Nonlinear function: nonlinear functions include exponential function, power function, logarithmic function, polynomial function and their composite functions.
The following is a comparison between linear function and nonlinear function:
1, linearity refers to the proportion and linear relationship between quantities, which can be mathematically understood as a function with a constant first derivative.
Nonlinear nonlinearity refers to the relationship between proportionality and linearity, and the first derivative is not constant.
2. Linearity can be considered as 1 degree curve, such as y=ax+b? , that is, in a straight line.
Non-linearity can be considered as a curve with more than two degrees, such as y = ax 2+bx+c (x 2 is the quadratic power of x), that is, it is not a straight line.
3. The relationship between two variables is a linear function-the image is a straight line, so the relationship between the two variables is a "linear relationship".
If it is not a linear function-the image is either a straight line or a "nonlinear relationship".
4. "Linear" and "nonlinear" are often used to distinguish the function y? =? f？ (x) Dependence on Independent Variable X A linear function is like a straight line.
Other functions are nonlinear, and their images are not straight lines.
5. Linearity refers to the proportion and linear relationship between quantity and quantity, which means regular smooth movement in space and time. Nonlinear refers to the non-proportional and nonlinear relationship, which is characterized by irregular movement and mutation.
For example, an ordinary resistor is a linear element, and the voltage u across the resistor R has a linear relationship with the current I flowing through it, that is, R=U/I, and r is a constant. The forward characteristic of diode is a typical nonlinear relationship. The voltage u across the diode is not in a fixed proportion to the current I flowing, that is, the forward resistance value of the diode varies with different operating points (u, i).
5. Mathematically, linear relationship means that the independent variable X and the dependent variable yo can be expressed as y=ax+b? (a, b are constants), that is, there is a linear relationship between x and y.
Can't it be expressed by y=ax+b? (a, b are constants), that is, nonlinear relationship, which may be quadratic, cubic and other functional relationships, or it may not be related.
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Linear relationship:
When there is a functional relationship between two variables, there is a linear relationship between them.
Positive proportional relationship is a special case of linear relationship, while inverse proportional relationship is not linear relationship.
More generally speaking, if these two variables are taken as the abscissa and ordinate of a point respectively, and they look like a straight line on the plane, then the relationship between these two variables is linear.
In advanced mathematics, a linear function is a linear mapping, which maintains vector addition and scalar multiplication between two vector spaces.
For example, suppose we use a coordinate vector to represent it.
X and f(x). Then, the linear function can be expressed as f(x)=Mx. Where m is a matrix.
Reference link Baidu Encyclopedia? linear function