## Mathematical Analysis## Calculus Basics |

## How is modern calculus divided? |

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.