRIGONOMETRIC FUNCTIONS.
Introduction.
Measuring Angles.
Length of a Circular Arc. Area of a Circular Sector.
The Sine and Cosine Functions.
Graphs of the Sine and Cosine Functions.
Other Trigonometric Functions.
The Graph of the Tangent Function.
Trigonometric Identities.
Pythagorean Identities.
Sum and Difference Formulas.
Double Angle Formulas.
Half Angle Formulas.
Products of Sines and Cosines.
Right-Triangle Trigonometry.
Inverse Trigonometric Functions.
Applications of Trigonometric Functions.
Law of Cosines.
Law of Sines.
Simple Harmonic Motion.
Heron's Formula.
5. EXPONENTIAL AND LOGARITHM FUNCTIONS.
Introduction.
The Natural Exponential Function.
Compound Interest.
Logarithm Functions.
Exponential Growth and Decay.
6. CONIC SECTIONS, POLAR COORDINATES, AND PARAMETRIC EQUATIONS.
Introduction. Parabolas.
Ellipses.
Hyperbolas.
Polar Coordinates.
Graphs of Polar Equations.
Conic Sections in Polar Coordinates.
Parametric Equations.