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Calculus: The Language of Change (third edition)

A new approach to calculus - available free as .pdf files with accompanying Mathematica or Maple programs

Calculus really is "the language of science."  Students who want to study technical careers from physics to finance need to speak this language. Calculus: The Language of Change shows them how.

  • A text of over 500 pages
  • Software integrated into the development - both Mathematica and Maple.
  • A book of detailed projects.
  • A supplemental book of mathematical theory

    • The text table of contents is quite different from the contents of the popular text format used for over 50 years in the US.

    Modern computing with Mathematica or Maple makes it possible for beginning students to solve real problems while they are learning the basics.

    Projects for Calculus: The Language of Change: aimed at answering the student's question: "What good is it?"

    • Why did we eradicate polio by vaccination, but not measles?
    • Drug concentration and "biexponential" functions.
    • How far will a bungee diver fall?
    • Landing on an aircraft carrier.

    The book of projects is very different from the shortened examples from traditional books. Modern computing makes the real open-ended projects possible.

    Click here for the .html version of the Project book
     Project help notebooks - preliminary version Projects Contents


    Integrated computing in Calc:TLC helps students learn difficult ideas

     
    Zooming in 2-D and 3-D


    Contours and the explicit graph.


    The flow of a vector field.


    Four plots of the solution to predator-prey equations.

    These materials are "proven" in two respects:

    Calc:TLC develops student skills

    First, the skills developed in this table of contents prepares students for later technical work. In a follow-up study of 2286 students at B.Y.U., our students did about better in six traditional courses and averaged 2.93 vs. 2.95 in a seventh.  (See summary and link below.)

    Projects let students solve real problems

    Second, conscientious students really do learn that calculus has important things to say about their world. I have met students on the sidewalk 3 years after the course who can still describe their project in detail. Calculus really means something to them and they began learning to write and think about math and work in teams in the process of working their memorable project.

    Student projects include answering questions like: Why did we eradicate polio by vaccination, but not measles?

    The B. Y. U. Outcomes Study: followup of 2286 students

    Average grades in later technical courses for 2286 students taking caluclus using  Calculus:The Language of Change, The Harvard Consortium Calculus (HCC) text, and a traditional text.

    Physics 221 (with Calculus prerequisite)
     C:TLC      HCC     Traditional
     3.32          3.09          2.99

    Physics 122 (Calculus co-requisite, second semester)
     C:TLC      HCC     Traditional
     2.97          2.93          2.91

    Theory of Analysis 315
     C:TLC      HCC     Traditional
     3.16          2.44          2.72

    Linear algebra 343
     C:TLC      HCC     Traditional
     2.96          2.80          2.74

    Multivariable Calculus
     C:TLC      HCC     Traditional
     3.33          2.99          3.02

    Advanced Engineering Math 312
     C:TLC      HCC     Traditional
     2.93          2.86          2.95

    Stat 321
     C:TLC      HCC     Traditional
     3.20          3.16         3.09

    For more information go to the article:

    Does Traditional or Reformed Calculus Prepare Students Better for Subsequent Courses?
    A Preliminary Study.
    by
    Gerald M. Armstrong and Lee J. Hendrix

    Keith Stroyan's Page