Introduction of Jacobian determinant;
Jacobian determinant is usually called Jacobian determinant, which takes partial derivatives of n functions of n variables as elements. In fact, on the premise that all functions are continuously differentiable (that is, all partial derivatives are continuous), it is the determinant of the coefficient matrix in the differential form of the function group.
If the dependent variable is continuously differentiable to the independent variable and the independent variable is continuously differentiable to the new variable, then the dependent variable is continuously differentiable to the new variable. This can be directly verified by the multiplication rule of determinant and the chain rule of partial derivative. It is also similar to the chain rule of derivatives. The chain rule of partial derivatives has a similar formula; This is often used in the calculation of multiple integrals.
How to learn mathematics well;
1, and establish a good mathematical foundation.
The first step to learn mathematics well is to establish a good mathematical foundation. To master the advanced concepts and skills of mathematics, we need to master the basic mathematical concepts and operation rules first. So it takes time to consolidate and review the basic knowledge, such as addition, subtraction, multiplication and division, fractions and decimals.
2. Understand concepts instead of rote learning.
Mathematics is not a subject of rote learning, but a subject that needs to be understood and applied. Therefore, when learning mathematics, we should pay attention to understanding concepts, not just remembering formulas and calculation methods. By understanding the concept, we can better grasp the essence and thought of mathematics.
3. Do more exercises.
Doing problems is an important way to learn mathematics well. By doing a lot of exercises, you can consolidate your knowledge and improve your ability to solve problems. When doing the problem, we should pay attention to understanding the meaning of the problem, cultivate the ability of logical thinking, and at the same time pay attention to summarizing the methods and ideas of solving the problem.
4. Learn to think and explore.
Mathematics is a subject that needs to be considered and explored. When learning mathematics, we should cultivate the ability to think and solve problems independently. You can try to solve some interesting math problems, participate in math competitions or join math interest groups, communicate with people, and share your own thinking and problem-solving process.