Home > Precalculus through Modeling and... > Instructor Resources > Conversion Guide >

Instructor Resources
Conversion Guide

CONVERSION GUIDE

College Algebra through Modeling and Visualization

Gary Rockswold, Mankato State University

College Algebra through Modeling and Visualization offers an innovative approach that consistently links mathematical concepts to real-world applications by moving from the concrete to the abstract. It answers a student's question: "When will I ever need to know this?" This text provides a comprehensive curriculum with the balance and flexibility necessary for today's college algebra courses. With a flexible approach to the rule of four (verbal, graphical, numerical, symbolic methods), instructors can easily emphasize one rule more than another to meet their students' needs. This flexible approach also extends to modeling, applications, and graphing calculator use. The text contains numerous applications, including modeling of real-world data with functions and problem solving strategies for applied problems. It is not necessary for an instructor to discuss any particular application; rather, an instructor has the option to pick and choose from a wide variety of topics. There is appropriate use of technology throughout the text, which helps students visualize mathematical concepts. However, technology is not a requirement for students to benefit from this applications-based text.

The Second Edition has added a host of new examples, skill-building exercises, updated applications, real-data modeling, and extended exercises directed toward increasing a student's understanding of mathematics. Its new organization and seamless presentation allows students to easily understand each topic. The extensive exercise sets are carefully graded, covering a diverse assortment of topics with several levels of difficulty. The presentation and exercise sets provide instructors with the ability to enhance their courses in several different directions.

This conversion guide is designed to help you adapt your syllabus for Rockswold's College Algebra Through Modeling and Visualization from the first edition to the second edition by providing a section by section objective by cross-reference between the two books.

College Algebra through Modeling and Visualization, First Edition College Algebra through Modeling and Visualization, Second Edition

Sect. Title Sect. Title

1.1 Data, Numbers, and Algorithms 1.1 Numbers, Data, and Problem Solving

1.2 Visualization of Data 1.2 Visualization of Data

1.3 Functions and Their Representations 1.3 Functions and Their Representations

1.4 Types of Functions and Their Rates of Change 1.4 Types of Functions and Their Rates of Change

1.5 Modeling Data with Functions 2.1 Modeling Data with Functions

1.6 Transformations of Graphs 3.4 Transformations of Graphs

2.1 Linear Equations 2.3 Linear Equations

2.2 Linear Equations 2.4 Linear Equations

2.3 Equations of Lines 2.2 Equations of Lines

2.4 Piecewise-Defined Functions 2.5 Piecewise-Defined Functions

2.5 Linear Approximation 2.6 Linear Approximation

3.1 Quadratic Equations and Inequalities 3.1 Quadratic Functions; Constructing Models
(new section)

3.2

Quadratic Equations and Problem Solving
(new section)

3.3
Quadratic Inequalities (new section)

3.2 Nonlinear Functions and Their Graphs 4.1
Nonlinear Functions and Their Graphs

4.7 Power Functions and Radical Equations
(new section)

3.3 Polynomial Functions and Their Graphs 4.2 Polynomial Functions; Constructing Models

3.4 Real Zeros of Polynomial Functions 4.3 Real Zeros of Polynomial Functions

3.5 The Fundamental Theorem of Algebra 4.4 The Fundamental Theorem of Algebra

3.6 Rational Functions 4.5 Rational Functions and Models

4.6 Polynomial and Rational Inequalities
(new section)

4.1 Combining Functions 5.1 Combining Functions

4.2 Inverse Functions and Their Representations 5.2 Inverse Functions and Their Representations

4.3 Exponential Functions 5.3 Exponential Functions and Models

4.4 Logarithmic Functions 5.4 Logarithmic Functions and Models

5.7 Constructing Nonlinear Models
(new section)

5.1 Angles and their Measure 6.1 Angles and their Measure

5.2 Right Triangle Trigonometry 6.2 Right Triangle Trigonometry

5.3 The Sine and Cosine Functions and their Graphs 6.3 The Sine and Cosine Functions and their Graphs

5.4 Other Trigonometric Functions and their Graphs 6.4 Other Trigonometric Functions and their Graphs

5.5 Modeling with Trigonometric Functions 6.5 Modeling with Trigonometric Functions

5.6 Inverse Trigonometric Functions 6.6 Inverse Trigonometric Functions

6.1 Fundamental Identities 7.1 Fundamental Identities

6.2 Verifying Identities 7.2 Verifying Trigonometric Identities

6.3 Trigonometric Equations 7.3 Trigonometric Equations

6.4 Sum and Difference Identities 7.4 Sum and Difference Identities

6.5 Multiple-Angle Identities 7.5 Multiple-Angle Identities

7.1 Law of Sines 8.1 Law of Sines

7.2 Law of Cosines 8.2 Law of Cosines

7.3 Vectors 8.3 Vectors

7.4 Parametric Equations 8.4 Parametric Equations

7.5 Polar Equations 8.5 Polar Equations

7.6 Trigonometric Form and Roots of Complex Numbers 8.6 Trigonometric Form and Roots of Complex Numbers

8.1 Functions and Equations of More Than One Variable 9.1 Functions and Equations of More Than One Variable

8.2 Linear Systems of Equations and Inequalities in Two Variables 9.2 Linear Systems of Equations and Inequalities in Two Variables

8.3 Solutions of Linear Systems Using Matrices 9.3 Solutions of Linear Systems Using Matrices

8.4 Properties and Applications of Matrices 9.4 Properties and Applications of Matrices

8.5 Inverses of Matrices 9.5 Inverses of Matrices

8.6 Determinants 9.6 Determinants

9.1 Sequences 11.1 Sequences

9.2 Series 11.2 Series

9.3 Conic Sections 10.1 Parabolas (new section)

10.2 Ellipses (new section)

10.3 Hyperbolas (new section)

9.4 Counting 11.3 Counting

11.4 Binomial Theorem (new section)

9.5 Probability 11.5 Probability