# Category:Analysis

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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 139 subcategories, out of 139 total.

### A

- Antiperiodic Functions (6 P)

### B

- Bernoulli Polynomials (3 P)
- Binet Form (4 P)

### C

- Cauchy's Convergence Criterion (20 P)
- Cauchy's Inequality (6 P)
- Cauchy-Crofton Formula (empty)
- Chebyshev Polynomials (3 P)
- Convergent Mappings (empty)
- Convergent Products (empty)

### D

- Dependent Variables (empty)
- Diffeomorphisms (empty)
- Discontinuities (empty)

### E

- Euler-Gompertz Constant (2 P)
- Exponent Combination Laws (22 P)
- Exponential Sums (1 P)

### F

- Function Theory (1 P)
- Fundamental Theorem of Algebra (10 P)

### G

### H

- Homogeneous Functions (1 P)
- Hölder's Inequality for Sums (12 P)

### I

- Independent Variables (empty)
- Inverse Fourier Transforms (empty)

### L

- Limits of Sequence of Sets (5 P)

### M

- Multinomial Coefficients (2 P)
- Möbius Transformations (3 P)

### N

- Non-Standard Analysis (empty)

### O

- Oscillation (5 P)

### P

- Parametric Equations (empty)

### Q

### R

- Regions (empty)

### S

- Subadditive Functions (1 P)
- Superadditive Functions (empty)

### T

### U

- Umbral Calculus (empty)

### V

## Pages in category "Analysis"

The following 59 pages are in this category, out of 59 total.

### C

- Cauchy's Convergence Criterion
- Cauchy's Inequality
- Cauchy-Bunyakovsky-Schwarz Inequality
- Cauchy-Bunyakovsky-Schwarz Inequality/Definite Integrals
- Cesàro Mean
- Closed Bounded Subset of Real Numbers is Compact
- Compact Subspace of Real Numbers is Closed and Bounded
- Completeness Axiom
- Continuous Function on Compact Subspace of Euclidean Space is Bounded
- Continuous Image of Connected Space is Connected/Corollary 2
- Contraction Mapping Theorem
- Convergent Subsequence in Closed Interval
- Countable Set has Measure Zero