When most students started to learn physics competitions, they only knew junior high school mathematics and some senior high school mathematics. Therefore, many teachers, including the teachers of centroid education, suggest avoiding advanced mathematics, following people's cognitive laws in history, and using infinitesimal method and other skills to model and calculate. However, with the familiarity with infinitesimal method and the deepening understanding of physics, advanced mathematics must be used to describe the physical model. After years of teaching experience, the mass education center put the systematic study of calculus after the first round of mechanics and before the first round of electricity (only in history, people first established mechanics, then understood calculus, and then established electricity). The second round of learning, mathematical tools such as degree of freedom, complex number, linear operator, differential equation, derivative of angular momentum of energy, gradient, divergence, curl, symmetry conservation quantity, etc. Is systematically used to describe physics. High school physics competition questions can avoid the method of advanced mathematics, and can also be described more accurately by the method of advanced mathematics. Give a simple example, like the classic problem of chickens and rabbits in the same cage or cows eating grass in the primary school Olympics. When you can't work out the equation, you can also use the hypothesis method to figure it out (of course, you may not have thought of it). When you can make an equation, it is natural to think from the perspective of variables and model the result.
Important senior high school mathematics knowledge needed in physics competition includes: functions (including trigonometric functions, power functions, logarithmic functions, exponential functions, etc. ), inequalities (including Cauchy inequality, mean inequality, etc. ), vector, multivariate linear equation, quadratic equation. They are all learned within the scope of the high school entrance examination, but students had better teach themselves in advance before the math teacher talks about these parts. In this part, just look through the math reference books for the college entrance examination and do a few math problems for the college entrance examination. Of course, Centroid Education helps you record vectors and trigonometric functions as free videos for students to learn (log in to Centroid official website and click on Learning-Knowledge-Math Foundation). The advanced mathematics required by physics competition is scattered. Beginners are advised to buy a book called "Calculus" (be careful not to be a book called "Mathematical Analysis"), and focus on the application of formulas rather than the proof of its existence, correctness and uniqueness. Similarly, centroid education helps you record the integral of unit function as a free video (log in to official website and click Learning-Knowledge Point-Calculus of Unit Function). We will also release more free videos about math tools later.