[Book Cover]

Algebra & Trigonometry Enhanced with Graphing Utilities, 2/e

Michael Sullivan, Chicago State University
Michael Sullivan, Joliet Junior College

Published October, 1999 by Prentice Hall Engineering/Science/Mathematics

Copyright 2000, 1151 pp.
Cloth
ISBN 0-13-083334-7


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    Algebra/Trig with Graphing Calculators-Mathematics


Summary

For courses in College Algebra, Algebra & Trigonometry, Precalculus, and Trigonometry which requires student use of a graphing calculator. Using the graphing utility to enhance mathematics, not replace it, this text approaches technology as a tool to solve problems, motivate concepts, and explore ideas. Many problems are solved using both algebra and a graphing utility, with the benefits of each illustrated. Throughout, applications and examples using real data enable students to make connections between the mathematics learned and familiar situations. The authors' user-friendly approach helps students develop the skills needed to succeed in subsequent mathematics courses.

Features


NEW—Modeling Emphasis Throughout—Includes dedicated sections on Linear Functions and Models, Quadratic Models, Power Functions and Models, and Exponential and Logarithmic Functions and Models, with many applications coming from the areas of business, finance and economics.

  • Allows students to build models and model building skills that they can transfer to other areas of their studies and lives.
NEW—Pedgogical Four Color Design—Using an attractive design and layout allows students and instructors to better utilize the text through visual queues.
  • Helps students and instructors to easily and quickly identify key elements in the text through effective use of color.
NEW—Updated Use of Technology—The new edition has kept current with available technologies incorporating the useful and time saving features of the TI-83 and TI-86.
  • Students have a text that utilizes the most commonly used technologies in this market.
NEW—Table of Contents—The organization of the new edition has been changed to reflect the comments and suggestions from users.
  • Instructors and students will find the material flows smoothly and builds logically from one concept to another.
NEW—Section Objectives—Section objectives give students a quick view of the most important concepts of the section. These objectives also tie together the integrated learning package. Each of the supplements references the section objectives throughout—i.e. the lecture videos, MathPro, etc.
  • Students have an easier time determining the key concepts and have an increased opportunity to use the supplements in a meaningful way.
NEW—Chapter Projects—Two to three end of chapter projects put the content of the chapter into context. Each set of projects includes at least one set of real world sources data and company circumstances. The others are good for modeling real world situations to.
  • Students are able to roll up all the information from the chapter and place it into context.
Clear Writing Style—Mike Sullivan's writing style is one of the most widely praised features of this series. Sullivan uses both visuals and analogies to explain concepts. He writes the book for students to understand the concept.
  • A well written text allows students to get the most out of increasingly limited study hours.
Now Work Problems—This icon appears after many examples throughout the text. The student is then instructed to go work a similar problem in the end of section exercises. This allows students to test their understanding as they read and gain confidence that they can handle the exercises in the end of section problem sets.
  • Students gain confidence in their knowledge of the subject and have a tendency to ask more specific questions when they have difficulties.
Step by Step Examples—Each step of the process is illustrated throughout many of the examples in the text. These often include “English” explanations off to the side explaining the procedures.
  • Students are far less likely to get “stuck” working homework problems when there are similar step by step examples.
Preparing for this Chapter—Serves as a “Just in Time” algebra review at the beginning of each chapter. It supports the idea of learning mathematics as a building block process. Students and professors can use this to determine if they have covered the materials and concepts required to move into the new chapter.
  • Students gain a new understanding of maintaining their base of knowledge as the course progresses.
Chapter Review—Allows students to check their own understanding of the chapter materials in several ways. “Things to Know” give a general overview of the topics and concepts. “How To” requires the student to have the mathematical skills. “True/False” tests the students vocabulary for the chapter. “Review Exercises” give a good indication of what types of problems could be on a test. Students can use the Review Exercises in blue as a sample chapter test.
  • Students understand that concepts, vocabulary and skills are all apart of the learning process.
NEW—Chapter Projects—Two to three end of chapter projects put the content of the chapter into context. Each set of projects includes at least one set of real world sources data and company circumstances. The others are good for modeling real world situations to.
  • Students are able to roll up all the information from the chapter and place it into context.
Sourced Real World Data—Real World Data is incorporated into examples and exercise sets to emphasize that mathematics is a tool used to understand the world around us. When a student solves a problem using real data, they learn that the skill is both relevant and useful.
  • Students become more motivated by the relevancy of the materials.
Historical Notes and Intro's—Most chapters open with a brief historical introduction of the chapter topic. These introductions as well as the Historical Notes (denoted by the roman column icon) offer a basic historical context for the chapter and gives the student insight as to the original application of the mathematical concepts and the people who developed them.
  • Students see the human side of mathematics, which makes them more motivated.
End of Section Exercises—Sullivan provides an excellent selection of quality problems ranging from basic recognition of concepts, to skill and drill and finally moving to advance applications requiring applied problem solving and multiple mathematical skills.
  • Students and Professors are offered numerous quality questions which can be used to learn/teach the materials more fully.
Discussion, Writing and Research Problems—Denoted by the red pen and notebook icon (or red number) require students to think about the implications and use of the solutions they obtain.
  • Students see the connections between the numerical answers and their implications.
Visual Exercises—Almost every set of exercises opens with visual exercises developed to foster intuitive understanding in students.
  • Students are able to intuitively understand the mathematical concepts prior to testing their skills.


