From Calculus to Analysis

• Κύριος συγγραφέας: Schinazi, Rinaldo B. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston : Birkhäuser Boston : Imprint: Birkhäuser, 2012.
• Έκδοση: 1.
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Approximation theory.; Measure theory.; Sequences (Mathematics).; Analysis.; Sequences, Series, Summability.; Approximations and Expansions.; Measure and Integration.

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...

Πίνακας περιεχομένων:

• 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.