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A thorough study. It is the branch of mathematics that includes calculus. A careful study of something to learn about its parts, what they do, and how they are related to each other; · why is analysis essential in understanding complexity? Modern mathematical analysis is the study of infinite processes. The act of studying or examining something in detail, in order to discover or understand more…. An explanation of the nature and meaning of something An analysis is an explanation or description that results from considering something carefully. Discover how this term evolved to define critical thinking and examination. The meaning of analysis is a detailed examination of anything complex in order to understand its nature or to determine its essential features : The separation of a substance into its constituent elements to determine either their nature (qualitative analysis) or their proportions (quantitative analysis).