Title
The Development Of The Foundations Of Mathematical Analysis From Euler To Riemann-used
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[Opening Paragraph Of The Introduction]Our Account Of The Historical Development Of Mathematical Analysis Concentrates Only On Its Foundational Aspects. We Start In The Eighteenth Century With The Achievements And Difficulties Of The Calculus Epitomized In The Mathematical Examination Of The Motion Of The Vibrating String, And From There We Follow Lines Of Development Which Led In The Early Decades Of The Nineteenth Century To The Broadening Of The Subject Into What We Now Know As 'Mathematical Analysis': Theories Of Functions And Continuity, Limits, And The Convergence Of Series (Including Fourier Series), As Well As The Formation And Use Of The Derivative And The Integral. The Story Is Divided Into Six Chapters, According Both To The Selection Of Problems And Also To The Historical Circumstances Of Their Progress, And An Appendix Is Given Over To The Introduction Of Convergence Tests. From Time To Time We Meet Other Branches Of Mathematics Which Were Related To Or Which Applied The New Ideas In Analysis, But Their Detailed History Has Not Been Attempted Here, On The Grounds That They Would Constitute Digressions Too Extensive From Our Main Theme; Instead, Either A Brief Summary Has Been Given In A Footnote, Or Else Reference Has Been Made To Other Sources Which Do Discuss The History Of The Problem In Question. Of Especial Importance In This Context Is The Fact That This Study Itself Ends With The Work Of Riemann On The Foundations Of The Calculus, For His Other Ideas And Their Consequences Led To A New Era In Analysis (Of Which Set Theory And Measure Theory Were The Most Important Components), Whose Own Development Would Require A Separate Volume. In Addition, We Have Not Attempted To Recount The Manysided Applications Of The Techniques In Classical Analysis Itself.
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- Q: How many pages is this book? A: This book contains one hundred ninety-two pages. It provides a detailed exploration of the historical development of mathematical analysis.
- Q: What is the binding type of this book? A: This book is available in hardcover binding. This durable format is suitable for long-term use and preservation.
- Q: Who is the author of this book? A: The author is Ivor Grattan-Guinness. He is known for his expertise in the history of mathematics.
- Q: What is the main focus of this book? A: This book focuses on the foundational aspects of mathematical analysis. It traces the historical development from Euler to Riemann.
- Q: Is this book suitable for beginners in mathematics? A: Yes, this book is suitable for beginners. It provides a clear historical context that can enhance understanding.
- Q: What topics does this book cover? A: The book covers topics like functions, continuity, limits, and convergence of series. It also discusses the derivative and integral.
- Q: How should I care for this hardcover book? A: To care for this hardcover book, keep it in a dry place and avoid exposure to direct sunlight. This will help preserve its condition.
- Q: Are there any special storage instructions for this book? A: Store this book upright on a shelf to prevent warping. Using a bookend can help keep it in good condition.
- Q: What if the book arrives damaged? A: If the book arrives damaged, you can typically request a return or exchange. Check the retailer's return policy for specific instructions.
- Q: Can this book be used as a reference for advanced studies? A: Yes, this book can serve as a reference for advanced studies in mathematical analysis. It covers significant historical developments.
- Q: Is this book appropriate for academic use? A: Yes, this book is appropriate for academic use. Its thorough examination of mathematical analysis makes it a valuable resource.
- Q: Does this book include any additional materials or appendices? A: Yes, the book includes an appendix on convergence tests. This adds further value to the main content.
- Q: What era of mathematics does this book focus on? A: This book focuses primarily on the eighteenth and nineteenth centuries. It highlights key developments in mathematical analysis.
- Q: Is there a specific audience for this book? A: The book is aimed at students and scholars of mathematics. It is particularly useful for those interested in its historical context.
- Q: How does this book compare to other texts in mathematical analysis? A: This book provides a unique historical perspective, distinguishing it from many other texts that focus solely on mathematical concepts.