Category:Analysis

From ProofWiki

Jump to navigation Jump to search

This category contains results about Analysis.
Definitions specific to this category can be found in Definitions/Analysis.

Analysis is a branch of mathematics that studies continuous change, and the use of limits.

It subsumes the fields of calculus, differential equations, the calculus of variations, power series, Fourier series, real analysis and complex analysis.

It is one of the main branches of mathematics, alongside geometry, number theory and algebra.

Subcategories

This category has the following 146 subcategories, out of 146 total.

A

Abel's Limit Theorem‎ (1 C, 4 P)
Abel's Theorem‎ (1 C, 2 P)
Absolute Continuity‎ (2 C)
Absolute Convergence‎ (5 C, 10 P)
Addition‎ (23 C, 20 P)
Additive Functions‎ (4 C, 8 P)
Algebraic Functions‎ (1 C)
Algebraic Numbers‎ (4 C, 5 P)
Analytic Functions‎ (1 C, 3 P)
Analytic Number Theory‎ (25 C, 44 P)
Antiperiodic Functions‎ (6 P)
Asymptotics‎ (2 C, 2 P)

B

Bernoulli Numbers‎ (4 C, 22 P)
Bernoulli Polynomials‎ (3 P)
Bifurcation Theory‎ (2 C)
Bilinear Forms‎ (2 C)
Binet Form‎ (4 P)
Binomial Coefficients‎ (46 C, 136 P)

C

Calculus‎ (14 C, 13 P)
Cauchy's Convergence Criterion‎ (20 P)
Cauchy's Inequality‎ (6 P)
Cauchy-Bunyakovsky-Schwarz Inequality‎ (1 C, 13 P)
Cauchy-Crofton Formula‎ (empty)
Ceiling Function‎ (3 C, 36 P)
Chebyshev Polynomials‎ (3 P)
Closed Bounded Subset of Real Numbers is Compact‎ (3 P)
Closed Forms‎ (4 C, 18 P)
Compact Subspace of Real Numbers is Closed and Bounded‎ (3 P)
Completely Multiplicative Functions‎ (1 C, 9 P)
Complex Analysis‎ (111 C, 114 P)
Complex Numbers‎ (44 C, 54 P)
Continuity‎ (21 C, 21 P)
Continuous Functions‎ (4 C, 23 P)
Convergence‎ (21 C, 62 P)
Convergent Mappings‎ (empty)
Convergent Products‎ (empty)
Convergent Sequences‎ (9 C, 8 P)
Convergent Series‎ (1 C, 1 P)
Convex Analysis‎ (4 C, 3 P)

D

Dependent Variables‎ (empty)
Diffeomorphisms‎ (empty)
Dirichlet's Test for Uniform Convergence‎ (3 P)
Discontinuities‎ (empty)
Distance Function‎ (4 C, 15 P)
Divergence‎ (6 C)
Dot Product‎ (15 C, 33 P)
Dynamical Systems Theory‎ (3 C, 1 P)

E

Elementary Functions‎ (1 C, 1 P)
Elliptic Curves‎ (1 C)
Equations‎ (3 C)
Euler Numbers‎ (2 C, 9 P)
Euler's Number‎ (6 C, 44 P)
Euler-Gompertz Constant‎ (2 P)
Exponent Combination Laws‎ (22 P)
Exponential Function‎ (30 C, 81 P)
Exponential Sums‎ (1 P)
Extended Real Numbers‎ (2 C, 15 P)
Extraction of Roots‎ (1 C)

F

Fixed Point Theorems‎ (3 C, 9 P)
Floor Function‎ (4 C, 53 P)
Fourier Analysis‎ (7 C, 7 P)
Fourier Transforms‎ (3 C, 15 P)
Fractals‎ (4 C, 3 P)
Function Theory‎ (1 P)
Functional Analysis‎ (44 C, 50 P)
Functional Equations‎ (2 C, 1 P)
Functional Series‎ (1 C)
Fundamental Theorem of Algebra‎ (10 P)

G

Gelfond-Schneider Theorem‎ (5 P)
Genera‎ (4 C, 1 P)
Generating Functions‎ (4 C, 21 P)

