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Calculus
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Topics in calculus
Fundamental theorem
Limits of functions
Continuity
Mean value theorem
Rolle's theorem
Definitions
Derivative
Differential (infinitesimal)
Differential of a function
Generalizations of the derivative
Concepts
Notation for differentiation
Second derivative
Third derivative
Change of variables
Implicit differentiation
Related rates
Taylor's theorem
Rules and identities
Sums
Products
Chain rule
Powers
Quotients
Faà di Bruno's formula
Definitions
Antiderivative
Integral
Improper integral
Riemann integral
Lebesgue integration
Contour integral
Integration by
parts
disks
cylindrical shells
substitution
trigonometric substitution
partial fractions
changing order
Integration by reduction formulae
look up in lists of integrals
Geometric series
Arithmetico-geometric sequence
Harmonic series
Alternating series
Power series
Binomial series
Taylor series
Convergence tests
Limit of the summand
Ratio test
Root test
Integral test
Comparison test
Alternating series test
Gradient
Divergence
Curl
Laplacian
Gradient theorem
Green's theorem
Stokes' theorem
Divergence theorem
Directional derivative
Formalisms
Matrix calculus
Tensor calculus
Exterior calculus
Geometric calculus
Definitions
Partial derivative
Multiple integral
Line integral
Surface integral
Volume integral
Jacobian
Fractional calculus
Stochastic calculus
Calculus of variations
v
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Calculus is the mathematical 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. It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Calculus has widespread uses in science, economics, and engineering and can solve many problems that algebra alone cannot.This subject is a major part of modern mathematics education. 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 historically been called "the calculus of infinitesimals", or "infinitesimal calculus". The word "calculus" comes from Latin (calculus) and means a small stone used for counting. 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 calculus, calculus of variations, lambda calculus, and process calculus.
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