عنوان

A Concrete Introduction to Real Analysis.

1420011545

9781420011548

b569984

A Concrete Introduction to Real Analysis.

[Book]

Robert Carlson

Philadelphia

PA CRC Press

2006. ©2006.

(308 pages).

Textbooks in Mathematics.

Front cover --; Contents --; Preface --; Chapter 1. Discrete Calculus --; Chapter 2. Selected Area Computations --; Chapter 3. Limits and Taylor's Theorem --; Chapter 4. Infinite Series --; Chapter 5. A Bit of Logic --; Chapter 6. Real Numbers --; Chapter 7. Functions --; Chapter 8. Integrals --; Chapter 9. More Integrals --; References.

DISCRETE CALCULUSIntroductionProof by InductionA Calculus of Sums and DifferencesSums of PowersProblemsSELECTED AREA COMPUTATIONSIntroductionAreas under Power Function Graphs The Computation of pNatural LogarithmsStirling's FormulaProblemsLIMITS AND TAYLOR'S THEOREM IntroductionLimits of Infinite Sequences Series RepresentationsTaylor SeriesProblemsINFINITE SERIESIntroductionPositive SeriesGeneral SeriesGrouping and RearrangementProblemsA BIT OF LOGICSomemathematical PhilosophyPropositional Logic Predicates and QuantifiersProofsProblemsREAL NUMBERS Field Axioms Order Axioms Completeness Axioms Subsequences and Compact Intervals Products and FractionsProblemsFUNCTIONSIntroduction BasicsLimits and Continuity Derivatives ProblemsINTEGRALSIntroductionIntegrable Functions Properties of Integrals Numerical Computation of IntegralsProblemsMORE INTEGRALSIntroductionImproper IntegralsIntegrals with Parameters ProblemsREFERENCESINDEX.

Mathematical analysis.

Robert Carlson

Robert Carlson

[Book]

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