H

Harmonic Analysis‎ (2 C, 2 P)
Harmonic Mean‎ (1 C, 5 P)
Homogeneous Functions‎ (1 P)
Hyperbolic Functions‎ (14 C, 9 P)
Hyperbolic Identities‎ (2 C, 2 P)
Hölder's Inequality for Sums‎ (12 P)

I

Implicit Functions‎ (2 C, 9 P)
Independent Variables‎ (empty)
Inductive Sets‎ (2 C, 5 P)
Infinite Products‎ (9 C, 47 P)
Infinitesimals‎ (empty)
Inverse Fourier Transforms‎ (empty)
Inverse Hyperbolic Functions‎ (9 C, 1 P)
Inverse Trigonometric Functions‎ (15 C, 2 P)

K

Kronecker Delta‎ (empty)

L

Laurent Series Expansions‎ (1 C, 1 P)
Limits‎ (6 C, 3 P)
Limits of Mappings‎ (5 C, 10 P)
Limits of Sequence of Sets‎ (5 P)
Limits of Sequences‎ (21 C, 88 P)
Linear Forms‎ (2 C)
Logarithms‎ (28 C, 72 P)

M

Measure Theory‎ (51 C, 92 P)
Minkowski's Inequality for Sums‎ (8 P)
Monotone Convergence Theorem‎ (2 C, 3 P)
Multinomial Coefficients‎ (2 P)
Multiplication‎ (16 C, 24 P)
Möbius Transformations‎ (3 P)

N

Non-Closed Set of Real Numbers is not Compact‎ (4 P)
Non-Standard Analysis‎ (1 C)
Null Sequences‎ (2 C)
Number Bases‎ (18 C, 13 P)
Number Fields‎ (1 C, 6 P)
Numbers‎ (41 C, 25 P)

O

Operator Theory‎ (6 C, 21 P)
Order Notation‎ (5 C)
Oscillation‎ (5 P)

P

Parametric Equations‎ (empty)
Partial Fractions Expansions‎ (2 C, 1 P)
Periodic Functions‎ (7 C, 19 P)
Pointwise Operations‎ (6 C, 33 P)
Polynomial Equations‎ (6 C, 5 P)
Polynomial Functions‎ (4 C)
Polynomial Theory‎ (64 C, 116 P)
Power Series‎ (11 C, 17 P)
Powers‎ (19 C, 51 P)

Q

Quadratic Forms‎ (2 C)

R

Radon Transforms‎ (1 C)
Rational Functions‎ (2 C)
Real Analysis‎ (152 C, 180 P)
Real Numbers‎ (39 C, 90 P)
Regions‎ (empty)
Riemann Zeta Function‎ (16 C, 63 P)
Roots of Numbers‎ (10 C, 10 P)

S

Sequences‎ (43 C, 35 P)
Series‎ (23 C, 34 P)
Singular Points‎ (4 C)
Special Functions‎ (32 C, 1 P)
Square Function‎ (2 C, 28 P)
Subadditive Functions‎ (1 P)
Subset of Finite Dimensional Normed Vector Space is Compact iff Closed and Bounded‎ (1 P)
Superadditive Functions‎ (empty)

T

Taylor Series‎ (2 C, 11 P)
Telescoping Series‎ (1 C, 7 P)
Topology‎ (139 C, 112 P)
Transcendental Functions‎ (1 C)
Transcendental Numbers‎ (2 C, 16 P)
Trigonometric Functions‎ (14 C, 6 P)
Trigonometric Identities‎ (16 C, 62 P)
Trigonometric Series‎ (1 C, 10 P)
Trigonometry‎ (8 C, 3 P)

U

Umbral Calculus‎ (empty)
Unbounded Set of Real Numbers is not Compact‎ (4 P)

V

Vector Analysis‎ (8 C, 2 P)
Vector Cross Product‎ (10 C, 23 P)

Pages in category "Analysis"

The following 58 pages are in this category, out of 58 total.

A

B

C

D

E

F

Fundamental Theorem of Algebra

G

H

I

L

M

N

Non-Closed Set of Real Numbers is not Compact

O

Open Rectangles Closed under Intersection

P

R

S

U

Unbounded Set of Real Numbers is not Compact

Retrieved from "https://proofwiki.org/w/index.php?title=Category:Analysis&oldid=331327"

Proofs by Topic