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Mathematical analysis is a branch of mathematics that involves the study of continuous functions, limits, and related theories, such as differentiation, integration, infinite sequences, series and analytic functions in the context of real and complex numbers, and functions. The field of mathematical analysis developed from calculus, which involves the basic concepts and techniques of analysis. The study of mathematical analysis encompasses the study of various topics such as differential equations, measure theory, numerical analysis and vector analysis. These branches of mathematical analysis are applied in various fields of study. Differential equations are used in a wide range of disciplines such as engineering, physics, economics and biology. Newton's second law, the Schrodinger equation, and the Einstein field equations are also based on differential equations. This book is a detailed explanation of the various concepts, theories, and applications of mathematical analysis. It will prove to be immensely beneficial to the students and researchers associated with this area of mathematics.