Advanced mathematics and linear algebra are generally taught separately in schools.
The contents of advanced mathematics are as follows:
The limit and continuity of 1. unary function. Theoretical proof, such as ε-N, ε-X, ε-δ, does not require in-depth study; Pinch theorem and monotone boundedness are very important, so we should master some equivalent substitutions. It is not difficult to learn the continuity of functions.
2. Differential calculus of unary function. Be sure to learn derivatives well, or you will suffer from learning definite integrals; The essence of differentiation is derivative; The basic theorem of differential calculus and Lagrange mean value theorem must be easy to learn, and the proof problem basically depends on it; L' the hospital is quite important; Taylor formula is often used to prove problems.
3. Integral of unary function. Learn the variable limit function well; Integration by parts and substitution integral method are also very easy to learn; There are many application problems in this chapter.
4. Ordinary differential equations. Forget the details. Anyway, it's not difficult, just annoying. Just remember the formula.
5. Differential calculus of multivariate functions. Not only diversity, but also a lot of content. The complex variable function came out.
6. Multivariate function integration. Double integral and triple integral have come out, involving the calculation of the first kind of curves and surfaces.
7. Integration of vector functions. It involves the calculation of the second kind of curves and surfaces.
8. Complex variable function integration. Cauchy integral theorem is the foundation and the key point, lz will do it.
9. Constant term series.
10. Function term series.
Lz, linear algebra is to be learned, otherwise you will learn the content behind high numbers very hard; But linear algebra is also very annoying, because there are too many contents, but they are not very deep. They basically revolve around three points: solving equations with matrices, explaining quadratic forms with matrices, eigenvalue and its transformation (orthogonal transformation is very important).
I hope I can help lz.