Reading for students
Evgeny Shchepin
On Euler's footsteps. Evgeny Shchepin's Uppsala lectures on Calculus
in single pdf-file.
Contents
Preface
The Legend of Euler's Series
Chapter 1. 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
Chapter 2. 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
Chapter 3. 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
Chapter 4. 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
Evgeny Shchepin
2001-11-19