Modern calculus is divided into many different types. The following lists just a few of the many divisions:

Basic calculus—Basic calculus is the branch of mathematics concerned with limits and with the differentiation and integration of functions. There is also advanced calculus that takes an even more complex view of calculus, with an emphasis on proofs.

Differential calculus—Differential calculus deals with the variation of a function with respect to changes in the independent variable(s). It does this by determining derivatives and differentials.

Integral calculus—Integral calculus (logically) deals with integration and its application to solve differential equations; it is also used to determine areas and volumes.

Predicate calculus—Predicate calculus, or functional calculus, is a branch of formal logic that involves logical connections between statements as well as the statements themselves.

Multivariable calculus—This is a branch of calculus that studies functions of more than one variable.

Functional calculus—Functional calculus is actually an older name for calculus of variations; it’s sometimes used in place of predicate calculus.

Propositional calculus—This is the formal basis of logic dealing with the notion and usage of words such as “OR” or “AND.”

Malliavin calculus—Malliavin calculus is one of the more esoteric studies; it is an infinite-dimensional differential calculus on the Wiener space, also called stochastic calculus of variations.

Other various analyses—Other parts of calculus entail various types of analyses, such as vector, tensor, and complex analyses, and differential geometry.