Advanced Analysis and Measure

Released on by Dr Jitendra Singh
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  • Advanced Analysis and Measure Book Detail

  • Author : Dr Jitendra Singh
  • Release Date : 2024-09-29
  • Publisher : Dr. Jitendra Singh
  • Genre : Education
  • Pages : 195
  • ISBN 13 :
  • File Size : 29,29 MB
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Advanced Analysis and Measure by Dr Jitendra Singh PDF Summary

Book Description: This book, Advanced Analysis and Measure, is designed as a comprehensive resource for students preparing for competitive exams such as the UGC NET/JRF in Mathematical Sciences and other similar mathematics-oriented examinations. It serves as a detailed guide to advanced topics in real analysis, measure theory, and multivariable calculus, all of which are critical for understanding the deeper mathematical foundations required in these exams. The primary goal of this book is to bridge the gap between undergraduate-level analysis and the more advanced topics that frequently appear in competitive exams. Each chapter introduces fundamental concepts, provides detailed explanations, and demonstrates theorems that are often examined in both theory and application. Additionally, we have taken special care to explain results that are critical for the rigorous study of measure theory and multivariable calculus, including Lebesgue integration, functions of bounded variation, directional derivatives, and the Jacobian matrix. A significant feature of the book is the inclusion of topics that directly align with the syllabus for exams like NET/JRF, GATE, and other mathematics examinations. The structure of the content facilitates not only theoretical understanding but also problem-solving techniques that are essential in competitive exams. The focus on topics such as the Lebesgue Measure and Integral, Jordan Decomposition, and the Inverse and Implicit Function Theorems reflects the evolving trends in these examinations, ensuring that the material is both current and relevant. We hope that this book serves as a valuable resource for aspirants looking to solidify their understanding of advanced analysis and measure theory, and helps them achieve success in their academic and professional endeavors.

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