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Functions, Their Limits and Their Derivatives

In: Mathematics and Methodology for Economics

Author

Listed:
  • Wolfgang Eichhorn

    (Karlsruhe Institute of Technology (KIT))

  • Winfried Gleißner

    (University of Applied Sciences Landshut)

Abstract

This chapter deals with functions, their limits and their derivatives. We start with sequences and their limits. Then we discuss the continuity of functions and derivatives. We introduce some rules which make derivations easier: linearity, product rule, and chain rule. We discuss the laws of the mean, Taylor series, and Bernoulli-L’Hospital rules. We lay the foundation for the analysis of functions in one variable using the notions of monotinicty, local extrema, and convexity. We explain Newton’s algorithm to calculate zeroes of functions of one real variable. Then we turn to functions of several variables: their continuity, and their partial derivatives. The chain rule is explained, as well as Euler’s partial differential equation. We finish this chapter discussing implicitly given functions.

Suggested Citation

  • Wolfgang Eichhorn & Winfried Gleißner, 2016. "Functions, Their Limits and Their Derivatives," Springer Texts in Business and Economics, in: Mathematics and Methodology for Economics, edition 1, chapter 6, pages 209-300, Springer.
    • Handle: RePEc:spr:sptchp:978-3-319-23353-6_6
    DOI: 10.1007/978-3-319-23353-6_6
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