Calculus

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Davies told me the trick for Problem 11-66, which previously was proved only in Problem 20-8 [21-8 in the third edition], and Marina Ratner suggested several interesting problems, especially ones on uniform continuity and infinite series. They range from straightforward, but not overly simple, exercises which develop basic techniques and test understanding of concepts, to problems of considerable diffi­ culty' and, I hope, of comparable interest. Si hay convergencias entre estos mundos formales y el mundo humano es más sorprendente que necesario, como lo sugirió Bertrand Russell en su Autobiografía. Moreover, the Appendix to Chapter 12 has been extended to treat vector operations on vector-valued curves.

This is a beautiful exposition of the theory of calculus from the axiomatic approach with full motivation and proof of the major theorems and some interesting facts that are seldom presented at this level. Many problems are so difficult, especially if the hints are not consulted, that the best of students will probably have to attempt only those which especially interest them; from the less difficult problems it should be easy to select a portion which will keep a good class busy, but not frustrated. Richard Serkey helped collect the material which provides historical sidelights in the problems, and Richard Weiss supplied the answers appearing in the back of the book. For this reason, it would be of little value merely to list the topics covered, or to mention pedagogical practices and other innovations.Al principio puede hacerse algo espeso cuando no se está familiarizado con el tipo de razonamiento, pero creo que a la postre merece mucho la pena. It is almost obligatory in such circumstances to report that the preliminary version was a gratifying success. Since the most exciting concepts of calculus do not appear until Part III, it should be pointed out that Parts I and II will probably require less time than their length suggests—although the entire book covers a one-year course, the chapters are not meant to be covered at any uniform rate. But seriously--if you're looking for practical application or pragmatic knowledge then this book isn't exactly for you.

It is Hemingway wedded with Mathematics--the grand iceberg of thought that is analysis lends weight and a grace of movement to the crystal clear tip of Calculus as it glides through the waters of mathematical thought. This arrangement corresponds to the traditional organization of most calculus courses, but I feel that it will only diminish the value of the book for students who have seen a small amount of calculus previously, and for bright students with a reasonable background.Considerable attention is paid to motivating the discussion, showing why each result is important (though mainly in the pure mathematics context, applications of calculus being mainly found in the problems at the end of each chapter). For me the best introduction to calculus in one variable, yet absolutely rigurous it is more focussed in explain fundamental concepts in deep that in long full of calculations demostrations;also has some touchs of subtle humour ,some uncommon in a textbook and a lot of remarkable exercises. I am content to hope that some other students will be able to use the book to such good purpose, and with such enthusiasm.