Mathematical analysis, often simply referred to as "analysis," is a branch of mathematics that focuses on the rigorous study of limits, continuity, and calculus. It is a foundational field in mathematics and is essential for many areas of science, engineering, and economics. Here are some key topics in mathematical analysis:

Real Analysis:

Complex Analysis:

Functional Analysis:

Measure Theory:

Differential Equations:

Functional Analysis:

Mathematical Logic:

Mathematical analysis is the foundation for many other areas of mathematics and has extensive applications in science, engineering, economics, and various other fields. It provides the tools and concepts needed to rigorously study and understand the behavior of functions and sequences.