课程一

课程名称：Trigonomeric Series

主讲教师：Daniel J. Grubb 副教授( Department of Mathematical ciences Northern Illionois University DeKalb, IL 60115 USA)

中方对接教师：刘少伟副教授

上课时间：2019年7月8日至7月21日

上课地点：第八教学楼

课程简介：

Trigonometric series are used to describe many different physical phenomena as well as providing deep and interesting mathematical questions. This course will cover summability methods, uniqueness of representation, issues of divergence, Gibb’s phenomenon, absolutely convergent Fourier series, and small sets (synthesis, uniqueness, Kronecker, Dirichlet). Students are supposed to master the basic knowledge of Fourier and trigonometric series and be prepared to understand research questions in this area of harmonic analysis. This requires giving full and correct proofs in homework and to relate the different types of sets that come up in the subject.

课程二

课程名称：Linear Complex Analytic Differential Equationswith Applications to Special Functions

主讲教师： Jacques Sauloy 助理教授( Pure Mathematics and in Computer Science, 2002-present, Université Paul Sabatier, Toulouse)

中方对接教师：杨会兰副教授

上课时间：2019年7月8日至7月21日

上课地点：第八教学楼

课程简介：

Complex differential equations are pervasive in most parts of pure and applied mathematics. One of its main applications is the study of special functions which appear e.g. in Number Theory, Geometry, Probability Theory and of course Physics and Engineering. The heart of the theory involves linear differential equations, and the most accessible part of this deals with so-called fuchsian equations: those will therefore be the main theme of the course. Ever since Riemann founded the theory, analysis of singularities (local resolution, growth, . . . ) and qualitative description of the global behaviour (multivaluedness, monodromy matrices, . . . ) have been the foremost approaches: so we expect the students who will follow the course to under[1]stand these approaches, to master the basic techniques and to be able to apply them to particular functions.