Primer of Modern Analysis

Directions for Knowing All Dark Things, Rhind Papyrus, 1800 B.C.

(Autor)

Buch | Hardcover
446 Seiten
1983 | 2nd ed. 1983
Springer-Verlag New York Inc.
978-0-387-90797-0 (ISBN)

Lese- und Medienproben

Primer of Modern Analysis - K.T. Smith
80,24 inkl. MwSt
The honors course (at the University of Wisconsin) which inspired this book was, I think, more fun than the book itself. 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.
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.

I.- 1 Applications.- 2 Calculation of Derivatives.- 3 Deeper Properties of Continuous Functions.- 4 Riemann Integration.- 5 Taylor’s Formula.- 6 Sequences and Series.- II.- 7 Metric Spaces.- 8 Functions From R1to Rn.- 9 Algebra and Geometry in Rn.- 10 Linear Approximation.- 11 Surfaces.- 12 Higher Derivatives.- III.- 14 Differentiation.- 15 Surface Area.- 16 The Brouwer Degree.- 17 Extensions of Differentiable Functions.

Erscheint lt. Verlag 8.8.1983
Reihe/Serie Undergraduate Texts in Mathematics
Zusatzinfo XV, 446 p.
Verlagsort New York, NY
Sprache englisch
Maße 178 x 254 mm
Themenwelt Mathematik / Informatik Mathematik Allgemeines / Lexika
Mathematik / Informatik Mathematik Analysis
ISBN-10 0-387-90797-1 / 0387907971
ISBN-13 978-0-387-90797-0 / 9780387907970
Zustand Neuware
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