@article{1400522,
      author = {Bourchtein, Andrei, and Bourchtein, Ludmila,},
      url = {http://library.usi.edu/record/1400522},
      title = {Counterexamples : from elementary calculus to the  beginnings of analysis /},
      abstract = {"In this 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"--},
      recid = {1400522},
      pages = {1 online resource (358 pages) :},
}