Uppsala Lectures on Calculus

by Evgeny Shchepin in single ps-file.

Table of Contents

• Legends
• Series
• 1.1 Autorecursion of Infinite Expressions
• 1.2 Positive Series
• 1.3 Unordered Sums
• 1.4 Infinite Products
• 1.5 Telescopic Sums
• 1.6 Complex Series
• Integrals
• 2.1 Natural Logarithm
• 2.2 Definite Integral
• 2.3 Stieltjes Integral
• 2.4 Asymptotics of Sums
• 2.5 Quadrature of circle
• 2.6 Virtually Monotone Functions
• Derivatives
  • 3.1 Newton-Leibniz Formula
  • 3.2 Exponential Function
  • 3.3 Euler Formula
  • 3.4 Abel's Theorem
  • 3.5 Residues Theory
  • 3.6 Analytic Functions
• Differenceses
  • 4.1 Newton Series
  • 4.2 Bernoulli Numbers
  • 4.3 Euler-Maclaurin Formula
  • 4.4 Gamma Function
  • 4.5 The Cotangent
  • 4.6 Divergent Series
  Bibliography
  2001-11-19