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...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
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:
Διαθέσιμο Online:Full Text via HEAL-Link
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.