数学物理方法

课程编码：180101070201P2005Y 英文名称：Mathematical Methods for Physics 课时：50 学分：2.50 课程属性：专业核心课 主讲教师：周宇峰等

Mathamatical methods for physics, which is a basic mathematics course for physics classes, mainly provides the basic knowledge of ordinary differential and partial differential equations necessary for the study of other courses in the future. The course adopts the method of teaching in English to enable students to master ordinary differential calculus and the basic solution of partial differential equations, improving students' ability to abstract mathematics from physical phenomena, and cultivating students' physical intuition.

Calculus

第一章 Preliminaries
第1节 1.1 Infinite series, series of functions 2学时 周宇峰
第2节 1.2 Vectors, complex numbers, 1学时 周宇峰
第3节 1.3 Determinants and Matries 2学时 周宇峰
第二章 Vector analysis
第1节 2.1 Review of basics properties 1学时 周宇峰
第2节 2.2 Differential vector operators 2学时 周宇峰
第3节 2.3 Vector integrations, potential theory 1学时 周宇峰
第三章 Tensors and differential forms
第1节 3.1 Tensor analysis 2学时 周宇峰
第2节 3.2 Tensor in General Coordinates 2学时 周宇峰
第3节 3.3 Jacobians 1学时 周宇峰
第四章 Vector spaces
第1节 4.1 Vector in Function Spaces 2学时 周宇峰
第2节 4.2 Operators 2学时 周宇峰
第3节 4.3 Transformations of Operators 2学时 周宇峰
第五章 Eigenvalue problems5.1 Eigenvalue Equations
第1节 5.1 Eigenvalue Equations 1学时 周宇峰
第2节 5.2 Matrix Eigenvalue Problems 1学时 周宇峰
第3节 5.3 Hermitian Eigenvalue Problems 2学时 周宇峰
第六章 Ordinary differential equations
第1节 6.1 First ‐ Order Equations 2学时 郭怀珂
第2节 6.2 Second‐Order Linear ODEs 2学时 郭怀珂
第3节 6.3 Inhomogeneous Linear ODEs 2学时 郭怀珂
第七章 Partial differential equations
第1节 7.1 First ‐ Order Equations 1学时 郭怀珂
第2节 7.2 Second – Order Equations 2学时 郭怀珂
第3节 7.3 Separation of Variables 2学时 郭怀珂
第八章 Complex variable theory
第1节 8.1 Cauchy – Riemann Conditions, Cauchy’s Integral Theorem 2学时 郭怀珂
第2节 8.2 Laurent Expansion, Singularities 2学时 郭怀珂
第3节 8.3 Calculus of Residues, Evaluation of Definite Integrals 1学时 郭怀珂
第九章 Fourier series and Fourier transforms
第1节 9.1 General Properties, Application of Fourier Series 1学时 郭怀珂
第2节 9.2 Fourier Transforms, Properties of Fourier Transforms 2学时 郭怀珂
第3节 9.3 Fourier Convolution Theorem, Discrete Fourier Transforms 2学时 郭怀珂
第十章 Probability and Statistics
第1节 10.1 Random Variables 1学时 郭怀珂
第2节 10.2 Binomial Distribution, Poisson Distribution, Gauss’ Nomal Distribution 2学时 郭怀珂
第3节 10.3 Transformation of Random Variables, Statistics 2学时 郭怀珂

Prof. YuFeng Zhou received his PhD from the Institute of Theoretical Physics, Chinese Academy of Sciences (CAS) in 2002, and then worked as a postdocal research fellow at Ludwig-Maximilians-University、Dortmund University、KEK and KIAS. After 2009, he worked as a professor at Institute of Theoretical Physics, Chinese Academy of Sciences (CAS). His research interests focus on Dark matter, new physics beyond the Standard Model, baryon number generation, CP symmetry breaking, and flavor physics. Huaike Guo is an associate professor in the International Centre for Theoretical Physics Asia-Pacific, University of Chinese Academy of Sciences. He received his PHD from the University of Massachusetts Amherst in 2016, and did postdocs at the institute of theoretical physics (CAS), the University of Oklahoma, and the University of Utah. His research lies in fundamental physics studies based on gravitational waves.
He is also a member of the LIGO-Virgo-KAGRA scientific collaboration.