Calculus And Analysis In Euclidean Space Pdf
File Name: calculus and analysis in euclidean space .zip
- Calculus and Analysis in Euclidean Space-Jerry Shurman
- 1: Vectors in Euclidean Space
- From Calculus to Analysis - Steen Pedersen [Springer]
Calculus and Analysis in Euclidean Space-Jerry Shurman
While we are building a new and improved webshop, please click below to purchase this content via our partner CCC and their Rightfind service. You will need to register with a RightFind account to finalise the purchase. This book offers an introduction to differential geometry for the non-specialist. It includes most of the required material from multivariable calculus, linear algebra, and basic analysis. An intuitive approach and a minimum of prerequisites make it a valuable companion for students of mathematics and physics. The main focus is on manifolds in Euclidean space and the metric properties they inherit from it. Among the topics discussed are curvature and how it affects the shape of space, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.
1: Vectors in Euclidean Space
The graceful role of analysis in underpinning calculus is often lost to their separation in the curriculum. This book entwines the two subjects, providing a conceptual approach to multivariable calculus closely supported by the structure and reasoning of analysis. The setting is Euclidean space, with the material on differentiation culminating in the inverse and implicit function theorems, and the material on integration culminating in the general fundamental theorem of integral calculus. More in-depth than most calculus books but less technical than a typical analysis introduction, Calculus and Analysis in Euclidean Space offers a rich blend of content to students outside the traditional mathematics major, while also providing transitional preparation for those who will continue on in the subject. The writing in this book aims to convey the intent of ideas early in discussion. The narrative proceeds through figures, formulas, and text, guiding the reader to do mathematics resourcefully by marshaling the skills of.
Literature The following is a list of books on which the lecture is based. They are available in the library. Although we will not follow a book strictly, the material can be found in them and they may sometimes offer a different approach to the material. Books relevant for the first term: E. Copson, Metric Spaces. Cambridge University Press. Dieudonne, Foundations of modern analysis.
From Calculus to Analysis - Steen Pedersen [Springer]
Undergraduate Texts in Mathematics are generally aimed at third- and fourth- year undergraduate mathematics students at North American universities. These texts strive to provide students and teachers with new perspectives and novel ap- proaches. The books include motivation that guides the reader to an appreciation of interrelations among different aspects of the subject. They feature examples that illustrate key concepts as well as exercises that strengthen understanding. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microlms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition. I have never met, or had any other kind of contact with, Jerry Shurman, the author of the book now under review, but despite this lack of familiarity, I would be willing to bet that he is an excellent teacher. He has certainly written an excellent book, one which reflects a considerable amount of time and effort spent thinking about the best way to present this material to an undergraduate audience.