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Calculus is a branch of mathematics that deals with the study of change and motion. It focuses on concepts such as limits, derivatives, integrals, and infinite series. Calculus is primarily divided into two main branches: 1. **Differential Calculus**: This branch focuses on the concept of the derivative, which represents the rate of change of a function with respect to a variable.

Complex analysis is a branch of mathematics that studies functions of complex numbers and their properties. It is a significant area of mathematical analysis and has applications in various fields, including engineering, physics, and applied mathematics.

Computable analysis is a branch of mathematical analysis that focuses on the study of computable functions and their properties, particularly in the context of real numbers and more general spaces such as metric spaces and topological spaces. As a subfield of theoretical computer science and mathematical logic, it connects the areas of computation and analysis. Key concepts in computable analysis include: 1. **Computable Functions**: Functions that can be computed by a finite algorithm in a stepwise manner.

Functional analysis is a branch of mathematical analysis that deals with function spaces and the study of linear operators acting on these spaces. It is a subfield of both mathematics and applied mathematics and is particularly important in areas such as differential equations, quantum mechanics, and optimization.

Measure theory is a branch of mathematics that deals with the systematic way of assigning a numerical "size" or "measure" to subsets of a given space. It provides a foundational framework for many areas of mathematics, particularly in integration, probability theory, and functional analysis.

Microlocal analysis is a branch of mathematical analysis that studies the properties of partial differential equations (PDEs) by examining their behavior at a more refined level than the traditional pointwise analysis. Specifically, it involves analyzing solutions and their singularities in both the spatial and frequency (or oscillatory) domains. The main tools of microlocal analysis include: 1. **Wavefront Sets**: The wavefront set of a distribution captures both its singularities and the directions of those singularities.

Real analysis is a branch of mathematical analysis that deals with the study of real numbers, sequences and series of real numbers, and functions of real variables. It provides the foundational tools and concepts for rigorous study in calculus and is concerned with understanding the properties and behavior of real-valued functions. Key topics in real analysis include: 1. **Real Numbers**: Exploration of the properties of real numbers, including their completeness, order, and properties of irrational numbers.

Global analysis is a comprehensive approach used primarily in mathematics and related fields to study systems, functions, or phenomena in a broad and holistic manner. While the term can apply to various disciplines, it is often associated with the following contexts: 1. **Mathematics and Differential Equations**: In this context, global analysis typically refers to the study of differential equations and differential geometry with an emphasis on understanding the global properties of solutions rather than local properties.