Mathematical physics equations: applicable majors: electronic information science and technology, applied physics majors: college physics, advanced mathematics, complex variable function, field theory, vector algebra 1. Teaching objectives and tasks of the course Mathematical physics equations are important public basic courses and tools for physics, electronic information science and communication science. Its main feature lies in the close combination of mathematics and physics. Mathematical methods are applied to the analysis of specific problems in practical physics and interdisciplinary science, and mathematical models (partial differential equations) are established through physical processes. By solving and analyzing the model, we can further understand the specific physical process and improve the ability to analyze and solve practical problems. Mathematical physics method is a pure theoretical course. In teaching, we combine classroom teaching (mainly), after-class exercises and computer exercises, and pay attention to the classroom discussion in the practice class. The course content includes three parts: the first part is the review of transcendental knowledge such as vector analysis and field theory; The second part is the establishment and routine solution of mathematical and physical equations; Including: definite solution problem, traveling wave method, variable separation method, integral transformation method, Green's function method, variational method and so on. The third part is special functions, including legendre polynomials, Bessel function and Sturm-Liu Wei eigenvalue problem. This course will combine the professional characteristics of applied physics and electronic information, make full use of numerical calculation technology, combine the characteristics of mathematical physics methods, break through the difficulties of the course of mathematical physics methods by optimizing the teaching material system and visual analysis of calculation examples, and improve students' learning interest and ability to analyze and solve problems. Second, the connection and division of labor between this course and other courses. Before entering this course, students should take courses including: college physics, advanced mathematics, complex variable function, field theory and vector algebra. The study of these courses has laid a good mathematical foundation for this course. After the completion of this course, you can enter the following courses: four major mechanics, electromagnetic field and microwave technology, modern physical experiments, etc. Third, the course content and basic requirements (1) Introduction, prerequisite knowledge review: (2 hours) 1, the basic concept of vector, the basis of algebraic operation vector analysis; 2. Basis of field theory (gradient, divergence and curl of vector field); 3. Complex variable function integration; 4. Surplus theory. 2) Establishment and definite solution of mathematical and physical equations: (8 hours) 1. Three basic equations are established: string vibration equation, heat conduction equation and Poisson equation; 2. Definite solution conditions: initial conditions, three boundary conditions, natural boundary conditions and connection conditions. (3) Traveling wave method: (6 hours) 1, D'Alembert formula, traveling wave solution of one-dimensional problem; 2. Poisson's formula and the average method of transforming three-dimensional problems into one-dimensional problems; 3. Pulse method is used to solve the non-homogeneous problem and delay potential. (4) Variable separation method: (10 class hour) 1, free vibration and heat conduction of bounded strings; 2. The eigenvalue problem of 2.Sturm-Liouville equation (ordinary differential equation); 3. The definite solution of nonhomogeneous general equation problem: 4. The treatment method of nonhomogeneous boundary conditions; 5. Separate variables in orthogonal curvilinear coordinates (spherical coordinates and cylindrical coordinates). (5) Special functions: (12 class hours) 1, basic properties of legendre polynomials and legendre polynomials; 2. Correlate Legendre function and spherical harmonic function; 3. Separation of variables in spherical coordinate system: 4. Bessel function and its properties, integrated by Bessel function; 5. Calculation and simulation of other column functions and special functions; 6. Separation of variables in column coordinates. (6) Integral transformation method: (8 hours) 1, Fourier integral and Fourier transformation properties; 2. Solving mathematical equations by Fourier transform; 3. Laplace transform and its properties; 4. Laplace transform method. (7) Green's function method: (8 hours) 1, function, Poisson equation boundary value problem, Green's formula; 2. General solution of Green's function; 3. Solving Dirichlet Green's function in some special areas by electric image method: 4. Calculation and simulation of application of Green's function method. (8) Other common solutions of mathematical and physical equations: (6 hours) 1, solutions of nonlinear equations; 2. Integral equation method; 3. Variational method. 1. Basic requirements This course requires students to understand the establishment methods of mathematical and physical equations, with emphasis on the establishment and conventional solution of three commonly used partial differential equations; Including: definite solution problem, traveling wave method, variable separation method, integral transformation method, Green's function method, variational method and so on. Master the application of special functions (including legendre polynomials, Bessel function, Sturm-Liuwei eigenvalue problem, etc.). ) in mathematical and physical equations. 2. Emphasis and difficulty Emphasis: definite solution problem, traveling wave method, variable separation method, integral transformation method and Green's function method Difficulties: special function, Green's function method "Numerical calculation method" preparatory course: mathematical analysis, advanced algebra, ordinary differential equations, functional analysis 1. Basic contents Absolute error and relative error, influence of error on calculation, stability 1. Basic requirements 1. Understand absolute error and relative error.