by Judith A. Beecher, Judith A. Penna and Marvin L. Bittinger

ISBN13: 978-0321460066

ISBN10: 0321460065

Cover type:

Edition/Copyright: 3RD 08

Publisher: Addison-Wesley Longman, Inc.

Published: 2008

International: No

ISBN10: 0321460065

Cover type:

Edition/Copyright: 3RD 08

Publisher: Addison-Wesley Longman, Inc.

Published: 2008

International: No

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These authors have created a book to really help students visualize mathematics for better comprehension. By creating algebraic visual side-by-sides to solve various problems in the examples, the authors show students the relationship of the algebraic solution with the visual, often graphical, solution. In addition, the authors have added a variety of new tools to help students better use the book for maximum effectiveness to not only pass the course, but truly understand the material.

Features

- Functions Early and Integrated: Functions are introduced right away in Chapter 1 to get students interested in a new topic. Equations and expressions are reviewed in the second chapter showing their connection to functions. This approach engages students from the start and gives them a taste of what they will learn in this course, instead of starting out with a review of concepts learned in previous courses.
- Algebraic Visual Side-by-Sides: Examples are worked out both algebraically and visually to increase student understanding of the concepts. Additionally, seeing these solutions side-by-side helps students make the connection between algebraic manipulation and the graphical interpretation.
- Zeros, Solutions, and x-Intercepts Theme: This theme allows students to reach a new level of mathematical comprehension through connecting the concepts of the real zeros of the function, the solutions of the associated equation, and the x-coordinates of the x-intercept of the graph of the function.
- Technology Connection: In each chapter, optional Technology Connections guide students in the use of the graphing calculator as another way to check problems.
- Review Icon: These notes reference an earlier, related section where a student can go to review a concept being used in the current section.
- Study Tips: These occasional, brief reminders appear in the margin and promote effective study habits such as good note taking and exam preparation.
- Connecting the Concepts: Comprehension is streamlined and retention is maximized when the student views a concept in a visual form, rather than a paragraph. Combining design and art, this feature highlights the importance of connecting concepts. Its visual aspect invites the student to stop and check that he or she has understood how the concepts within a section or several sections work together.
- Visualizing the Graph: This feature asks students to match an equation with its graph. This focus on visualization and conceptual understanding appears in every chapter to help students see ''the big picture.''
- Vocabulary Review: Appearing once per chapter in the Skill Maintenance portion of an exercise set, this feature checks and reviews students' understanding of the language of mathematics.
- Classify the Function: With a focus on conceptual understanding, students are asked to identify a number of functions by their type (i. e., linear, quadratic, rational, and so forth). As students progress through the text, the variety of functions they know increases and these exercises become more challenging. These exercises appear with the review exercises in the Skill Maintenance portion of an exercise set.

