This book discusses some of the first principles of modern analysis. I t can be used for courses at several levels, depending upon the background and ability of the students. It was written on the premise that today's good students have unexpected enthusiasm and nerve. When hard work is put to them, they work harder and ask for more. The honors course (at the University of Wisconsin) which inspired this book was, I think, more fun than the book itself. And better. But then there is acting in teaching, and a typewriter is a poor substitute for an audience. The spontaneous, creative disorder that characterizes an exciting course becomes silly in a book. To write, one must cut and dry. Yet, I hope enough of the spontaneity, enough of the spirit of that course, is left to enable those using the book to create exciting courses of their own. Exercises in this book are not designed for drill. They are designed to clarify the meanings of the theorems, to force an understanding of the proofs, and to call attention to points in a proof that might otherwise be overlooked. The exercises, therefore, are a real part of the theory, not a collection of side issues, and as such nearly all of them are to be done. Some drill is, of course, necessary, particularly in the calculation of integrals.
"synopsis" may belong to another edition of this title.
This edition is a comprehensive introduction to the basic ideas of modern mathematical analysis. Coverage proceeds form the elementary level to advanced and research levels. Additions to this edition include Rademacher's theorem on differentiability of Lipschitz Functions, deeper formulas on change of variables in multiple integrals, and recent results on the extension of differentiable functions.
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Book Description Springer-Verlag New York Inc., 1983. HRD. Book Condition: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # I1-9780387907970
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Book Description Springer, 1983. Hardcover. Book Condition: New. book. Bookseller Inventory # 0387907971
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Book Description Springer 1983-08-08, 1983. Hardcover. Book Condition: New. 2nd. 0387907971. Bookseller Inventory # 511659
Book Description Springer-Verlag New York Inc., 1983. HRD. Book Condition: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # I1-9780387907970
Book Description Springer, 1983. Hardcover. Book Condition: New. 2nd. This item is printed on demand. Bookseller Inventory # DADAX0387907971
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