First of all, calculus is a mathematical method used to study the changes and limits of functions. It includes two main branches: differential and integral. Differential mainly studies the rate of change of a function at a certain point, that is, the derivative; Integral studies the cumulative effect of a function in a certain interval, that is, definite integral or indefinite integral. Calculus is widely used in physics, engineering, economy and other fields.
Total differential is a concept in calculus, which is a linear approximation of a function at a certain point. The total differential represents the slight change of the function near this point, which can be used to calculate the slope of the function at this point. The calculation of total differential involves the first partial derivative of function.
Secondly, there are some differences between calculus and total differential in application. Calculus can be used to solve practical problems, such as speed, acceleration and area. Total differential is mainly used in theoretical research, such as analyzing the properties of functions and proving theorems.
In addition, calculus and total differential are also different in symbolic representation. Calculus is represented by derivative and integral symbols, and total differential is represented by symbol "D".
In a word, calculus is a mathematical method to study the changes and limits of functions; Total differential is a concept in calculus, which represents the linear approximation of a function at a certain point. They also have some differences in application and symbolic representation.