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Mathematical Theoretical Analysis and Research
A derivative can form a new continuous function.
However, the mathematical value and role of this derivative function in mathematical research have not been explained.
In fact, it is a set of average values related to the change in increments.
For example, the average value of acceleration, which is the change in velocity, is represented by this derivative function.
A derivative can form a new continuous function.
Derivative function
However, the mathematical value and role of this derivative function in mathematical research have not been explained.
In fact, it is a set of average values related to the change in increments.
For example, the average value of acceleration, which is the change in velocity, is represented by this derivative function.
Derivative function
However, the mathematical value and role of this derivative function in mathematical research have not been explained.
In fact, the derivative function is a set of function values related to the instantaneous increase or decrease of a variable.
Their average value is the Y-value of the variable. For example, the Y-value of velocity is the average value of the change in acceleration or the acceleration variable itself.
The velocity Y is also the actual value of the velocity variable.
Such as velocity
Velocity Y can be regarded as the integral of acceleration, or velocity Y is the average acceleration.
Velocity can also be the derivative of average velocity, because integrating velocity Y can yield the average velocity.
In fact, velocity itself is also a derivative, being the derivative of average velocity.
Because integrating the average velocity gives velocity.
The rectangle formed by the velocity Y-values represents the distance traveled by an object under acceleration over time X.
The rectangle formed by the Y-values obtained by integrating the velocity Y-values represents the distance traveled by the object at the average velocity over time X.
Velocity Y can be regarded as the average value of acceleration.
The distance traveled by an object with acceleration is calculated using velocity Y.
Velocity can be regarded as the Y-value at a certain time X.
However, the distance cannot be directly calculated by multiplying this variable velocity value Y by time.
It is necessary to use the average velocity obtained by integrating this velocity and multiply it by time X to get the accurate distance.
Velocity can also be a derivative function, serving as the value of the derivative function of average velocity.
Calculating the distance of variable speed motion over a certain time X.
Only by integrating the Y-values of the variable speed curve and multiplying by the corresponding time X can the accurate distance be obtained.
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Mathematical research initially aimed to calculate the precise area enclosed by curves. It envisioned a calculation method involving infinitely dividing the area of small rectangles and taking the limit, but in reality, it invented an integration method to calculate the average value of Y-values.
However, when explaining integration, the principle of integral calculation is still illustrated using area calculation.
Obviously, there is some logical confusion here. |
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