Counterexamples in Analysis (eBook)

Bernard R. Gelbaum, John M. H. Olmsted (Autoren)

eBook Download: EPUB

2012
Dover Publications (Verlag)
9780486134918 (ISBN)

Infos

These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.

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These counterexamples, arranged according to difficulty or sophistication, deal mostly with the part of analysis known as "e;real variables,"e; starting at the level of calculus. The first half of the book concerns functions of a real variable; topics include the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, uniform convergence, and sets and measure on the real axis. The second half, encompassing higher dimensions, examines functions of two variables, plane sets, area, metric and topological spaces, and function spaces. This volume contains much that will prove suitable for students who have not yet completed a first course in calculus, and ample material of interest to more advanced students of analysis as well as graduate students. 12 figures. Bibliography. Index. Errata.

Inhalt

1. The Real Number System.2. Functions and Limits.3. Differentiation.4. Riemann Integration.5. Sequences.6. Infinite Series.7. Uniform Convergence.8. Sets and Measure on the Real Axis.9. Functions of Two Variables.10. Plane Sets.11. Area.12. Metric and Topological Spaces.13. Function Spaces. Bibliography. Special Symbols. Index.

Produkt-Details

• Erscheint lt. Verlag: 12.7.2012
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Gewicht: 281 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Schlagworte: abstract algebra • Advanced Calculus • advanced material • advanced undergraduate • algebra class • Algebraic Geometry • algebraic topology • Algebras • axler • books on abstract algebras • books on advanced calculus • books on advanced materials • books on advanced undergraduates • books on algebra classes • books on algebraic geometries • books on algebraic topologies • books on algebras • books on axler • books on category theories • books on dedekinds • books on exteriors • books on field theories • books on functional analysis • books on galois theories • books on graduate levels • books on graduate students • books on hungerford • books on lang • books on lebesgue • books on lemma • books on level mathematics • books on linear algebras • books on measure theories • books on modules • books on phd students • books on polynomials • books on self studies • books on steen • books on studying mathematics • books on tensors • books on topologies • books on vector spaces • Burnside • category theory • chapter talked • Compactness • counter-examples • counterexamples • Dedekind • Exercises • exteriors • fairly thorough • Field Theory • Finite • foote • Functional Analysis • Functions • Galois Theory • Graduate level • graduate students • Hungerford • Lang • Lebesgue • Lemma • level mathematics • linear algebra • material covered • Mathematical • mathematician • measure theory • modules • nontrivial • Notation • PhD student • polynomials • Probability • proofs • Proposition • self study • Steen • students preparing • studying mathematics • study mathematics • Tensor • Theorems • Topological • Topologies • Variables • varying difficulty • vector spaces
• ISBN-13: 9780486134918 / 9780486134918