**Chapter R Basic Concepts of Algebra**

R.1 The Real-Number System

R.2 Integer Exponents, Scientific Notation, and Order of Operations

R.3 Addition, Subtraction, and Multiplication of Polynomials

R.4 Factoring

R.5 Rational Expressions

R.6 Radical Notation and Rational Exponents

R.7 The Basics of Equation Solving

**Chapter 1 Graphs, Functions, and Models**

1.1 Introduction to Graphing

1.2 Functions and Graphs

1.3 Linear Functions, Slope, and Applications

1.4 Equations of Lines and Modeling

1.5 More on Functions

1.6 The Algebra of Functions

1.7 Symmetry and Transformations

**Chapter 2 Functions, Equations, and Inequalities**

2.1 Linear Equations, Functions, and Models

2.2 The Complex Numbers

2.3 Quadratic Equations, Functions, and Models

2.4 Analyzing Graphs of Quadratic Functions

2.5 More Equation Solving

2.6 Solving Linear Inequalities

**Chapter 3 Polynomial And Rational Functions**

3.1 Polynomial Functions and Models

3.2 Graphing Polynomial Functions

3.3 Polynomial Division; The Remainder and Factor Theorems

3.4 Theorems about Zeros of Polynomial Functions

3.5 Rational Functions

3.6 Polynomial and Rational Inequalities

3.7 Variation and Applications

**Chapter 4 Exponential and Logarithmic Functions**

4.1 Inverse Functions

4.2 Exponential Functions and Graphs

4.3 Logarithmic Functions and Graphs

4.4 Properties of Logarithmic Functions

4.5 Solving Exponential and Logarithmic Equations

4.6 Applications and Models: Growth and Decay, and Compound Interest

**Chapter 5 The Trigonometric Functions**

5.1 Trigonometric Functions of Acute Angles

5.2 Applications of Right Triangles

5.3 Trigonometric Functions of Any Angle

5.4 Radians, Arc Length, and Angular Speed

5.5 Circular Functions: Graphs and Properties

5.6 Graphs of Transformed Sine and Cosine Functions

**Chapter 6 Trigonometric Identities, Inverse Functions, and Equations**

6.1 Identities: Pythagorean and Sum and Difference

6.2 Identities: Cofunction, Double-Angle, and Half-Angle

6.3 Proving Trigonometric Identities

6.4 Inverses of the Trigonometric Functions

6.5 Solving Trigonometric Equations

**Chapter 7 Applications of Trigonometry**

7.1 The Law of Sines

7.2 The Law of Cosines

7.3 Complex Numbers: Trigonometric Form

7.4 Polar Coordinates and Graphs

7.5 Vectors and Applications

7.6 Vector Operations

**Chapter 8 Systems of Equations and Matrices**

8.1 Systems of Equations in Two Variables

8.2 Systems of Equations in Three Variables

8.3 Matrices and Systems of Equations

8.4 Matrix Operations

8.5 Inverses of Matrices

8.6 Determinants and Cramer's Rule

8.7 Systems of Inequalities and Linear Programming

8.8 Partial Fractions

**Chapter 9 Analytic Geometry Topics **

9.1 The Parabola

9.2 The Circle and the Eclipse

9.3 The Hyperbola

9.4 Nonlinear Systems of Equations and Inequalities

9.5 Rotation of Axes

9.6 Polar Equations of Conics

9.7 Parametric Equations

**Chapter 10 Sequences, Series, and Combinatorics**

10.1 Sequences and Series

10.2 Arithmetic Sequences and Series

10.3 Geometric Sequences and Series

10.4 Mathematical Induction

10.5 Combinatorics: Permutations

10.6 Combinatorics: Combinations

10.7 The Binomial Theorem

10.8 Probability

Appendix: Basic Concepts from Geometry

Judith A. Beecher, Judith A. Penna and Marvin L. Bittinger

ISBN13: 978-0321460066ISBN10: 0321460065

Cover type:

Edition/Copyright: 3RD 08

Publisher: Addison-Wesley Longman, Inc.

Published: 2008

International: No

These authors have created a book to really help students visualize mathematics for better comprehension. By creating algebraic visual side-by-sides to solve various problems in the examples, the authors show students the relationship of the algebraic solution with the visual, often graphical, solution. In addition, the authors have added a variety of new tools to help students better use the book for maximum effectiveness to not only pass the course, but truly understand the material.

Features

- Functions Early and Integrated: Functions are introduced right away in Chapter 1 to get students interested in a new topic. Equations and expressions are reviewed in the second chapter showing their connection to functions. This approach engages students from the start and gives them a taste of what they will learn in this course, instead of starting out with a review of concepts learned in previous courses.
- Algebraic Visual Side-by-Sides: Examples are worked out both algebraically and visually to increase student understanding of the concepts. Additionally, seeing these solutions side-by-side helps students make the connection between algebraic manipulation and the graphical interpretation.
- Zeros, Solutions, and x-Intercepts Theme: This theme allows students to reach a new level of mathematical comprehension through connecting the concepts of the real zeros of the function, the solutions of the associated equation, and the x-coordinates of the x-intercept of the graph of the function.
- Technology Connection: In each chapter, optional Technology Connections guide students in the use of the graphing calculator as another way to check problems.
- Review Icon: These notes reference an earlier, related section where a student can go to review a concept being used in the current section.
- Study Tips: These occasional, brief reminders appear in the margin and promote effective study habits such as good note taking and exam preparation.
- Connecting the Concepts: Comprehension is streamlined and retention is maximized when the student views a concept in a visual form, rather than a paragraph. Combining design and art, this feature highlights the importance of connecting concepts. Its visual aspect invites the student to stop and check that he or she has understood how the concepts within a section or several sections work together.
- Visualizing the Graph: This feature asks students to match an equation with its graph. This focus on visualization and conceptual understanding appears in every chapter to help students see ''the big picture.''
- Vocabulary Review: Appearing once per chapter in the Skill Maintenance portion of an exercise set, this feature checks and reviews students' understanding of the language of mathematics.
- Classify the Function: With a focus on conceptual understanding, students are asked to identify a number of functions by their type (i. e., linear, quadratic, rational, and so forth). As students progress through the text, the variety of functions they know increases and these exercises become more challenging. These exercises appear with the review exercises in the Skill Maintenance portion of an exercise set.

