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Item #:
20581332
Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus 1st Edition
Item #:
20581332
CHF 34
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This little book is especially concerned with those portions of ?advanced calculus? in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.
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Product Details
- Focuses on advanced calculus with modern methods
- Uses elementary versions of sophisticated mathematics
- Requires linear algebra and basic set theory knowledge
- Assumes familiarity with first-year calculus and real number concepts
- Ideal for those with a rapport with abstract mathematics
- Aims to make advanced calculus rigor attainable at an elementary level
| Item Weight | 1.5 lbs (680 grams) |
Product Description
Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus 1st Edition
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Customer Questions & Answers
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Question:
What is the main focus of 'Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus'?
Answer: The book primarily focuses on the advanced concepts of calculus as they apply to manifolds, bridging the gap between classical calculus and modern mathematical theories. It introduces readers to manifold theory while addressing classical theorems in a contemporary context. This is crucial for students and professionals aiming to grasp the intricacies of differential geometry and analytical methods, making it ideal for courses in advanced calculus or mathematical physics. -
Question:
Who is the target audience for this book?
Answer: The book is aimed at advanced undergraduate and graduate students in mathematics and related fields. It is particularly beneficial for those who have a foundational understanding of calculus and wish to delve into more complex topics such as topology and differential forms. Researchers and educators involved in higher mathematics will also find this resource invaluable for enhancing their coursework or research endeavors. -
Question:
What prerequisites should I have before reading this book?
Answer: A solid understanding of undergraduate calculus, linear algebra, and introductory analysis is recommended before tackling this text. Familiarity with basic concepts of topology will also enhance comprehension significantly, as the book builds upon these foundations to explain more complex theories. Engaging with the material requires analytical thinking and problem-solving skills that are honed through prior mathematical study. -
Question:
How does this book differ from traditional calculus textbooks?
Answer: Unlike traditional calculus textbooks that typically focus on computational techniques, 'Calculus On Manifolds' emphasizes abstraction and theory. It provides a rigorous approach to understanding how calculus applies in higher dimensions and nonscalar contexts. This distinction is crucial for students preparing for future studies in advanced mathematics, physics, or engineering, where a deeper conceptual framework is advantageous. -
Question:
Are there practical applications discussed in the book?
Answer: Yes, the book illustrates various practical applications of manifold theory, particularly in physics and engineering. Understanding calculus on manifolds is essential for fields such as general relativity, fluid dynamics, and robotics. By exploring these applications, readers can see the relevance of advanced calculus in real-world scenarios, reinforcing their learning and interest in the subject matter. -
Question:
Does the book include exercises or examples?
Answer: Absolutely, the book contains numerous exercises and examples that enhance the learning experience. These problems range in difficulty and encourage readers to apply the concepts discussed in each chapter, solidifying their understanding. Engaging with these exercises is vital for mastering the intricate ideas of manifold theory and is especially useful for instructors seeking to assign practical work for students. -
Question:
What mathematical concepts are introduced in this book?
Answer: Key mathematical concepts introduced include differentiable manifolds, smooth maps, tangent spaces, and integration on manifolds. The book builds a framework around these ideas, allowing readers to explore their interrelations and applications in various mathematical contexts. Understanding these concepts lays the groundwork for further study in specialized fields such as differential geometry or topological spaces, enabling a well-rounded mathematical education. -
Question:
Is this book suitable for self-study?
Answer: Yes, 'Calculus On Manifolds' is suitable for self-study, provided the reader has the necessary background knowledge. The clear explanations and structured layout facilitate independent learning, making it easier to follow complex ideas without needing a formal classroom environment. This is ideal for learners aiming to deepen their understanding at their own pace while obtaining a comprehensive grasp of advanced calculus. -
Question:
What are some key features of this book?
Answer: Some key features include a focus on theoretical rigor, numerous examples and exercises, and detailed explanations of complex topics. These elements collectively enhance comprehension and retention of advanced calculus concepts. The book encourages critical thinking and problem-solving, vital skills that are beneficial for any mathematician or scientist aiming for proficiency in advanced mathematical methods. -
Question:
Where can I buy Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus in Switzerland?
Answer: You can purchase 'Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus' on Ubuy. Ubuy offers a convenient online shopping experience, allowing customers in Switzerland to easily access this book along with various options and deals. Explore Ubuy to find this essential mathematical resource and elevate your understanding of advanced calculus.
Vector Analysis Editorial Review
"Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus" by Michael Spivak is a book that may have gained popularity due to its inventive proof of Stoke's Theorem, but it falls short in other aspects. The book contains a significant number of errors, not just typographical errors, but also mathematical mistakes. While some reviewers claim that these errors do not affect the development of the mathematics, this is not entirely true. The book now includes an addenda to address some of the incorrect mathematics, but there are still lingering issues. One example is a circularity in the development of integration apparatus, where an unproven assumption is used to prove a general case. These errors make the book unsuitable for those new to the subject. Comparisons are made to other books on the subject, such as Rudin's undergraduate text and Munkres' book. Rudin also suffers from similar issues with the change of variables theorem, while Munkres' book is Considered the most rigorous and complete in proving Stoke's Theorem. Despite its flaws, the book can still serve as a resource for instructors interested in teaching this material. However, for self-study, other options like Munkres' book are recommended.
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Pros
- The first half of the book covers a typical multivariable analysis course concisely.
- Clear and understandable presentation.
- Incorporates concepts from linear algebra.
Cons
- Numerous errors, both typographical and mathematical.
Product Price History
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CHF 34
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Features & Benefits
- Focuses on advanced calculus concepts
- Uses modern methods in mathematics
- Minimal prerequisites: linear algebra, set theory, and calculus
- Ideal for those with a rapport with abstract mathematics
- Helps achieve rigor in difficult concepts
- Suitable for those with some mathematical background