Lectures on Standard and Less Standard Asymptotic Methods - Lecture 1

Explore advanced asymptotic methods in mathematics through this comprehensive lecture series. Delve into techniques for evaluating infinite sums and recognizing asymptotic laws of numerical sequences. Learn both standard approaches like the Euler-Maclaurin formula and less conventional methods, illustrated with numerous examples. Tackle challenging problems such as evaluating slowly convergent sums to high precision, analyzing asymptotic behavior of complex sequences, and computing highly oscillatory series. Gain insights into power series, smooth and divergent series, numerical computations, and special values. Investigate intriguing mathematical phenomena like Euler's mysterious formula and the Basel problem. Develop skills in time management, order analysis, and rough asymptotics while exploring the philosophical aspects of mathematical inquiry.

Intro
Poster
Questions
Duration
Course Outline
Philosophical Remarks
Power series
Smooth
Divergent series
Numerical computations
Pakis
Eulers mysterious formula
The basel problem
The mysterious formula
Why is it connected to asymptotics
Special values
Powerseries
Easy theorem
Motivation
Time Management
Order
Rough asymptotics
Variants
The calcimir effect
The sum
Computing a function
The second main topic
The philosophical part
General method
Euler
Question