题目为“Theoretical Numerical Analysis”。

具体时间、地点如下：

  时间：第7周 周一（10.8）晚7:10—10:00，周三（10.10）下午4:10--6:00
        第8周 周一（10.15）晚7:10—10:00，周三（10.17）下午4:10--6:00
        第9周 周一（10.22）晚7:10—10:00，周三（10.24）下午4:10--6:00

  地点：教学主楼A105

  欢迎有兴趣的师生参加！

 

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                                              2012.9.26 

Weimin Han教授讲课简要内容提纲

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The lectures cover some basic ideas and tools for students in mathematics
who are interested in working on applied mathematics, especially on
numerical analysis, from a theoretical perspective.  They are meant to
help the students to move more rapidly into a research program.

Lectures 1 & 2: Normed spaces and Banach spaces, inner product spaces and Hilbert spaces, and concrete function spaces.

Lectures 3 & 4: Linear operators and functionals, geometric series theorem, principle of uniform boundedness, Riesz representation theorem, weak convergence.

Lectures 5 & 6: Different means of approximation, best approximations in normed spaces and in inner product spaces.

Lectures 7 & 8: Sobolev spaces, definitions and properties; knowledge on Sobolev spaces is a must for modern PDE and the numerical solution of PDEs.

Lectures 9 & 10: Weak formulations of elliptic boundary value problems of PDEs, solution existence and uniqueness.

Lectures 11 & 12: An introduction to the finite element method, the most
popular numerical method for solving elliptic boundary value problems and problems in some areas of sciences and engineering.