Precalculus, 2nd edition

Published by Pearson (June 23, 2019) © 2019

  • Eric Schulz Walla Walla Community College
  • Julianne Connell Sachs Walla Walla Community College
  • William L. Briggs University of Colorado Denver

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For courses in Precalculus.

Interactive figures are worth a thousand words

The Precalculus, 2nd Edition eText seamlessly integrates exposition, interactive figures, author videos and progress checks to immerse students in a rich learning environment within MyLab Math. It is a concise presentation of material needed for success in precalculus. Each of the 365 interactive figures helps build students' geometric intuition of a concept with the narrative supporting its analytic development. This innovative eText, paired with the author-created printed note-taking guide Explorations & Notes, creates a framework for conceptual learning that builds a strong mathematical foundation for calculus.

Hallmark features of this title

  • The intuitive, visual approach helps students build a strong mathematical foundation by allowing them to explore difficult concepts through memorable interactive figures, leading to long-term retention.
  • The authors emphasize multiple representations of the mathematics and weave numeric (tabular), graphical, symbolic and descriptive presentations of functions and concepts throughout Precalculus.
  • Continuous reinforcement throughout the narrative ensures that students understand the material.
  • Exercise sets assess student understanding in multiple ways and include exercises that require technology.

New and updated features of this title

  • 2 new chapters: Vectors (Chapter 9) and Matrices and Systems of Equations (Chapter 10) now each have their own fully developed chapters.
  • Revised Explorations & Notes note-taking guide has been developed by the authors to help students stay focused and to provide a tool for further exploration with the interactive figures.  

Highlights of the DIGITAL UPDATE for MyLab Math

Instructors, contact your sales rep to ensure you have the most recent version of the course.

  • The Wolfram CDF Player has been replaced by Wolfram Cloud. Now, the interactive eText with its 365 Interactive Figures runs on all browsers, with no plug-in or downloads required.
  • GeoGebra Exercises are gradable graphing exercises that help students demonstrate their understanding. Assigned alongside our MyLab Math homework exercises, they enable students to interact directly with the graph in a manner that reflects how they would graph on paper.

Features of MyLab Math for the 2nd Edition; published 2021

  • Hundreds of interactive figures are integrated into the eText and are also available for teaching and learning tools in the Multimedia Library. Assessment exercises using the interactive figures are also assignable in MyLab Math.
  • Video Assessment exercises are tied to the Guided Figure Videos, giving students a more meaningful experience with the videos by quizzing them on the concepts presented. Instructors may choose to assign them as a prerequisite to the homework assignment.
  • Getting Ready integrates prerequisite review right when students need it most. Skill-review quizzes test prerequisite knowledge and from these quizzes, each student receives a personalized, just-in-time review assignment, allowing them to refresh forgotten concepts.

Features of Pearson eText for the 2nd Edition

  • Additional Guided Figure Videos and new Solution Videos are integrated at point of need.
  • The Explorations & Notes note-taking guide has been developed by the authors to help students stay focused and to provide a tool for further exploration with the interactive figures.  
    • Improved "Explore" questions drive students back to the rich interactive figures, guiding them to a deeper understanding of the concept presented.
    • New “Algebra Checks” introduce each section for a quick refresh on prerequisite material and sections end with a “Check Your Progress” checklist to keep students on track.
    • Improved key definitions, theorems, concepts and procedures are presented for efficient studying. Improved Examples from the eText are included with dedicated space to take notes and work out solutions. Files are now fully editable.
  • Revised exercise sets include Getting Started exercises that check students' conceptual understanding of the essential ideas from the section; Practice Exercises that make up the bulk of the exercise set and comprise exercises from Basic Skills, Further Explorations and Applications, gradually progressing in difficulty; Explorations and Challenges consisting of harder problems and those that extend the content of the section; Application questions sprinkled throughout.

