Mathematical Analysis Malik Arora Pdf

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Mathematical Analysis by Malik and Arora: A Comprehensive Textbook for Undergraduate and Postgraduate Students

Mathematical analysis is a branch of mathematics that deals with the study of functions, limits, continuity, differentiation, integration, series, sequences, and other topics. It is a fundamental subject for students of mathematics, physics, engineering, and other sciences.

One of the most popular and widely used textbooks on mathematical analysis is Mathematical Analysis by S. C. Malik and Savita Arora. This book is intended to serve as a text for undergraduate and postgraduate students of various universities. It covers the theory from its very beginning, with a rigorous and modern approach. It also provides a large number of solved examples and exercises to illustrate the concepts and techniques.

The book consists of 15 chapters and two appendices. The first chapter introduces the essential properties of rational numbers and real numbers, using Dedekind's cut. The second chapter discusses the topological framework of real numbers, such as open sets, closed sets, compact sets, connected sets, etc. The third chapter deals with real sequences and series, including convergence tests, power series, Fourier series, and improper integrals. The fourth and fifth chapters cover the concepts of continuity, differentiability, mean value theorems, Taylor's theorem, and applications of derivatives. The sixth chapter introduces the Riemann integral and its properties, as well as the Riemann-Stieltjes integral. The seventh chapter presents the Lebesgue integral and its comparison with the Riemann integral. The eighth chapter studies the functions of several variables, such as partial derivatives, differentials, implicit functions, inverse functions, etc. The ninth chapter explores the multiple integrals over regions in two or three dimensions. The tenth chapter explains the line integrals and surface integrals in vector fields. The eleventh chapter introduces the metric spaces and their properties, such as completeness, compactness, and connectedness. The twelfth chapter discusses the function spaces and their norms, such as Banach spaces and Hilbert spaces. The thirteenth chapter covers some topics in complex analysis, such as analytic functions, Cauchy's theorem, residue theorem, etc. The fourteenth chapter deals with some topics in differential equations, such as existence and uniqueness theorems, linear differential equations, systems of differential equations, etc. The fifteenth chapter presents some topics in functional analysis, such as linear operators, eigenvalues and eigenvectors, spectral theory, etc. The two appendices provide some background material on beta-gamma functions and Cantor's theory of real numbers.

The book is written in a clear and concise style, with a logical flow of ideas. It provides a thorough exposition of the theory along with numerous examples and exercises to enhance the understanding of the students. It also contains references to other books for further reading.

The book is available in pdf format for free download from various websites[^1^] [^3^]. Alternatively, it can be purchased from online or offline bookstores[^2^]. 66dfd1ed39

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