偏微分方程哲学博士

PDE的研究生课程以真实，复杂和功能分析的标准课程为基础。该入门课程几乎每年开设一次，涉及诸如基本分布理论，热，波动和Laplace方程的基本解，线性PDE的Cauchy问题，椭圆方程和Sobolev空间等主题。近年来，其他课程涉及分布理论，伪微分和傅立叶积分算子，微局部分析，超微分算子，变分方程的度量理论方法以及奇异点的非线性传播。通常每两年提供一次非线性泛函分析和一些复杂变量的函数课程。在每年进行的基本一年调查中，每年都会进行数值分析，其中包括对PDE数值解的一些研究。每隔一年，将提供有关该主题的更专
The graduate curriculum in PDE builds on the standard courses in real, complex, and functional analysis. The introductory course, which is given almost every year, treats such topics as elementary distribution theory, fundamental solutions of the heat, wave, and Laplace equations, the Cauchy problem for linear PDE's, elliptic equations, and Sobolev spaces. In recent years other courses have dealt with distribution theory, pseudodifferential and Fourier integral operators, microlocal analysis, paradifferential operators, measure theoretic methods for variational equations, and nonlinear propagation of singularities. Courses in nonlinear functional analysis and functions of several complex variables are usually offered every other year. Some study of the numerical solution of PDE's is included in the basic one year survey course in numerical analysis given each year. Every other year, a more specialized course is offered on this topic.