is the systematic study of real and complex-valued continuous functions.
Mathematical structures in analysis.
Figure: Mathematical structures in analysis, $(X, \cdots)$:
(A) topological and algebraic structures; (B) set-theoretic structure.
Mathematical structures in (A) and (B) are independent but can be related via $L^2_\mu$.
Course Notes on Mathematical Analysis 1&2
Notes on Mathematical Analysis 3
Real number; function; continuity; convergence; differentiation; integration.
Set Theory and Measure Space
Course Notes on Complex Analysis
Topological space: open set and closed set, continuous mapping;
Vector Space: spaces with algebraic structure;
Metric Space: convergence (of sequences);
Normed Space (and Banach Space);
Inner Product Space (and Hilbert Space);
- Peter Lax, 1966. Functional Analysis;
- Michael Reed and Barry Simon, 1972. Functional Analysis;
- Erwin Kreyszig, 1978. Introductory Functional Analysis with Applications;