1. Learn basic concepts and symbols: First, you need to understand the basic concepts of calculus, such as limit, derivative and integral. At the same time, you should be familiar with some commonly used symbols, such as dy/dx (derivative of y about x) and ∫ (integer symbol).
2. Learn indefinite integral and definite integral: indefinite integral is an application of derivative, and the original function can be obtained by solving indefinite integral. The definite integral is a method to calculate the area under the curve. You need to master the basic indefinite integral formula and definite integral formula, such as indefinite integral of power function and indefinite integral of trigonometric function.
3. Learn derivative and differential: the derivative represents the tangent slope of the function at a certain point, and the local change of the function at a certain point can be understood by finding the derivative. You need to learn how to find derivatives and how to use derivatives to study the properties of functions.
4. Learn the differential mean value theorem and Taylor formula: the differential mean value theorem is one of the basic theorems in calculus, which describes the local linear approximation of a function near a certain point. Taylor formula is an important tool to solve the approximate value of functions, and complex functions can be expressed by simple polynomials.
5. Learn the integral mean value theorem and substitution integration method: the integral mean value theorem is used to judge whether the integral value of a function must exist or must be unique in a certain interval. Substitution integration method is a method to solve complex integration, which simplifies the calculation by replacing the integral variable with another variable.
6. Learning series and convergence of series: series is a method of expressing a function as infinite series, which can be used to describe the laws of some phenomena. You need to learn how to judge the convergence of series and how to solve the sum of series.
7. Learn differential equations: differential equations are mathematical models that describe the changing laws of natural phenomena, such as equations of motion in physics and population growth models in biology. You need to learn how to establish differential equations and how to solve them.
8. Do more exercises and practical applications: consolidate what you have learned and improve your problem-solving ability through a large number of exercises. At the same time, try to apply what you have learned to practical problems, such as physics, engineering, economy and other fields.
9. Attend courses and discussions: If possible, you can attend online or offline calculus courses to track the teacher's teaching progress. In addition, you can join relevant study groups or forums to exchange learning experiences with others and make progress together.
10. Read related books and materials: In the process of learning, you can read some classic calculus textbooks and reference books, such as TomM. Apostol and Michael spivak. These books usually explain the concepts and theories of calculus in depth, which is helpful to better understand calculus.