Applied Calculus with R

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ABOUT THE BOOK

This textbook integrates scientific programming with the use of R and uses it both as a tool for applied problems and to aid in learning calculus ideas.  Adding R, which is free and used widely outside academia, introduces students to programming and expands the types of problems students can engage. There are no expectations that a student has any coding experience to use this text.
While this is an applied calculus text including real world data sets, a student that decides to go on in mathematics should develop sufficient algebraic skills so that they can be successful in a more traditional second semester calculus course. Hopefully, the applications provide some motivation to learn techniques and theory and to take additional math courses. The book contains chapters in the appendix for algebra review as algebra skills can always be improved. Exercise sets and projects are included throughout with numerous exercises based on graphs.

TABLE OF CONTENTS

  1. A Brief Introduction to R

    • Thomas J. Pfaff
    Pages 1-19
  2. Describing a Graph

    • Thomas J. Pfaff
    Pages 21-27
  3. The Function Gallery

    • Thomas J. Pfaff
    Pages 29-45
  4. Change and the Derivative

    1. Front Matter

      Pages 47-47

    2. How Fast is CO2 Increasing?

      • Thomas J. Pfaff
      Pages 49-58
    3. The Idea of the Derivative

      • Thomas J. Pfaff
      Pages 59-63
    4. Formulas Quantifying Change

      • Thomas J. Pfaff
      Pages 65-76
    5. The Microscope Equation

      • Thomas J. Pfaff
      Pages 77-89
    6. The Derivative Graphically

      • Thomas J. Pfaff
      Pages 109-133
    7. The Formal Derivative as a Limit

      • Thomas J. Pfaff
      Pages 135-143
    8. Basic Derivative Rules

      • Thomas J. Pfaff
      Pages 145-155
    9. Product Rule

      • Thomas J. Pfaff
      Pages 157-167
    10. Quotient Rule

      • Thomas J. Pfaff
      Pages 169-174
    11. Chain Rule

      • Thomas J. Pfaff
      Pages 175-184
    12. Derivatives with R

      • Thomas J. Pfaff
      Pages 185-197
  5. Applications of the Derivative

    1. Front Matter

      Pages 209-209

    2. How Do We Know the Shape of a Function?

      • Thomas J. Pfaff
      Pages 211-226



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