Titlebook: Mathematical Analysis and the Mathematics of Computation; Werner R?misch,Thomas Zeugmann Textbook 2016 Springer International Publishing S

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Textbook 2016theory at a modern level and it directly relates modern mathematical ideas to their diverse applications...The authors develop the whole theory. Starting with a simple axiom system for the real numbers, they then lay the foundations, developing the theory, exemplifying where it‘s applicable, in turn

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Metric Spaces,e so far studied properties are inherited by a product metric space. In the remaining part of this chapter we take a closer look at real sequences and deal with series and power series. In particular, fundamental elementary functions are defined and their basic properties are investigated.

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Continuous Functions in Metric Spaces,e problem of under what conditions a continuous mapping allows for a continuation to a larger domain is studied. We finish this chapter by looking at continuous functions over the reals. In the course of this chapter several functions considered previously will be studied again with respect to the problem of whether or not they are continuous.

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The Differential Calculus,es are shown, including mean value theorems, the chain rule, and a generalization of Taylor’s theorem. The central notion studied in this chapter is the . of a function. It describes the local rate at which quantities change. We start with functions on . into . and outline the basic properties and rules.

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