This is a list of articles that are considered real analysis topics.
Limit of a sequence
Subsequential limit – the limit of some subsequence
Limit of a function (see List of limits for a list of limits of common functions)
One-sided limit – either of the two limits of functions of real variables x, as x approaches a point from above or below
Squeeze theorem – confirms the limit of a function via comparison with two other functions
Big O notation – used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions
(see also list of mathematical series)
Arithmetic progression – a sequence of numbers such that the difference between the consecutive terms is constant
Generalized arithmetic progression – a sequence of numbers such that the difference between consecutive terms can be one of several possible constants
Geometric progression – a sequence of numbers such that each consecutive term is found by multiplying the previous one by a fixed non-zero number
Harmonic progression – a sequence formed by taking the reciprocals of the terms of an arithmetic progression
Finite sequence – see sequence
Infinite sequence – see sequence
Divergent sequence – see limit of a sequence or divergent series
Convergent sequence – see limit of a sequence or convergent series
Cauchy sequence – a sequence whose elements become arbitrarily close to each other as the sequence progresses
Convergent series – a series whose sequence of partial sums converges
Divergent series – a series whose sequence of partial sums diverges
Power series – a series of the form
Taylor series – a series of the form
Maclaurin series – see Taylor series
Binomial series – the Maclaurin series of the function f given by f(x) = (1 + x) α
Telescoping series
Alternating series
Geometric series
Divergent geometric series
Harmonic series
Fourier series
Lambert series
Cesàro summation
Euler summation
Lambert summation
Borel summation
Summation by parts – transforms the summation of products of into other summations
Cesàro mean
Abel's summation formula
Convolution
Cauchy product –is the discrete convolution of two sequences
Farey sequence – the sequence of completely reduced fractions between 0 and 1
Oscillation – is the behaviour of a sequence of real numbers or a real-valued function, which does not converge, but also does not diverge to +∞ or −∞; and is also a quantitative measure for that.
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En mathématiques, un nombre réel est un nombre qui peut être représenté par une partie entière et une liste finie ou infinie de décimales. Cette définition s'applique donc aux nombres rationnels, dont les décimales se répètent de façon périodique à partir d'un certain rang, mais aussi à d'autres nombres dits irrationnels, tels que la racine carrée de 2, π et e.
Dans ce cours, nous étudierons les notions fondamentales de l'analyse réelle, ainsi que le calcul différentiel et intégral pour les fonctions réelles d'une variable réelle.
This course is an introduction to the theory of Riemann surfaces. Riemann surfaces naturally appear is mathematics in many different ways: as a result of analytic continuation, as quotients of complex