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This textbook has been designed as per the UGC Choice Based Credit System (CBCS) curriculum to meet the requirements of undergraduate students of mathematics. Systematically written, it acquaints the students with the basic concepts and techniques of real analysis. Important topics such as sets & functions, sequences, infinite series, fundamental properties of limits of functions, uniqueness of limit, continuous functions, basic theory of derivatives & its applications have been thoroughly explained.
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This book presents a concise and sharpley focused introduction to the basic concepts of analysis - from the development of real numbers through uniform convergences of a sequence of functions - and includes coverage both of the analysis of functions of more than one variable and of differential equations. Examples and figures are used extensively to assist the reader in understanding the concepts and then applying them.
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This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors. This third edition includes corrections as well as some additional material. Some features of the text include: The text is completely self-contained and starts with the real number axioms; The integral is defined as the area under the graph, while the area is defined for every subset of the plane; There is a heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero; There are applications from many parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more; Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals; and There are 385 problems with all the solutions at the back of the text.
As an excellent, easy-to-understand introduction to analysis, this book involves rigorous analysis, computational dexterity, and a breadth of applications, making it ideal for undergraduate majors. The book contains many remarkable features, including a heavy emphasis on computational problems and applications from many parts of analysis. The work completely avoids treating complex numbers. Nearly 350 problems with solutions are included in the back of the book.
Real Analysis is a comprehensive introduction to this core subject and is ideal for self-study or as a course textbook for first and second-year undergraduates. Combining an informal style with precision mathematics, the book covers all the key topics with fully worked examples and exercises with solutions. All the concepts and techniques are deployed in examples in the final chapter to provide the student with a thorough understanding of this challenging subject. This book offers a fresh approach to a core subject and manages to provide a gentle and clear introduction without sacrificing rigour or accuracy.
For ten editions, readers have turned to Salas to learn the difficult concepts of calculus without sacrificing rigor. Wiley is proud to publish a new revision of Calculus: One and Several Variables 10th Edition, known for its elegant writing style, precision and perfect balance of theory and applications. The Tenth Edition is refined to offer students an even clearer understanding of calculus and insight into mathematics. It includes a wealth of rich problem sets which makes calculus relevant for students. Salas/Hille/Etgen is recognized for its mathematical integrity, accuracy, and clarity that will help readers master these concepts and understand their relevance to the real world.
This book is an attempt to make presentation of Elements of Real Analysis more lucid. The book contains examples and exercises meant to help a proper understanding of the text. For B.A., B.Sc. and Honours (Mathematics and Physics), M.A. and M.Sc. (Mathematics) students of various Universities/ Institutions.As per UGC Model Curriculum and for I.A.S. and Various other competitive exams.