Calculus pp 142-180 | Cite as


  • Harley Flanders
Part of the Textbooks in Mathematical Sciences book series (TIMS)


Calculus solves two main problems. The first problem is measuring how fast quantities change. This is solved by diiffferential calculus through the concept of the derivative of a function. The second problem is measuring things that can be approximated as sums of many small pieces; its solution constitutes integral calculus. Integral calculus solves many seemingly unrelated problems of computing: area, volume, work, and pressure on a dam are examples. The most striking thing of all in calculus is that the two problems are closely related; each problem is the “inverse” of the other!


Shade Region Trapezoidal Rule Fundamental Theorem Numerical Integration Method Mean Value Theorem 
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Harley Flanders
    • 1
  1. 1.University of MichiganAnn ArborUSA

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