Differentiation and Integration

  • Kenneth R. Davidson
  • Allan P. Donsig
Part of the Undergraduate Texts in Mathematics book series (UTM)


In this chapter, we examine the mathematical foundations of differentiation and integration. The theorems of this chapter are useful not only to make calculus work but also for studying functions in many other contexts.We do not spend any time on the important applications that typically appear in courses devoted to calculus, such as optimization problems. Rather we will highlight those aspects that either depend on or apply to results in real analysis.

Since we assume that the reader has already seen calculus, we dive right in with key definitions, assuming that the motivating examples are familiar.


Differentiable Function Product Rule Tangent Line Fundamental Theorem Chain Rule 
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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of WaterlooOntarioCanada
  2. 2.Department of MathematicsUniversity of Nebraska-LincolnLincolnUSA

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