Abstract
This chapter is devoted to some applications of the derivative which form part of the basic skills in modelling. We start with a discussion of features of graphs. More precisely, we use the derivative to describe geometric properties like maxima, minima and monotonicity. Even though plotting functions with Matlab or maple is simple, understanding the connection with the derivative is important, for example, when a function with given properties is to be chosen from a particular class of functions.
In the following section we discuss Newton’s method and the concept of order of convergence. Newton’s method is one of the most important tools for computing zeros of functions. It is nearly universally in use.
The final section of this chapter is devoted to an elementary method from data analysis. We show how to compute a regression line through the origin. There are many areas of application that involve linear regression. This topic will be developed in more detail in Chap. 18.
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Notes
- 1.
I. Newton, 1642–1727.
- 2.
C.F. Gauss, 1777–1855.
References
Textbooks
S. Lang: Undergraduate Analysis. Springer, New York 1983.
Further Reading
STATISTIK AUSTRIA: Statistisches Jahrbuch Österreichs. Verlag Österreich GmbH, Wien 2007 (http://www.statistik.at).
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© 2011 Springer-Verlag London Limited
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Oberguggenberger, M., Ostermann, A. (2011). Applications of the Derivative. In: Analysis for Computer Scientists. Undergraduate Topics in Computer Science. Springer, London. https://doi.org/10.1007/978-0-85729-446-3_8
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DOI: https://doi.org/10.1007/978-0-85729-446-3_8
Publisher Name: Springer, London
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