Titlebook: Mathematical Analysis; Functions of Several Nicola Fusco,Paolo Marcellini,Carlo Sbordone Textbook 2022 The Editor(s) (if applicable) and Th

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978-3-031-04150-1The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

obtuse

cluster

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Metric Spaces and Banach Spaces,This chapter collects the main notions from . regarding metric spaces and Banach spaces. Although this material might already be known in particular cases (at least for the standard topology of .) we shall recall it in order to keep the text self-contained. Certain sections might be postponed for a subsequent study.

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Linear Differential Equations,Consider the ODE of order . in normal form.

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Multiple Integrals,In this chapter we present the theory of integration for functions of . real variables. We start in Sects. 8.1–8.4, with the simpler case . = 2, namely . of continuous functions over .. Section 8.5 addresses . (. = 3). Finally, from Sect. 8.6 we study the general case (. ≥ 2) of ., and discuss the general theory of Riemann integration.