Introduction to Mathematical Analysis (International Library of Psychology, Philosophy and Scientif) - Brossura

Clapham, C.

 
9780710075291: Introduction to Mathematical Analysis (International Library of Psychology, Philosophy and Scientif)

Sinossi

I have tried to provide an introduction, at an elementary level, to some of the important topics in real analysis, without avoiding reference to the central role which the completeness of the real numbers plays throughout.

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Contenuti

Content.- 1. Axioms for the Real Numbers.- 1 Introduction.- 2 Fields.- 3 Order.- 4 Completeness.- 5 Upper bound.- 6 The Archimedean property.- Exercises.- 2. Sequences.- 7 Limit of a sequence.- 8 Sequences without limits.- 9 Monotone sequences.- Exercises.- 3. Series.- 10 Infinite series.- 11 Convergence.- 12 Tests.- 13 Absolute convergence.- 14 Power series.- Exercises.- 4. Continuous Functions.- 15 Limit of a function.- 16 Continuity.- 17 The intermediate value property.- 18 Bounds of a continuous function.- Exercises.- 5. Differentiable Functions.- 19 Derivatives.- 20 Rolle’s theorem.- 21 The mean value theorem.- Exercises.- 6. The Riemann Integral.- 22 Introduction.- 23 Upper and lower sums.- 24 Riemann-integrable functions.- 25 Examples.- 26 A necessary and sufficient condition.- 27 Monotone functions.- 28 Uniform continuity.- 29 Integrability of continuous functions.- 30 Properties of the Riemann integral.- 31 The mean value theorem.- 32 Integration and differentiation.- Exercises.- Answers to the Exercises.

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