From calculus to analysis 1st Edition by Rinaldo B Schinazi ISBN 0817682880 9780817682880
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Product details:
ISBN 10: 0817682880
ISBN 13: 9780817682880
Author: Rinaldo B. Schinazi
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, allowing students to master the calculus tools that are crucial in understanding analysis.
From Calculus to Analysis prepares readers for their first analysis course—important because many undergraduate programs traditionally require such a course. Undergraduates and some advanced high-school seniors will find this text a useful and pleasant experience in the classroom or as a self-study guide. The only prerequisite is a standard calculus course.
Table of contents:
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 Monotone sequences, Bolzano-Weierstrass 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 Trigonometric functions
3.3 Inverse trigonometric functions
3.4 Exponential and logarithmic functions
Ch. 4 Fifty Ways to Estimate the Number π
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 π 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 Representation of Numbers
Ch. 8 Countable and Uncountable Sets
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Tags: Rinaldo B Schinazi, Calculus, Analysis