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Precalculus with Limits : Functions and Graphs

Precalculus with Limits : Functions and Graphs - 02 edition

ISBN13: 978-0201703337

Cover of Precalculus with Limits : Functions and Graphs 02 (ISBN 978-0201703337)
ISBN13: 978-0201703337
ISBN10: 0201703335
Edition: 02
Copyright: 2002
Publisher: Addison-Wesley Longman, Inc.
Published: 2002
International: No

Precalculus with Limits : Functions and Graphs - 02 edition

ISBN13: 978-0201703337

Mark Dugopolski

ISBN13: 978-0201703337
ISBN10: 0201703335
Edition: 02
Copyright: 2002
Publisher: Addison-Wesley Longman, Inc.
Published: 2002
International: No

Building on Mark Dugopolski's name, this graphing optional text is designed for the one or two semester precalculus course and includes coverage of analytic geometry, vectors, and the limit. With faster pacing and less review, this is an excellent choice for those students going on to calculus.

Features :

  • Chapter Opener Each chapter begins with a Chapter Opener that discusses a real-world situation in which the mathematics of the chapter is used. Examples and exercises that relate back to the opener are included within the chapter.
  • Function Gallery organizes and clarifies various functions in a consistent and easy to understand manner--helping students to master one of the most important concepts in the course.
  • Foreshadowing Calculus notes appear throughout the text to help students identify and focus on important calculus topics.
  • Regression Problems Many regression problems have been included in the text so that students can start with real data and use a calculator to obtain mathematical models of real problem situations.
  • For Thought Each exercise set begins with a set of true or false questions that reviews the basic concepts in that section, helps check student understanding before beginning the exercises, and offers opportunities for writing and/or discussion.
  • Exercise Sets Applications The exercise sets have been examined carefully to ensure that the exercises range from easy to challenging, and are arranged in order of increasing difficulty. Some exercises require a graphing calculator and most are based on or involve applications of real-world situations. The emphasis of many exercises is on understanding concepts and relationships.
  • Linking Concepts, located at the end of nearly every exercise set, is a multi-part exercise or exploration that can be used for individual or group work. The idea of this feature is to use a concept from the current section along with concepts from previous sections, and ask questions that help students see the links among various concepts. Some parts of these questions are open-ended, and require somewhat more thought than standard exercises. Answers to this feature are given only in the Instructor's Solutions Manual.
  • Tying It All Together is a review of selected concepts from the present and prior chapters, and requires students to integrate multiple concepts and skills.
  • Graphing Calculator Exercises Optional exercises that require a graphing calculator are located in the exercise sets and are clearly marked with a graphing calculator icon.
  • Graphing Calculator Discussions Optional graphing calculator discussions have been integrated into the text, but are identified by a graphing calculator icon so that they can be easily skipped by those not using this technology.
  • Highlights This end-of-chapter feature presents an overview of each section of the chapter, and is a useful summary of the basic information that students should have mastered in that chapter.
  • Chapter Review Exercises These exercises are designed to review the chapter without reference to the individual sections, and prepare students for the Chapter Test.
  • Chapter Test The problems in the Chapter Test are designed to help students measure their readiness for a classroom test, and instructors may use them as a model for their own end of chapter tests.
  • Index of Applications lists many applications contained within the text and immediately follows the Table of Contents. The applications are page-referenced, and grouped by subject matter.

Author Bio

Dugopolski, Mark : Southeastern Louisiana University

Table of Contents

1. Equations, Inequalities, and Modeling.

Equations in One Variable.
Equations and Graphs in Two Variables.
Scatter Diagrams and Curve Fitting.
Constructing Models to Solve Problems.
Quadratic Equations.
Linear and Absolute Value Inequalities.
Quadratic and Rational Inequalities.

2. Functions and Graphs.

Graphs of Relations and Functions.
Families of Functions: Transformations and Symmetry.
Operations with Functions.
Inverse Functions.
Constructing Functions with Variation.

3. Polynomial and Rational Functions.

Linear Functions.
Quadratic Functions.
Complex Numbers.
Zeros of Polynomial Functions.
The Theory of Equations.
Graphs of Polynomial Functions.
Graphs of Rational Functions.

4. Exponential and Logarithmic Functions.

Exponential Functions and Their Applications.
Logarithmic Functions and Their Applications.
Properties of Logarithms.
More Equations and Applications.

5. The Trigonometric Functions.

Angles and Their Measurements.
The Sine and Cosine Functions.
The Graphs of the Sine and Cosine Functions.
The Other Trigonometric Functions and Their Graphs.
The Inverse Trigonometric Functions.
Right Triangle Trigonometry.

6. Trigonometric Identities and Conditional Equations.

Basic Identities.
Verifying Identities.
Sum and Difference Identities.
Double-Angle and Half-Angle Identities.
Product and Sum Identities.
Conditional Trigonometric Equations.

7. Applications of Trigonometry.

The Law of Sines.
The Law of Cosines.
Trigonometric Form of Complex Numbers.
Powers and Roots of Complex Numbers.
Polar Equations.
Parametric Equations.

8. Systems of Equations and Inequalities.

Systems of Linear Equations in Two Variables.
Systems of Linear Equations in Three Variables.
Nonlinear Systems of Equations.
Partial Fractions.
Inequalities and Systems of Inequalities in Two Variables.
Linear Programming.

9. Matrices and Determinants.

Solving Linear Systems Using Matrices.
Operations with Matrices.
Multiplication of Matrices.
Inverses of Matrices.
Solution of Linear Systems in Two Variables Using Determinants.
Solution of Linear Systems in Three Variables Using Determinants.

10. The Conic Sections.

The Parabola.
The Ellipse and the Circle.
The Hyperbola.
Rotation of Axes.
Polar Equations of the Conics.

11. Sequences, Series, and Probability.

Geometric Sequences and Series.
Counting and Permutations.
Combinations, Labeling, and the Binomial Theorem.
Mathematical Induction.

12. Analytic Geometry and Vectors in Three Dimensions.

Graphs in Space.
Vectors in Space.
Cross Product and Scalar Triple Product.
Equations of Lines and Planes in Space.

13. Limits.

Finding Limits Numerically and Graphically.
Finding Limits Algebraically with Limit Theorems.
One-Sided Limits, Continuity, and Limits Involving Infinity.
Tangent Lines and the Derivative.

Appendix A: Basic Algebra Review.

Real Numbers and Their Properties.
Exponents and Radicals.
Factoring Polynomials.
Rational Expressions.

Appendix B: Techniques for Solving Miscellaneous Equations.

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