Editing Real Analysis (section)

== <span style="color: #FFFFFF;">Creating</span> ==
Advanced analysis directions:
# '''Measure theory and Lebesgue integration''': define integration for a vastly broader class of functions; prove dominated convergence, monotone convergence, Fubini's theorem.
# '''Functional analysis''': study spaces of functions (L², L^p, Sobolev spaces) as infinite-dimensional vector spaces; Hilbert spaces, Banach spaces, bounded linear operators.
# '''Complex analysis''': analysis over ℂ; holomorphic functions, Cauchy's theorem, conformal maps — remarkably richer than real analysis.
# '''Fourier analysis''': decompose functions into frequency components; Fourier series, transforms, and their applications in differential equations and signal processing.
# '''Ordinary and partial differential equations''': real analysis provides the existence-uniqueness theorems (Picard-Lindelöf) and regularity theory.

[[Category:Mathematics]]
[[Category:Real Analysis]]
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