Real analysis

Real analysis is the formal study of calculus using mathematical proofs.

Notions

• Continuity (including the Hölder/Lipschitz definitions)
• Derivatives (the limit definition)
• Integration (including multivariate integrals)

Important theorems

• Fundamental Theorem of Calculus (integration and differentiation are inverses)
• Green's Theorem (integration over a region equals integration over the region's boundary)

See also

• Complex analysis
• Partial differential equation

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