Functions, limits, continuity, differential calculus and integral. The search for counterexamples has been important in the history of mathematics. Understanding basic calculus graduate school of mathematics. In exactly the same format, we define a function f to be continuous at a if.
Functions, limits, continuity, differential calculus and i ntegral calculus. A big proportion of students seem to be able to find correct solutions to test and. Incorrect statements are grouped topically with sections devoted to functions, limits, continuity, differential calculus and integral calculus. Pdf using counterexamples in calculus researchgate. I mention three famous instances read online download pdf. You can access this textbook for free in web view or pdf through, and for a low cost in print. Show by a counterexample that the result does not generalize to arbitrary open sets a. Counterexamples in calculus pdf free download epdf. Benjamin filippenko, zhengyi zhou, katrin wehrheim download pdf. The book challenges students to provide counterexamples to care fully. Accompanying the pdf file of this book is a set of mathematica notebook files.
The following major topics from a typical course on calculus of a single variable are considered. Counterexamples in calculus is a resource for singlevariable calculus courses. Counterexamples in calculus mathematical association of america. The paper deals with a practical issue encountered by many lecturers teaching firstyear university calculus. This book aims to fill a gap in the literature and provide a resource for using counterexamples as a pedagogical tool. Know that ebook versions of most of our titles are still available and may be downloaded immediately after purchase.
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