1. Functions

  • Introduction to Functions
  • Graphs
  • Linear Functions
  • Combinations of Functions
  • Transformations of Functions
  • Families of Functions
  • Summary and Review Exercises

2. Polynomials and Rational Functions

  • Quadratic Functions
  • Polynomial Functions
  • Real Roots and Factors of Polynomial Functions
  • Complex Numbers
  • Complex Roots of Polynomial Functions
  • Rational Functions
  • Inequalities
  • Summary and Review Exercises

3. Exponentials and Logarithms

  • Exponential Functions
  • Inverse Functions
  • Logarithmic Functions
  • Logarithmic Identities
  • Solving Exponential and Logarithmic Equations
  • Summary and Review Exercises

4. Unit Circle Trigonometry

  • Angles and Their Measures
  • Unit Circle Definitions of Sine, Cosine, and Tangent
  • Sine, Cosine, and Tangent Functions
  • Secant, Cosecant, and Cotangent Functions
  • Inverse Trigonometric Functions
  • Summary and Review Exercises

5. Triangle Trigonometry

  • Right Triangle Trigonometry
  • Right Triangles and the Unit Circle
  • Law of Sines
  • Law of Cosines
  • Applications of Triangles
  • Summary and Review Exercises

6. Trigonometric Identities

  • Fundamental Identities
  • Sum, Difference, and Double-Angle Identities
  • Power-Reducing, Half-Angle, and Product-Sum Identities
  • Solving Trigonometric Equations
  • Summary and Review Exercises

7. Parametric and Polar Graphs

  • Parametric Equations
  • Polar Coordinates
  • Polar Graphs
  • Polar Form of Complex Numbers; DeMoivre's Theorem
  • Summary and Review Exercises

8. Conic Sections

  • Parabolas
  • Ellipses and Circles
  • Hyperbolas
  • Eccentricity and Polar Equations of Conic Sections
  • Summary and Review Exercises

9. Vectors

  • Vectors in Two Dimensions
  • Vectors in Three Dimensions
  • Dot Product
  • Cross Product
  • Summary and Review Exercises

10. Matrices and Systems of Equations

  • Systems of Equations and Inequalities
  • Matrices
  • Method of Partial Fractions
  • Summary and Review Exercises

Appendices

  1. Looking Forward to Calculus: Limits
  2. Looking Forward to Calculus: Sequences and Series

Index

Figure Index

App. Index

About our authors

Eric Schulz has been teaching mathematics at Walla Walla Community College since 1989 and began his work with Mathematica in 1992. He has an undergraduate degree in mathematics from Seattle Pacific University, and a graduate degree in mathematics from the University of Washington. Eric loves working with students and is passionate about their success. His interest in innovative and effective uses of technology in teaching mathematics has remained strong throughout his career. He is the developer of the Basic Math Assistant, Classroom Assistant, and Writing Assistant palettes that ship in Mathematica worldwide. He is an author on multiple textbooks: Calculus titles with Briggs, Cochran, and Gillett, and a Precalculus title with Sachs and Briggs (where he writes, codes and creates dynamic eTexts combining narrative, videos and interactive figures using Mathematica and CDF technology).

Julianne Connell Sachs has undergraduate degrees in Mathematics and Spanish, and a graduate degree in Mathematics from Western Washington University. She taught math and physics in Guatemala for 1 year before joining the faculty at Walla Walla Community College in 2001. Julianne teaches courses ranging from beginning algebra through differential equations at WWCC. Through active learning and the strategic use of technology, she strives to guide students toward a deeper understanding of mathematics.

William Briggs was on the mathematics faculty at the University of Colorado - Denver for 23 years, after teaching at the University of California at San Diego and Clarkson University. He received his BA in mathematics from the University of Colorado and his MS and PhD in applied mathematics from Harvard University. He taught undergraduate and graduate courses throughout the mathematics curriculum, with a special interest in mathematical modeling and differential equations as they apply to problems in the biosciences. He has written a series of calculus textbooks and a quantitative reasoning textbook, Using & Understanding Mathematics; an undergraduate problem-solving book, Ants, Bikes, and Clocks; and two tutorial monographs, The Multigrid Tutorial and The DFT: An Owner's Manual for the Discrete Fourier Transform. He was the Vice President for Education of the Society for Industrial and Applied Mathematics (SIAM), a University of Colorado President's Teaching Scholar, a recipient of the Outstanding Teacher Award of the Rocky Mountain Section of the Mathematical Association of America (MAA), and the recipient of a Fulbright Fellowship to Ireland.

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