Beijing Institute of Mathematical Sciences and Applications Beijing Institute of Mathematical Sciences and Applications

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About
President
Governance
Partner Institutions
Visit
People
Management
Faculty
Postdocs
Visiting Scholars
Staff
Research
Research Groups
Courses
Seminars
Join Us
Faculty
Postdocs
Students
Events
Conferences
Workshops
Forum
Life @ BIMSA
Accommodation
Transportation
Facilities
Tour
News
News
Announcement
Downloads
Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > Fourier Analysis and Partial Differential Equations
Fourier Analysis and Partial Differential Equations

We begin with Fourier series, examining their properties and essential results, including best square approximation, the Dirichlet kernel, convolutions, and convergence. These concepts are applied to solve key PDEs, such as the Laplace, heat, and wave equations. We then introduce the Fourier transform, a powerful tool for tackling PDEs in higher dimensions without the requirement of periodicity. Key foundational results are established, including the Fourier inversion formula, Plancherel's theorem, and the approximation of identity in \(\mathbb{R}^n\). We also investigate "good kernels," such as the heat and Poisson kernels. Using the Fourier transform, we provide solutions for the Laplace equation in the upper half-space and address the Cauchy problem for the heat equation. Additionally, we explore the Heisenberg uncertainty principle. The course further delves into boundary value problems for the Laplace equation in higher-dimensional domains, deriving representation formulas and studying fundamental solutions, the mean value property, Harnack’s inequality, and maximum principles.
Lecturer
Mahdi Hormozi
Date
9th October ~ 18th December, 2024
Location
Weekday Time Venue Online ID Password
Wednesday 19:20 - 20:55 A14-201 Zoom 17 442 374 5045 BIMSA
Audience
Undergraduate , Advanced Undergraduate , Graduate , Postdoc , Researcher
Video Public
No
Notes Public
No
Language
English
Beijing Institute of Mathematical Sciences and Applications
CONTACT

No. 544, Hefangkou Village Huaibei Town, Huairou District Beijing 101408

北京市怀柔区 河防口村544号
北京雁栖湖应用数学研究院 101408

Tel. 010-60661855
Email. administration@bimsa.cn

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