1. Understanding of the concept of limit: limit is the basis of calculus, but many students may be confused when they first contact. To understand the limit, we need to grasp the relationship between the local nature and the overall nature of the function, which may require some abstract thinking ability.
2. Calculation of derivative and differential: Derivative and differential are the core concepts of calculus, and their calculation involves a series of complicated steps. For beginners, mastering these calculation methods may require a lot of practice.
3. Calculation of higher derivative and higher differential: With the increase of derivative and differential order, the calculation process will become more and more complicated. This requires students to have strong logical thinking ability and calculation ability.
4. Calculation of indefinite integral and definite integral: Integral is another important concept of calculus, and its calculation also involves a series of complicated steps. For beginners, mastering these calculation methods may require a lot of practice.
5. Calculus of multivariate function: The calculus of multivariate function involves many variables, which makes the problem more complicated. Students need to learn how to transform a multivariate problem into multiple univariate problems and master the corresponding solutions.
6. Solution of differential equation: Differential equation is an important application field of calculus, and its solution usually needs to apply the basic concepts and methods of calculus. This may be a big challenge for beginners.
7. Concept and application of infinite series: Infinite series is an important branch of calculus, and its understanding and application require students to have strong abstract thinking ability. In addition, it is difficult to judge the convergence and divergence of infinite series.
8. Application of Taylor formula: Taylor formula is an important tool of calculus, which can approximate the function near a certain point as a polynomial. However, the application of Taylor formula usually requires students to have a strong mathematical foundation and logical thinking ability.
9. Understanding and application of Lagrange mean value theorem and Cauchy mean value theorem: These two theorems are important theorems in calculus, and their understanding and application require students to have strong abstract thinking ability and logical reasoning ability.
10. Learning attitude and methods: For many students, learning calculus may be difficult and frustrating. Therefore, it is very important to keep a positive learning attitude and adopt appropriate learning methods to overcome these difficulties.