Fundamentals of Mathematical Analysis

Author Rashmi Bhardwaj & Ajaya Kumar Singh
ISBN: 978-9392-54-93-66

₹ 999.00

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Book Detail
Publication Year	2024
ISBN-13	978-9392549366
Language	English
Edition	1st
Pages	880

Preface
Preface	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, Schröder–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.

Preface

Preface

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, Schröder–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.

Table of Contents
Table of Contents	1.Basic Concepts & Preliminaries 2. Numbers : Real & Complex 3. Cardinality of Sset & One -to-One Correspondence 4. Analytical Properties 5. Sequences and Subsequences 6. Infinite Series 7. Limits 8. continuous Functions 9.Differentiable Functions 10. The Riemann Integral & Darboux Integral 11. Bounded Variation & Rectification 12. Improper Integral 13. Sequence of Functions 14. Series of Functions 15. Power Series 16. Fourier Series , Integrals & Transforms 17.Complex Numbers & functions , Conformal Mapping & Analytic Functions 18. Complex Integration 19. Power Series & Taylor Series 20. Laurent Series 21. Metric Spaces , Compactness & Connectedness

Table of Contents

Table of Contents

1.Basic Concepts & Preliminaries 2. Numbers : Real & Complex 3. Cardinality of Sset & One -to-One Correspondence 4. Analytical Properties 5. Sequences and Subsequences 6. Infinite Series 7. Limits 8. continuous Functions 9.Differentiable Functions 10. The Riemann Integral & Darboux Integral 11. Bounded Variation & Rectification 12. Improper Integral 13. Sequence of Functions 14. Series of Functions 15. Power Series 16. Fourier Series , Integrals & Transforms 17.Complex Numbers & functions , Conformal Mapping & Analytic Functions 18. Complex Integration 19. Power Series & Taylor Series 20. Laurent Series 21. Metric Spaces , Compactness & Connectedness

Fundamentals of Mathematical Analysis

₹ 999.00