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Fundamentals of Mathematical Analysis, Textbook for Undergraduate Students

Fundamentals of Mathematical Analysis, Textbook for Undergraduate Students

          
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About the Book

Fundamentals of Mathematical Analysis is a comprehensive textbook designed for undergraduate and postgraduate students pursuing degrees in Mathematics, Autonomous Colleges, and Universities. This book covers a wide range of topics with a special emphasis on B.A. and B.Sc. (Mathematics) courses structured by UGC/CBCS syllabi. The preliminary ideas and scope of the book are clearly outlined, and detailed course contents are provided for better understanding. With twenty-one chapters, this text delves into Basic Concepts and Preliminaries, providing background materials for the development of ideas in subsequent chapters. It covers essential topics such as Basic Features, Preliminary Notions, Function and its Properties, Real Sequences, Mathematical Induction, Relation, and Real Analysis. The book introduces fundamental concepts like the Cantor Set, Relation between Variable Quantities, and the Function and Sequence's central role in Calculus and Real Analysis. Additionally, it explores important topics like Linear Transformations, Vector Spaces, Linear Transformations on Vector Spaces, and Expected Short and Long Questions. The book also includes Real and Complex numbers, providing ideas and background materials for the development of rationals and their inadequacy. It covers important concepts like Absolute Value Function, Completeness Property, Supremum and Infimum, Density and its Properties, and Decimal Representation of Real Numbers. Furthermore, it discusses Cardinality of Sets, One-to-One Correspondence, Bijection Map, Countability, Schroder–Bernstein Property, Transcendental Numbers, and related theorems. The book also covers Analytical (Metric) Properties of Real Line, Complex Plane, Distance Function, Neighbourhood of a Point, Open and Closed Sets, Limit Points, Bolzano-Weierstrass Theorem, and Limit Points of a Set. Finally, it explores Sequences (R and C) and their Convergences, with a special focus on Real Sequences and Complex Sequences.


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Product Details
  • ISBN-13: 9789392549366
  • Publisher: Khanna Publishers
  • Binding: Perfect
  • No of Pages: 880
  • ISBN-10: 9392549369
  • Publisher Date: 01 Jan 2024
  • Language: English


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