Univerzitní knihovna OU - Úplné zobrazení záznamu

"Inthis manuscript we present counterexamples to different false statements, which frequently arise in the calculus and fundamentals of real analysis, and which may appear to be true at first glance. A counterexample is understood here in a broad sense as any example that is counter to some statement. The topics covered concern functions of real variables. The first part (chapters 1-6) is related to single-variable functions, starting with elementary properties of functions (partially studied even in college), passing through limits and continuity to differentiation and integration, and ending with numerical sequences and series. The second part (chapters 7-9) deals with function of two variables, involving limits and continuity, differentiation and integration. One of the goals of this book is to provide an outlook of important concepts and theorems in calculus and analysis by using counterexamples.We restricted our exposition to the main definitions and theorems of calculus in order to explore different versions (wrong and correct) of the fundamental concepts and to see what happens a few steps outside of the traditional formulations. Hence, many interesting (but more specific and applied) problems not related directly to the basic notions and results are left out of the scope of this manuscript. The selection and exposition of the material are directed, in the first place, to those calculus students who are interested in a deeper understanding and broader knowledge of the topics of calculus. We think the presented material may also be used by instructors that wish to go through the examples (or their variations) in class or assign them as homework or extra-curricular projects. In order to make the majority of the examples and solutions accessible to"-- Provided by publisher..

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