Jumat, 18 Mei 2012

Calculus



Calculus (Latincalculus, a small stone used for counting) is a branch of mathematics focused on limitsfunctionsderivativesintegrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science,economics, and engineering and can solve many problems for which algebra alone is insufficient.
Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculusvariational calculuslambda calculuspi calculus, and join calculus.


Topics in calculus
Fundamental theorem
Limits of functions
Continuity
Vector calculus
Matrix calculus
Mean value theorem
Differentiation
Product rule
Quotient rule
Chain rule
Change of variables
Implicit differentiation
Taylor's theorem
Related rates
List of differentiation identities
Integration
Lists of integrals
Improper integrals
Integration by:
partsdiskscylindrical
shells
substitution,
trigonometric substitution,
partial fractionschanging order