# Asymptotic analysis (6ECTS)

Lecture: Do. B3 in A5 6, C014

Tutorial: Do. B5 in A5 6, C013

Description: Asymptotic analysis is to describe the behavior of a certain function near its limit. This method is widely used in many scientific fields, such as computer science and physics. In this course, we will focus on the topic of asymptotic approximations. We will start with the fundamental ideas underlying asymptotic approximations, and then we will demonstrate how to use this method to find approximate solutions for problems, including algebraic equations, ordinary differential equations and even partial differential equations arising from physical water waves, sound propagation, and aerodynamics of airplanes. Furthermore, we will also discuss how to use the matched asymptotic expansions to analyze problems with layers, and examine the stability.

Language: English

Prerequisites: Advanced calculus, basic knowledge of differential equations will also be helpful.

References:

[1] Mark H. Holmes, Introduction to perturbation methods. Springer-Verlag. 1995.

[2] J.D. Murray, Asymptotic analysis,Springer-Verlag.1992.