Final answer:
Differential calculus is the area of calculus that studies how functions change with variables, essential in fields like engineering and economics for analyzing dynamic systems and relationships within models.
Step-by-step explanation:
Differential calculus uses calculus to study how geometric functions respond to changing variables. It is a part of calculus, the mathematics of change, which includes the study of limits, derivatives, integrals, and infinite series. Differential calculus specifically allows us to find the rate at which one quantity changes with respect to another by finding the derivative of functions.
When examining dimensions in the context of physical quantities, taking the derivative results in the dimension of the derivative being the ratio of the dimension of the numerator over that of the denominator. Differential equations are an essential tool in various engineering applications, which relate functions to their derivatives to solve for changing quantities.
Moreover, understanding calculus is beneficial even for students majoring in fields like economics, where it can aid in learning advanced concepts more quickly by facilitating the understanding of relationships within algebraic models, which are often expressed as mathematical functions. For instance, an economic model may be expressed in terms of functions that define a relationship, such as the output of a factory as a function of the number of workers and machines.