Graphical Approach to Precalculus with Limits, A

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  • Edition: 3rd
  • Format: Hardcover
  • Copyright: 2003-01-01
  • Publisher: Addison Wesley
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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
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
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
Table of Contents provided by Publisher. All Rights Reserved.

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