From Calculus to Analysis
This comprehensive textbook is intended for a two-semester sequence in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts of calculus. The last five chapters present a first course in analysis. The presentation is clear and concise, allowin...
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| Format: | eBook |
| Language: | English |
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Boston, MA
Birkhäuser
2012, 2012
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| Edition: | 1st ed. 2012 |
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| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Preface
- Ch. 1 Number Systems
- 1.1 The algebra of the reals
- 1.2 Natural numbers and integers
- .1.3 Rational numbers and real numbers
- 1.4 Power functions
- Ch. 2 Sequences and Series
- 2.1 Sequences
- 2.2 Montone sequences, Bolzano-Weirestrass theorem and operations on limits
- 2.3 Series
- 2.4 Absolute convergence
- Ch. 3 Power series and special functions.-3.1 Power series.-3.2 Tigonometric functions
- 3.3 Inverse trigonometric functions
- 3.4 Exponential and logarithmic functions
- Ch 4 Fifty Ways to Estimate the Number pi.-4.1 Power series expansions
- 4.2 Wallis' integrals, Euler's formula, and Stirling's formula.-4.3 Convergence of infinite products
- 4.4 The number pi is irrational
- Ch. 5 Continuity, Limits, and Differentiation
- 5.1 Continuity
- 5.2 Limits of functions and derivatives
- 5.3 Algebra of derivatives and mean value theorems
- 5.4 Intervals, continuity, and inverse functions
- Ch. 6 Riemann Integration
- 6.1 Construction of the integral
- 6.2 Properties of the integral
- 6.3 Uniform continuity
- Ch 7 Decimal Represenation of Numbers
- Ch 8 Countable and Uncountable Sets
- Further Readings
- Index