Calculus is the study of differentials; It has plethoric real-world applications. There are two basic areas of calculus: integral calculus and differential calculus. The latter deals with finding instantaneous and generalized rates of change of a function , whereas the former exclusively deals with finding the area between two functions and . The fundamental theorem of calculus states that . Likewise, .
Sometimes, limits are considered to be a part of calculus. The notation is . Limits are used to describe the behaviour of functions as they approach a discontinuity, asymptote, or . The notation for a limit where approaches from the positive direction is , as the notation for a limit where approaches from the negative direction is . Limits can be used to describe differentials. Say we have some line that is secant to at points . We want to find the point derivative at a point , so we take the limit of the slope of as it approaches the function tangent to at .
One of the most basic notions of calculus is the differential, . This represents an extremely small change in , where . The area under a function must be given by , which is usually represented as the indefinite integral . Another type of integral, the definite integral, is used to represent the area under a curve along an interval . Its notation is .