From Calculus to Analysis
(Sprache: Englisch)
This concise textbook is an ideal preparation for an undergraduate's first analysis course. With exercises, unique examples, and coverage of the basic principles, it explains the calculus basics such as number systems required for more advanced analysis.
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Produktinformationen zu „From Calculus to Analysis “
This concise textbook is an ideal preparation for an undergraduate's first analysis course. With exercises, unique examples, and coverage of the basic principles, it explains the calculus basics such as number systems required for more advanced analysis.
Klappentext zu „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, 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.
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.
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.
Inhaltsverzeichnis zu „From Calculus to Analysis “
- PrefaceCh 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
- Indexs 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 Int
Bibliographische Angaben
- Autor: Rinaldo B. Schinazi
- 2011, 2012., 250 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 0817682880
- ISBN-13: 9780817682880
- Erscheinungsdatum: 27.09.2011
Sprache:
Englisch
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