Branches of Mathematics: Mathematical Analysis - Extending Calculus
Автор: A Meaningless Collection
Загружено: 2026-02-08
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Analysis is the rigorous extension of calculus. It seeks to define and prove the concepts of limits, continuity, and convergence with absolute precision.
While calculus uses these ideas intuitively, analysis ensures they are logically sound and works to generalize them to more complex settings — such as infinite series, multiple dimensions, or abstract spaces.
Subfields
Real analysis focuses on real numbers and functions.
Complex analysis studies functions of complex numbers — combining algebra and geometry in elegant ways.
Functional analysis generalizes calculus to spaces of functions, forming the backbone of quantum physics and modern engineering.
Applications
Analysis provides the tools needed for advanced physics, signal processing, economics, and any science involving continuous change. Its ideas shape our understanding of motion, energy, and optimization.
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