1, master the basic concepts of mathematical and physical equations, such as linearity, nonlinearity, quasilinearity, order, etc. Understand the establishment of typical second-order linear partial differential equations such as chord, rod, membrane, vibration, electromagnetic field, heat conduction, reaction diffusion, steady state, conservation law and the expression of definite solution conditions. Master the classification method of second-order linear partial differential equations.

2. Make clear the function of intrinsic value and intrinsic function system, skillfully handle homogeneous and nonhomogeneous elliptic, parabolic and hyperbolic equations and their first, second and third boundary conditions by using separation of variables, and understand the application of special functions such as legendre polynomials and Bessel functions in partial differential equations and the eigenvalue problem of Sturm-Liouville equation.

3. Master the D'Alembert solution of wave equation; Master Fourier, Laplace and other integral transformations and apply them to solving partial differential equations. Master the properties of harmonic function and the application of Green's function method in special fields such as sphere and half space. In the final analysis, mathematical equation is to study how to use partial differential equation to solve physical problems.

As for the calculation method, because the computer is discrete, it cannot directly deal with non-discrete mathematical problems. Linking the two is the research of calculation method, which is simply the method of using electronic computer to deal with mathematical problems.