Titlebook: Essential Mathematics for Undergraduates; A Guided Approach to Simon G. Chiossi Textbook 2021 The Editor(s) (if applicable) and The Author(

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https://doi.org/10.1007/978-3-0348-5144-2In this chapter we’ll undertake the study of polynomials with real coefficients in one variable. They are important because they are a major source of functions. A comprehensive reference is R.S. Irving (Integers, polynomials, and rings, Springer-Verlag, 2004).

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https://doi.org/10.1007/978-3-658-03394-1The general subject matter of Chap. . is here narrowed down to . .. An effective and comprehensive study of real functions is completed in analysis and differential geometry, fields that allow to appreciate both the global and the local (infinitesimal) features.

white-matter

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Tobias C. Breiner,Luca D. KolibiusThis chapter is devoted to the simplest transcendental functions: exponential maps (Sects. 12.1 and 12.3), logarithmic maps (Sect. 12.2) and trigonometric functions (Sect. 12.4). Also falling in this class are functions of type .?=?.. for ., or .?=?.. etc.

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https://doi.org/10.1007/978-3-662-57895-7This is the odd-one-out chapter, in that it could fit in any place because its content relate to virtually everything else in the book. Its current placing reflects the emphasis that was put on functions.

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Round-Up of Elementary LogicThis first chapter is an incomplete summary of classical intuitive logic. The importance of tackling this at the very beginning—of a book and of a curriculum—cannot go amiss. A satisfactory treatment deserves a specific course, that clearly cannot be taught in the first semesters, nor in one semester only.

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MAIM

FunctionsThis chapter introduces the general dictionary of functions, some properties and examples. Although many aspects (e.g., Sect. 3.2) holds for general binary relations, we shall concentrate on functions, probably the most important notion in mathematics. The theory of real functions of one real variable deserves separate treatment (Chap. .).

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