What knowledge does the physics competition need?
What mathematics does the mechanics part of physics competition need?
First of all, in order to understand the linear motion with uniform acceleration and linear motion with variable acceleration at the beginning of mechanics, it is essential for the simple calculus of univariate functions, and of course, it mainly focuses on the derivation and integration of polynomial functions, which is very easy to operate in practical operation.
Then, when the range of motion is extended to two dimensions and the form of motion becomes a curve, mathematical concepts such as vector algebra, analytic geometry, parametric equation, slope and radius of curvature are integrated into the physical model to understand the motion of projectile, circle and general curve. At this time, the application of calculus also extends to more complex functions, such as trigonometric functions.
With the introduction of Newton's second law on the relationship between motion and force, we gradually realize that it is not enough to understand motion by light. What we want to study is the function of mechanism force and the function of force behind the movement. The introduction of momentum theorem and kinetic energy theorem actually reflects the accumulation effect of force in time and space, and Newton equation itself is also a formal differential equation that physicists especially like.
The more comprehensive application of vector and calculus is embodied in a special form of motion-simple harmonic vibration, which is accompanied by the development of physics. The fluctuation of diffusion effect of vibration in medium leads to the concepts of wave equation and wave function.
To sum up, the mathematics needed in mechanics is the application of calculus, vector algebra, analytic geometry, ordinary differential equations and binary functions of univariate functions.
What mathematics is needed in the thermal part of physics competition?
Although it is relatively easy for senior high school to involve the contents of gas law and the first law of thermodynamics, calculus is generally not needed, but if we study the thermodynamic process, various state functions (internal energy and entropy) and the second law of thermodynamics in depth, then due to many variables in the thermodynamic system, appropriate basic knowledge of partial differential is necessary.
Thermodynamics is a macroscopic theory, and molecular dynamics theory is the basis behind it. The relationship between them is realized by the statistics of a large number of particle systems. So the knowledge of probability and statistics is very necessary.
To sum up, the mathematics needed in the thermal part is simple partial differential and probability statistics.
What mathematics does the electromagnetism part of the physics competition need?
According to previous years' experience, electromagnetism is the most difficult content for college entrance examination students to give up physics and competition students to give up physics competition. The reason is that mathematics is not in place, not only can't understand the concept of field, but also it is easy to produce memory models and formulas. The inherent thinking mode of doing problems with examples can be described as "not learning at all" for electromagnetism!
Starting from the electrostatic field, if we only study according to the requirements of senior high school, the understanding of the field is empty, just a phenomenological concept, and we can't deeply grasp the concepts of electric field line, potential, electrostatic balance, dielectric polarization and so on, let alone answer competition questions.
In fact, the electrostatic field directly enters the three-dimensional space from Coulomb's law of point charge, and all the laws are expressed in three dimensions, so it is required to use the functions of solid geometry and spatial position immediately. Then, Gauss theorem is derived from Coulomb's law to investigate the system with strong symmetry, so the spherical coordinates, cylindrical coordinates and rectangular coordinates are exchanged; The vector integral on the surface, the loop integral on the straight line, Green's theorem and so on must be followed.
At the same time, considering the problems in small local space, the differential form of electrostatic field equation, three-dimensional partial differential and Nabura operator must be understood.
Electrostatic field alone needs so many mathematical tools, which shows how difficult electromagnetism is to learn! In fact, the study of electromagnetism is a standard step-by-step process. We need to understand phenomenology first, and we need to dig deep into what we don't understand. Mathematical tools can start with vector integral and then understand the differential equation of the field, so we can get twice the result with half the effort.
The content of the circuit looks very similar to junior high school, but once it involves the conductive model inside the conductor, the differential form of ohm's law, the conservation of charge, etc., it needs the help of calculus. AC circuits need to understand complex methods to describe vibration. At the same time, some resistance network problems also need mathematical knowledge such as recursion of series, which should be like sponge absorbing water in the learning process to fill in the missing things!
After entering the magnetic field and electromagnetic induction, Maxwell's equations described by magnetic field equation and electromagnetic field, etc. , are the joint application of vector field calculus. At the same time, it also involves the wave equation of electromagnetic wave and the description of wave function by complex method.
To sum up, the mathematics needed in electromagnetism is the knowledge of calculus, complex number and vector field differential equation.
What mathematics does physics competition need in optics and modern physics?
Obviously, the knowledge of plane geometry required by geometric optics has been learned in junior high school, which is why geometric optics can be decentralized to Datong Cup, a key test center. However, in the past teaching, we found that students' understanding of the real imaging system is extremely insufficient, in other words, they can do problems, but they can't figure out the actual principle of optical instruments. Therefore, the difficulty of geometric optics lies not in mathematics, but in practical application.
Wave optics (interference, diffraction, polarization, interface optics) is nothing more than the application of wave properties of electromagnetic waves, and the required mathematics is consistent with that of electromagnetic fields.
