Very broadly speaking, real analysis is the study of real-valued functions and can be argued as the formal study of calculus via mathematical proofs. Some mathematical properties that are studied in real analysis include the construction of the real numbers field, defining continuity and its various types, and so on. Studying real analysis involves studying the geometric and topological properties of the real numbers as well as the -th dimensional spaces of .
- Continuity (including the Hölder/Lipschitz definitions)
- Derivative (the limit definition)
- Integral (including multivariate integrals)
- Fundamental Theorem of Calculus (integration and differentiation are inverses)
- Green's Theorem (integration over a region equals integration over the region's boundary)
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