Undergraduate Analysis: A Working Textbook by Aisling McCluskeyMy rating: 4 of 5 stars
This introduction to analysis is suitable for students who have had at least a year of calculus; “a familiarity with elementary calculus.” It is assumed the reader has “knowledge of how to differentiate basic exponential and trigonometric functions,” etc. The focus is convergence and limits of sequences and series (more than half of the chapters), as well as differentiation (a couple chapters) and a smaller foray into integration. The Cauchy condition for convergence receives a short, dedicated chapter. Other topics include L’Hôpital, Lipschitz, a gamut of mean value theorems, and Taylor series. The authors’ main concerns come across as a firm, even rigorous, foundation in limits and convergence theory...
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