Precalculus: A Functional Approach to Graphing and Problem Solving, 6th Edition

Book description


Precalculus: A Functional Approach to Graphing and Problem Solving prepares students for the concepts and applications they will encounter in future calculus courses. In far too many texts, process is stressed over insight and understanding, and students move on to calculus ill equipped to think conceptually about its essential ideas. This text provides sound development of the important mathematical underpinnings of calculus, stimulating problems and exercises, and a well-developed, engaging pedagogy. Students will leave with a clear understanding of what lies ahead in their future calculus courses. Instructors will find that Smith's straightforward, student-friendly presentation provides exactly what they have been looking for in a text!

Table of contents

  1. Cover Page
  2. Title Page
  3. Copyright Page
  4. Dedication Page
  5. Table of Contents
  6. A Note about Calculator Usage
  7. Preface
  8. Problem Solving
  9. Acknowledgments
  10. About the Author
  11. Fundamental Concepts
    1. Chapter 1: Algebraic and Geometrical Foundations
      1. 1.1: Real Numbers
      2. 1.2: Algebraic Expressions
      3. 1.3: Equations of Lines
      4. 1.4: Distance and Symmetry
      5. 1.5: Linear Inequalities and Coordinate Systems
      6. 1.6: Absolute Value Equations and Inequalities
      7. *1.7: What is Calculus?
      8. 1.8: Equations for Calculus
      9. 1.9: Inequalities for Calculus
      10. Chapter 1: Summary and Review
  12. Functions and Graphing
    1. Chapter 2: Functions with Problem Solving
      1. 2.1: Problem Solving
      2. 2.2: Introduction to Functions
      3. 2.3: Graph of a Function
      4. 2.4: Transformations of Functions
      5. 2.5: Piecewise Functions
      6. 2.6: Composition and Operations of Functions
      7. 2.7: Inverse Functions
      8. 2.8: Limits and Continuity
      9. Chapter 2: Summary and Review
    2. Chapter 3: Polynomial Functions
      1. 3.1: Linear Functions
      2. 3.2: Quadratic Functions
      3. 3.3: Optimization Problems
      4. 3.4: Parametric Equations
      5. 3.5: Graphing Polynomial Functions
      6. 3.6: Polynomial Equations
      7. Chapter 3: Summary and Review
    3. Chapter 4: Additional Functions
      1. 4.1: Rational Functions
      2. 4.2: Radical Functions
      3. 4.3: Real Roots of Rational and Radical Equations
      4. 4.4: Exponential Functions
      5. 4.5: Logarithmic Functions
      6. 4.6: Logarithmic Equations
      7. 4.7: Exponential Equations
      8. Chapter 4: Summary and Review
  13. Trigonometry
    1. Chapter 5: Trigonometric Functions
      1. 5.1: Angles
      2. 5.2: Fundamentals
      3. 5.3: Trigonometric Functions of Any Angle
      4. 5.4: Graphs of the Trigonometric Functions
      5. 5.5: Inverse Trigonometric Functions
      6. 5.6: Right Triangles
      7. 5.7: Oblique Triangles
      8. Chapter 5: Summary and Review
    2. Chapter 6: Trigonometric Equations and Identities
      1. 6.1: Trigonometric Equations
      2. 6.2: Proving Identities
      3. 6.3: Addition Laws
      4. 6.4: Miscellaneous Identities
      5. *6.5: De Moivre's Theorem
      6. Chapter 6: Summary and Review
  14. Advanced Algebra Topics and Analytic Geometry
    1. Chapter 7: Analytic Geometry
      1. 7.1: Parabolas
      2. 7.2: Ellipses
      3. 7.3: Hyperbolas
      4. 7.4: Rotations
      5. *7.5: Polar Coordinates
      6. 7.6: Graphing in Polar Coordinates
      7. 7.7: Conic Sections in Polar Form
      8. Chapter 7: Summary and Review
    2. Chapter 8: Sequences, Systems, and Matrices
      1. 8.1: Sequences
      2. *8.2: Limit of a Sequence
      3. 8.3: Series
      4. 8.4: Systems of Equations
      5. 8.5: Matrix Solution of a System of Equations
      6. 8.6: Inverse Matrices
      7. 8.7: Systems of Inequalities
      8. Chapter 8: Summary and Review
    3. Chapter 9: Vectors and Solid Analytic Geometry
      1. *9.1: Vectors in the Plane
      2. *9.2: Quadric Surfaces and Graphing in Three Dimensions
      3. *9.3: The Dot Product
      4. *9.4: The Cross Product
      5. *9.5: Lines and Planes in Space
      6. Chapter 9: Summary and Review
  15. Appendices
    1. Appendix A: Field Properties
    2. Appendix B: Complex Numbers
    3. Appendix C: Mathematical Induction
    4. Appendix D: Binomial Theorem
    5. Appendix E: Determinants and Cramer's Rule
    6. Appendix F: Library of Curves and Surfaces
    7. Appendix G: Answers
  16. Index

Product information

  • Title: Precalculus: A Functional Approach to Graphing and Problem Solving, 6th Edition
  • Author(s): Karl J. Smith
  • Release date: October 2011
  • Publisher(s): Jones & Bartlett Learning
  • ISBN: 9780763782214