2007- 1-23 15:32
1. The original outline of advanced mathematics (exercise book) includes unary function calculus, spatial analytic geometry and vector algebra, multivariate function calculus, ordinary differential equations and infinite series. However, the new syllabus does not include unary function calculus, but only spatial analytic geometry and vector algebra, multivariate function calculus, ordinary differential equations and infinite series.
2. In the part of spatial analytic geometry and vector algebra: the new syllabus does not contain hyperboloids (including hyperboloids with one leaf, hyperboloids with two leaves and hyperboloids) in the quadric surface part.
3. In the part of multivariate differential calculus, the knowledge points of directional derivative and gradient are added; The derivative rule of compound function requires that the original "comprehensive application" should be changed into "simple application". It is clear in the content that we should master the solution of the first-order partial derivative of three kinds of composite functions skillfully; Regarding the conditional extremum problem, it is clearly required to find the extremum of multivariate function under a constraint condition.
4. In the chapter "Multiple Integrals", the application of multiple integrals only puts forward that the area, volume, material surface area and mass of space objects can be calculated by multiple integrals. The requirements for finding the center of gravity and moment of inertia in the original profile are deleted.
5. In the part of curve integral and surface integral: the new syllabus does not require the relationship between two types of curve integral; The new syllabus requires that Gaussian formula be used to calculate the surface integral of coordinates on closed surfaces. It also adds divergent content. In the application of curve integral, in addition to geometric application, it is explicitly required to use curve integral to calculate the work done by variable force along the curve.
6. In the part of ordinary differential equations, the solutions of three kinds of equations (including separable variables, homogeneous equations and first-order linear differential equations) are clearly put forward, and the requirements of Bernoulli equation and fully differential equation are removed;
On the problem of finding the special solution of the second-order linear non-homogeneous differential equation with constant coefficients, it is clear that only the non-homogeneous term is needed, where the real number is a polynomial, and the form of the special solution is determined.
7. In the part of infinite series. Leibniz discriminant only requires that it can be used to judge the convergence of staggered series, and does not require the estimation of truncation error. Taylor expansion of function needs Kraulin expansion of memory horse, but not Kraulin expansion of memory horse. With regard to Fourier series, it is required to find the Fourier expansion formula of functions with periods above and expand the above functions into sine series or cosine series, but it is not required to expand the functions on sum into Fourier series and sine series or cosine series.