"Uppsala Lectures on Calculus. On Euler's footsteps" by E.V. Shchepin

ISBN: 0973086726

Category: Technical

Tag: Science/Engineering


Posted on 2011-12-12. By anonymous.

Description


"Uppsala Lectures on Calculus. On Euler's footsteps" by E.V. Shchepin
V.A. Steklov Institute of Mathematics Russian Academy of Sciences
Topology Atlas | 2003 | ISBN: ISBN 0973086726 | 137 pages | PDF | 1 MB

This is a textbook for an introductory course of Calculus. The material of the lectures covers much of the standard Calculus curriculum but the approach is from a new perspective and a classical motivation.

Contents
Preface
The Legend of Euler's Series
Chapter 1. Series
1.1. Autorecursion of In nite Expressions
1.2. Positive Series
1.3. Unordered Sums
1.4. In nite Products
1.5. Telescopic Sums
1.6. Complex Series
Chapter 2. Integrals
2.1. Natural Logarithm
2.2. De nite 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 Functions
3.3. Euler Formula
3.4. Abel's Theorem
3.5. Residue Theory
3.6. Analytic Functions
Chapter 4. Differences
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

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