The phenomenological content of modern physics is actually a great fusion of classical physics, and mathematics cannot break through all the mathematical tools introduced above. Preliminary quantum mechanics needs a probabilistic world view and an understanding of wave functions. If you want to calculate accurately, you must master the contents of mathematical and physical equations. We don't think it necessary to study at this age. Special relativity needs Lorentz transformation and the operation of four vectors, without adding new mathematics.
To sum up, the mathematics needed in optics and modern physics is not beyond the scope mentioned before. However, to understand this part, you need to know the four plates of thermoelectric light very well.
The content of the math class is specifically aimed at the competition of things?
Spring to summer: limit, derivative and differential; Integral; Analytic geometry and polar coordinates; Ordinary differential equation; Partial derivative;
Autumn: scalar field, vector field, divergence, curl, gradient, Nabura operator, Laplace operator; Integral of field, Green's theorem; Spherical coordinate and three-dimensional coordinate conversion; Matrix and determinant;
Winter vacation to spring: probability statistics; Series; Complex number; Solid geometry; Other senior high school entrance examination contents.
What are the physics competitions in senior high school?
What courses are there in high school physics?
Physics in senior high school is basically divided into honor physics, AP physics I, AP physics II, AP physics C mechanics and E &；; M. Each course takes about one year, so there is no time and no need to finish all five courses, usually starting from the seventh or eighth grade. After studying physics science, students can learn AP physics I directly according to their own mathematical foundation. There is no unified national standard for honor physics, and the teaching difficulty and content of different schools are different. If you don't study physics science or honor physics, you can study AP Physics I directly, but it will be a bit difficult at first. Most schools require students to complete AP Physics I before taking AP Physics C. Honor Physics emphasizes more concepts and less mathematics, which is relatively easier than AP Physics. AP Physcis I AP Physcis II is based on algebra, and AP Physics C is based on calculus. Since last year, the American College Board has divided AP Physics B into AP Physics I and AP Physics II. AP Physics I includes mechanics, wave theory and simple circuits. AP Physics II includes thermodynamics, optics, electronics and modern physics. AP physics C mechanics only includes mechanics, and AP physics C EMN only includes electromagnetism.
National unified examination of American physics
There are four AP physics exams in the United States, namely CIS I, II, C Mechanist and EMN. After learning the corresponding physics class, you can take these AP exams, and the exam time is the first week or the second week of May every year. After the exam, students can also take the physics SAT II exam. SAT II has a slightly wider range of questions, and the examination questions are relatively easy. For example, AP Physics I and AP Physics II do not require relativity, but SAT II will require some basic concepts. You can't take the SAT until you have completed AP Physics I and II. In addition, there are some in America, such as physics bowls and physics olympiad. The physics bowl represents the school and needs no special preparation.
Olympic physics competition
The Olympic Physics Competition is divided into two stages. The first stage is called F=ma Contest competition, and only the mechanics part is tested. One * * * is twenty-five multiple-choice questions, and calculus is not needed, so only AP Physics I and AP Physics II are needed. The Olympic exam is held in late January every year. Every year, about 350 to 400 students can pass the F=ma contest and enter the second round. The second round of competition is also called USAPHO (American Physics Olympiad) competition, which includes all general physics and is based on calculus. This is quite difficult. Students should learn the mechanics and electromagnetics of AP Physics C, and other AP Physics I and II should also be upgraded to the level based on calculus. USAPHO won gold, silver, bronze, honors and nominations, and then the top 20 entered various physical Olympic training teams.
Why do you want to take AP physics exam and take part in physics competition?
Some basic courses such as calculus and general physics in American universities are compulsory courses for many majors. In other words, you must prove that you can take some compulsory basic courses before you can study those majors. If you get five points in many AP exams, the corresponding required courses can be exempted in the university. This not only saves money, but also saves time in studying other more important courses. From the perspective of enrollment, you can imagine that the more you take the exam, the more you prove that you have the ability to study the corresponding major, and then you will naturally have an advantage in college application. In addition, participating in physics competitions and getting good grades can not only improve children's self-confidence, but also be of great benefit to their college application. It can add icing on the cake and help them get into first-class universities. Of course, good grades in school are the most important prerequisite. Many parents may think that only some excellent people will take part in physics competitions and get good grades. In fact, most children are equally smart, mainly by their own efforts. Many of my children have won gold medals and silver medals, and even the top 20 children have encountered great difficulties when they first started to learn physics. Many of them have struggled with their families, but they persisted in their efforts and finally achieved good results.
When is it better to learn AP physics?
For almost all senior high school students, if they study AP Physics I step by step, then AP Physics II, or AP Physics C, they often can't take more AP Physics exams before applying for university at the end of 1 1 grade. In fact, as long as you study physical science, algebra I and a little geometry, you can learn ApPhysics I. After learning Apphysics I, you can participate in the F=Ma competition in principle. If you start studying in the eighth grade, you can take part in the ninth, tenth and eleventh grades three times. In this way, the success rate will be higher, because the success rate of entering the semi-finals for the first time will be lower, and more importantly, you can prepare for further study of the mechanics and electromagnetics of AP Physics C, so that if you can win the gold medal in the second round, the chances of winning the silver medal will be much greater.
How to learn AP physics and prepare for physics competition