Table of Contents
(NOTE: Each chapter concludes with Chapter Review.)
    1. Graphs.

      Rectangular Coordinates; Graphing Utilities; Scatter Diagrams. Graphs of Equations. Solving Equations. Setting up Equations; Applications. Solving Inequalities. Lines. Circles.

    2. Linear and Quadratic Functions.

      Functions. Linear Functions and Models. Quadratic Equations and Functions. Quadratic Functions and Models.

    3. Functions and Their Graphs.

      Characteristics of Functions; Library of Functions. Graphing Techniques: Transformations. Operations on Functions; Composite Functions. Mathematical Models: Constructing Functions.

    4. Polynomial and Rational Functions.

      Power Functions and Models. Polynomial Functions and Models. Polynomial Division. The Real Zeros of a Polynomial Function. Complex Numbers; Quadratic Equations with a Negative Discriminant. Complex Zeros; Fundamental Theorem of Algebra. Rational Functions. Polynomial and Rational Inequalities.

    5. Exponential and Logarithmic Functions.

      One-to-One Functions; Inverse Functions. Exponential Functions. Logarithmic Functions. Properties of Logarithms. Logarithmic and Exponential Equations. Compound Interest. Growth and Decay. Exponential, Logarithmic, And Logistic Curve Fitting.

    6. Systems of Equations and Inequalities.

      Systems of Linear Equations: Two Equations Containing Two Variables. Systems of Linear Equations: Three Equations Containing Three Variables. Systems of Linear Equations: Matrices. Systems of Linear Equations: Determinants. Matrix Algebra. Systems of Linear Inequalities; Linear Programming. Partial Fraction Decomposition.

    7. Trigonometric Functions.

      Angles and Their Measure. Right Triangle Trigonometry. Computing The Values of Trigonometric Functions of Given Angles. Trigonometric Functions of General Angles. Properties of the Trigonometric Functions; Unit Circle Approach. Graphs of the Trigonometric Functions. Sinusoidal Graphs; Sinusoidal Curve Fitting.

    8. Analytic Trigonometry.

      Trigonometric Identities. Sum and Difference Formulas. Double-Angle and Half-Angle Formulas. Product-to-Sum and Sum-to-Product Formulas. The Inverse Trigonometric Functions. Trigonometric Equations (I). Trigonometric Equations (II).

    9. Applications of Trigonometric Functions.

      Solving Right Triangles. The Law of Sines. The Law of Cosines. The Area of a Triangle. Simple Harmonic Motion; Damped Motion.

    10. Polar Coordinates; Vectors.

      Polar Coordinates. Polar Equations and Graphs. The Complex Plane; DeMoivre's Theorem. Vectors. The Dot Product.

    11. Analytic Geometry.

      Conics. The Parabola. The Ellipse. The Hyperbola. Rotation of Axes; General Form of a Conic. Polar Equations of Conics. Plane Curves and Parametric Equations. Systems of Nonlinear Equations.

    12. Sequences; Induction; the Binomial Theorem.

      Sequences. Arithmetic Sequences. Geometric Sequences; Geometric Series. Mathematical Induction. The Binomial Theorem.

    13. Counting and Probability.

      Sets and Counting. Permutations and Combinations. Probability. Analyzing Univariate Data; Obtaining Probabilities from Data.

    Appendix Review.

      Real Numbers. Algebra Review. Geometry Review. Integer Exponents. Polynomials. Factoring Polynomials. Rational Expressions. Square Roots; Radicals. Rational Exponents.

    Answers.
    Index.


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