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Mathematical analysis : functions, limits, series, continued fractions

Author: L A Lyusternik; A R Yanpol'skii; Donald E Brown; E Spence
Publisher: Oxford, England : Pergamon Press, 1965. ©1965
Series: International series of monographs in pure and applied mathematics, Volume 69.
Edition/Format:   eBook : Document : English : First editionView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Mathematical analysis : functions, limits, series, continued fractions.
Oxford, England : Pergamon Press, ©1965
xiv, 404 pages
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: L A Lyusternik; A R Yanpol'skii; Donald E Brown; E Spence
ISBN: 9781483194363 1483194361
OCLC Number: 903965224
Description: 1 online resource (419 pages).
Contents: Front Cover ; Mathematical Analysis; Copyright Page; Table of Contents; FOREWORD; CHAPTER I. THE ARITHMETICAL LINEAR CONTINUUM AND FUNCTIONS DEFINED THERE; 1. Real numbers and their representation; 1. Real numbers; 2. The numerical straight line; 3. p-adic systems; 4. Sets of real numbers; 5. Bounded sets, upper and lower bounds; 6. The theory of irrational numbers; 2. Functions. Sequences; 1. Functions of one variable; 2. Upper and lower bounds of a function; 3. Even and odd functions; 4. Inverse functions; 5. Periodic functions; 6. Functional equations; 7. Numerical sequences. 13. Uniform convergence of functions14. Convergence in the mean; 15. The symbols o(x) and O(x); 16. Monotonic functions; 17· Convex functions; CHAPTER II. n-DIMENSIONAL SPACES AND FUNCTIONS DEFINED THERE; Introduction; 1. n-dimensional spaces; 1. n-dimensional coordinate space; 2. n-dimensional vector space; 3. Scalar product; 4. A linear system and its basis; 5. Linear functions; 6. Linear envelope; 7. Orthogonal systems of vectors; 8. Biorthogonal systems of vectors; 9. The projection of a vector on to a manifold; 2. Passage to the limit, continuous functions and operators. 1. Passage to the limit in n-dimensional space2. Series of vectors; 3. Continuous functions of n variables; 4. Periodic functions of n variables. Manifolds of constancy; 5. Passage to the limit for linear envelopes; 6. Operators from En into Em; 7. Iterative sequences; 8. The principle of contraction mappings; 3. Convex bodies in n-dimensional space; 1. Fundamental definitions; 2. Convex functions; 3. Convex bodies and the norm of a vector; 4. Support hyperplanes; 5. Support functions and conjugate spaces; 6. Fundamental theorems on support hyperplanes.
Series Title: International series of monographs in pure and applied mathematics, Volume 69.
Responsibility: edited by L.A. Lyusternik and A.R. Yanpol'skii ; translated by D.E. Brown ; translation edited by E. Spence.

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