Table of Contents

**Chapter R Basic Concepts of Algebra**

R.1 The Real-Number System

R.2 Integer Exponents, Scientific Notation, and Order of Operations

R.3 Addition, Subtraction, and Multiplication of Polynomials

R.4 Factoring

R.5 Rational Expressions

R.6 Radical Notation and Rational Exponents

R.7 The Basics of Equation Solving

**Chapter 1 Graphs, Functions, and Models**

1.1 Introduction to Graphing

1.2 Functions and Graphs

1.3 Linear Functions, Slope, and Applications

1.4 Equations of Lines and Modeling

1.5 More on Functions

1.6 The Algebra of Functions

1.7 Symmetry and Transformations

**Chapter 2 Functions, Equations, and Inequalities**

2.1 Linear Equations, Functions, and Models

2.2 The Complex Numbers

2.3 Quadratic Equations, Functions, and Models

2.4 Analyzing Graphs of Quadratic Functions

2.5 More Equation Solving

2.6 Solving Linear Inequalities

**Chapter 3 Polynomial And Rational Functions**

3.1 Polynomial Functions and Models

3.2 Graphing Polynomial Functions

3.3 Polynomial Division; The Remainder and Factor Theorems

3.4 Theorems about Zeros of Polynomial Functions

3.5 Rational Functions

3.6 Polynomial and Rational Inequalities

3.7 Variation and Applications

**Chapter 4 Exponential and Logarithmic Functions**

4.1 Inverse Functions

4.2 Exponential Functions and Graphs

4.3 Logarithmic Functions and Graphs

4.4 Properties of Logarithmic Functions

4.5 Solving Exponential and Logarithmic Equations

4.6 Applications and Models: Growth and Decay, and Compound Interest

**Chapter 5 The Trigonometric Functions**

5.1 Trigonometric Functions of Acute Angles

5.2 Applications of Right Triangles

5.3 Trigonometric Functions of Any Angle

5.4 Radians, Arc Length, and Angular Speed

5.5 Circular Functions: Graphs and Properties

5.6 Graphs of Transformed Sine and Cosine Functions

**Chapter 6 Trigonometric Identities, Inverse Functions, and Equations**

6.1 Identities: Pythagorean and Sum and Difference

6.2 Identities: Cofunction, Double-Angle, and Half-Angle

6.3 Proving Trigonometric Identities

6.4 Inverses of the Trigonometric Functions

6.5 Solving Trigonometric Equations

**Chapter 7 Applications of Trigonometry**

7.1 The Law of Sines

7.2 The Law of Cosines

7.3 Complex Numbers: Trigonometric Form

7.4 Polar Coordinates and Graphs

7.5 Vectors and Applications

7.6 Vector Operations

**Chapter 8 Systems of Equations and Matrices**

8.1 Systems of Equations in Two Variables

8.2 Systems of Equations in Three Variables

8.3 Matrices and Systems of Equations

8.4 Matrix Operations

8.5 Inverses of Matrices

8.6 Determinants and Cramer's Rule

8.7 Systems of Inequalities and Linear Programming

8.8 Partial Fractions

**Chapter 9 Analytic Geometry Topics **

9.1 The Parabola

9.2 The Circle and the Eclipse

9.3 The Hyperbola

9.4 Nonlinear Systems of Equations and Inequalities

9.5 Rotation of Axes

9.6 Polar Equations of Conics

9.7 Parametric Equations

**Chapter 10 Sequences, Series, and Combinatorics**

10.1 Sequences and Series

10.2 Arithmetic Sequences and Series

10.3 Geometric Sequences and Series

10.4 Mathematical Induction

10.5 Combinatorics: Permutations

10.6 Combinatorics: Combinations

10.7 The Binomial Theorem

10.8 Probability

Appendix: Basic Concepts from Geometry

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