Mangatiana A. Robdera

A Concise Approach to Mathematical Analysis (eBook, PDF)

• Format: PDF

Produktbeschreibung

This text introduces to undergraduates the more abstract concepts of advanced calculus, smoothing the transition from standard calculus to the more rigorous approach of proof writing and a deeper understanding of mathematical analysis. The first part deals with the basic foundation of analysis on the real line; the second part studies more abstract notions in mathematical analysis. Each topic contains a brief introduction and detailed examples.

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Produktdetails

• Verlag: Springer London
• Seitenzahl: 362
• Erscheinungstermin: 27. Juni 2011
• Englisch
• ISBN-13: 9780857293473
• Artikelnr.: 43999886

Autorenporträt

Mangatiana A. Robdera, Al Akhawayn University, Morocco

Inhaltsangabe

Numbers and Functions.- Real Numbers.- Subsets of ?.- Variables and Functions.- Sequences.- Definition of a Sequence.- Convergence and Limits.- Subsequences.- Upper and Lower Limits.- Cauchy Criterion.- 3. Series.- Infinite Series.- Conditional Convergence.- Comparison Tests.- Root and Ratio Tests.- Further Tests.- 4. Limits and Continuity.- Limits of Functions.- Continuity of Functions.- Properties of Continuous Functions.- Uniform Continuity.- Differentiation.- Derivatives.- Mean Value Theorem.- L'Hôspital's Rule.- Inverse Function Theorems.- Taylor's Theorem.- Elements of Integration.- Step Functions.- Riemann Integral.- Functions of Bounded Variation.- Riemann-Stieltjes Integral.- Sequences and Series of Functions.- Sequences of Functions.- Series of Functions.- Power Series.- Taylor Series.- Local Structure on the Real Line.- Open and Closed Sets in ?.- Neighborhoods and Interior Points.- Closure Point and Closure.- Completeness and Compactness.- Continuous Functions.- Global Continuity.- Functions Continuous on a Compact Set.- Stone-Weierstrass Theorem.- Fixed-point Theorem.- Ascoli-Arzelà Theorem.- to the Lebesgue Integral.- Null Sets.- Lebesgue Integral.- Improper Integral.- Important Inequalities.- Elements of Fourier Analysis.- Fourier Series.- Convergent Trigonometric Series.- Convergence in 2-mean.- Pointwise Convergence.- A. Appendix.- A.1 Theorems and Proofs.- A.2 Set Notations.- A.3 Cantor's Ternary Set.- A.4 Bernstein's Approximation Theorem.- B. Hints for Selected Exercises.

Rezensionen

From the reviews:

THE BULLETIN OF MATHEMATICS BOOKS

"It is written primarily for advanced students of mathematics - in the 3rd of 4th year of their degree - who wish to specialize in pure and applied mathematics, but it will also prove useful to students of physics, engineering and computer science who also use advanced mathematical techniques."