Now that the intuitive "infinitesimal" method of non-standard analysis has been proved rigorous (by at least two different approaches) it seems ridiculous that mathematics departments at universities cling to the harder method of teaching. I learned the delta-epsilon limit method, but it was not intuitive, albeit rigorous. Wished I had this text 35 years ago when I first took Calculus. I'm comparing the text to my undergrad (Amherst) text book which I found sub-standard. I'm just working through the book for fun. (It's nice having hard copy, and I hope at least some remuneration makes it back to the author.)įor background I have an undergrad in math and graduate degree in EE. I began with that but I also purchased the text when I realized how much I like it. ![]() (I'm always grateful to know that text book authors are human.) I am grateful to the author for the free PDF version. On occasion, there are errors in the answers provided. I am currently working through all the problems with answers. However, the nomenclature and presentation of calculus has always had references to infinitesimals, so presenting both epsilon delta and infinitesimal is actually clearer. I also really enjoy the infinitesimal approach. ![]() (Occasionally a proof may be omitted however the author is scrupulous in calling it out, and for the most part this is only the case for minor elements.) Throughout the text there is ample examples along with excellent diagrams. Concepts are described at an intuitive level, but at the same time the author follows a rigorous approach to the subject. Sections are short and cover a specific topic. Keisler follows a consistent, easy to follow approach.
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