Science Fair Project Encyclopedia
List of real analysis topics
This is a list of real analysis topics by Wikipedia page
NB The topics are in a deliberately chosen order, for the use of students.
| Contents |
Basic technique
- Sequence
- Supremum and infimum
- Limit of a sequence
- Monotone convergence theorem
- Cauchy sequence
- Limit superior and limit inferior
- Limit (mathematics)
- Oscillation (mathematics)
- Infinite series
- Geometric series
- Harmonic series
- Alternating series
- Telescoping series
- Binomial series
- Summation by parts
- Infinite product
- Convergence
- Interval (mathematics)
- Support
- Vanish at infinity
- Asymptotic notation
- Asymptotic analysis
- Extended real number line
- Partition of an interval
- Cantor set and Cantor space
- Sigma-algebra
Foundations
Fundamental theorems
- Rolle's theorem
- Mean value theorem
- Intermediate value theorem
- Euclidean space
- Heine-Borel theorem
- Bolzano-Weierstrass theorem
Conditions on real functions
- Continuous function
- Uniform continuity
- Semi-continuity
- Modulus of continuity
- Monotonic
- Convex function
- Smooth function
- Lipschitz continuity
- Nowhere continuous
- Weierstrass function
- Contraction mapping
- Analytic function
- Integrable function
- Bounded variation
- Devil's staircase
- Cantor function (example)
- Equicontinuous
- Weakly harmonic
Inequalities
- Bernoulli's inequality
- Inequality of arithmetic and geometric means
- Cauchy-Schwarz inequality
- Triangle inequality
- Hölder's inequality
- Minkowski inequality
- Jensen's inequality
- Chebyshev's inequality
Multivariate calculus
See also list of multivariable calculus topics
- Riemann sum
- Riemann integral
- Fundamental Theorem of Calculus
- Riemann-Stieltjes integral
- Improper integral
- Cauchy principal value
- Darboux integral
- Gamma function
- Rectifiable curve
- Path integral
- An elegant rearrangement of a conditionally convergent iterated integral
- Power series
- Lagrange inversion theorem
- Orthogonal polynomials
- Directional derivative
- Banach fixed point theorem
- Inverse function theorem
- Implicit function theorem
- Submersion
- Lagrange multiplier
Measure
For topics relating to measure theory and the Lebesgue integral, see list of integration and measure theory topics; and also list of probability theory topics
Distributions
Fractional calculus
Fourier series, Fourier transform
See list of harmonic analysis and representation theory topics
Fractals
History
- Michel Rolle (1652-1719)
- Joseph Louis Lagrange (1736-1813)
- Jean Baptiste Joseph Fourier (1768-1830)
- Augustin Cauchy (1789-1857)
- Johann Peter Gustav Lejeune Dirichlet (1805-1859)
- Karl Weierstrass (1815-1897)
- Bernhard Riemann (1826-1866)
- Richard Dedekind (1831-1916)
- Rudolf Lipschitz (1832-1903)
- Georg Cantor
- Pafnuty Chebyshev
- Camille Jordan
- Hermann Minkowski (1864-1909)
- Henri Lebesgue
- Emile Borel
- Felix Hausdorff
- Waclaw Sierpinski
- Karl Menger
- Johann Radon
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details