1, ordinary differential equations (ODEs) and partial differential equations (PDEs): Yao Zhengdong may discuss the solutions, properties and applications of various ordinary differential equations and partial differential equations. He may introduce some classical ordinary differential equations and partial differential equations and discuss their applications in physics.
2. Variational method: Variational method is a mathematical method, which is widely used in optimization problems, extreme problems and functional analysis in physics. Yao Zhengduan may explain the basic principle and application of variational method and its importance in mathematical and physical methods.
3. Analytical mechanics: Yao Zhengdong may discuss the basic theories and methods of analytical mechanics, including Lagrangian mechanics and Hamiltonian mechanics. He may introduce how to apply these mechanical theories to the modeling and analysis of physical systems.
4. Symbolic calculation and numerical calculation: Yao Zhengduan may discuss the application of symbolic calculation and computer numerical calculation in mathematical physics methods. He may introduce some commonly used computing tools and software and discuss their functions in solving practical problems.
5. Other methods in mathematical physics: In addition to the above contents, Chapter 8 of Yao Zhengduan may also involve some other methods in mathematical physics, such as function analysis, special functions and group theory. He may introduce the basic concepts and applications of these methods and their importance in solving complex physical problems.
Brief introduction of Yao Zhengduan
Yao Duanzheng, a second-class professor of Wuhan University, is a doctoral supervisor, enjoying the special allowance of the State Council, the winner of the first national award for famous teachers in teaching, a young and middle-aged expert with outstanding contributions in Hubei Province, and the vice chairman of the National Research Association of Mathematical Physics in colleges and universities.
Professor Yao Duanzheng has long been engaged in scientific research in the fields of nonlinear optics and mathematical physics. Mainly engaged in the theoretical research of optical nonlinearity such as semiconductor confinement structures (such as quantum wells and quantum dots) and coherent transient optical effects. In addition, he is also engaged in the analysis and research of nonlinear optical transmission characteristics in optical fibers.
He has presided over or undertaken scientific research projects 10 of Hubei Natural Science Foundation, National Natural Science Foundation and national defense projects, and published more than 80 papers in important academic journals at home and abroad, such as PHYSICAL-REVIEW-A, Applied-PhysicsLetters and Applied-Physics-B. And won the second prize of scientific and technological progress of the Ministry of Education as the first person to complete it. More than 30 master's and doctoral students have been instructed, and 4 doctoral students are being instructed.