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Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. My efforts have been encouraged by lec tures that I have given at Heidelberg under the auspices of the Alexander von Humboldt Stiftung, at the University of Chicago, and at the University of Minnesota, the latter under the auspices of the Institute for Mathematics and Its Applications.
Jean Benabou has carefully read the entire manuscript and has offered incisive comments. Narasimhan, and Dieter Puppe have provided similar comments on chosen chapters. Fred Linton has pointed out places requiring a more exact choice of wording. Many conversations with George Mackey have given me important insights on the nature of Mathematics.
Over the years, I have profited from discussions of general issues with my colleagues Felix Browder and Melvin Rothenberg.
Jerry Bona and B. Foster have helped with my examina tion of mechanics. Voreadou, Volker Weispfennig, and Hugh Woodin. This book is based on an honors course in advanced calculus that the authors gave in the 's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year.
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