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Calculus and Analysis in Euclidean Space

2016-11-26 Mathematics
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Release : 2016-11-26
Genre : Mathematics
Kind : eBook
Book Rating : 140/5 ( reviews)

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Book Synopsis Calculus and Analysis in Euclidean Space by : Jerry Shurman

Download or read book Calculus and Analysis in Euclidean Space written by Jerry Shurman. This book was released on 2016-11-26. Available in PDF, EPUB and Kindle. Book excerpt: 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 geometric intuition (the visual cortex being quickly instinctive) algebraic manipulation (symbol-patterns being precise and robust) incisive use of natural language (slogans that encapsulate central ideas enabling a large-scale grasp of the subject). Thinking in these ways renders mathematics coherent, inevitable, and fluid. The prerequisite is single-variable calculus, including familiarity with the foundational theorems and some experience with proofs.

Analysis in Euclidean Space

2019-07-17 Mathematics
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Release : 2019-07-17
Genre : Mathematics
Kind : eBook
Book Rating : 658/5 ( reviews)

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Book Synopsis Analysis in Euclidean Space by : Kenneth Hoffman

Download or read book Analysis in Euclidean Space written by Kenneth Hoffman. This book was released on 2019-07-17. Available in PDF, EPUB and Kindle. Book excerpt: Developed for an introductory course in mathematical analysis at MIT, this text focuses on concepts, principles, and methods. Its introductions to real and complex analysis are closely formulated, and they constitute a natural introduction to complex function theory. Starting with an overview of the real number system, the text presents results for subsets and functions related to Euclidean space of n dimensions. It offers a rigorous review of the fundamentals of calculus, emphasizing power series expansions and introducing the theory of complex-analytic functions. Subsequent chapters cover sequences of functions, normed linear spaces, and the Lebesgue interval. They discuss most of the basic properties of integral and measure, including a brief look at orthogonal expansions. A chapter on differentiable mappings addresses implicit and inverse function theorems and the change of variable theorem. Exercises appear throughout the book, and extensive supplementary material includes a Bibliography, List of Symbols, Index, and an Appendix with background in elementary set theory.

Lebesgue Integration on Euclidean Space

2001 Computers
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Release : 2001
Genre : Computers
Kind : eBook
Book Rating : 087/5 ( reviews)

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Book Synopsis Lebesgue Integration on Euclidean Space by : Frank Jones

Download or read book Lebesgue Integration on Euclidean Space written by Frank Jones. This book was released on 2001. Available in PDF, EPUB and Kindle. Book excerpt: "'Lebesgue Integration on Euclidean Space' contains a concrete, intuitive, and patient derivation of Lebesgue measure and integration on Rn. It contains many exercises that are incorporated throughout the text, enabling the reader to apply immediately the new ideas that have been presented" --

Analysis in Euclidean Space

2022 Calculus
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Release : 2022
Genre : Calculus
Kind : eBook
Book Rating : 719/5 ( reviews)

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Book Synopsis Analysis in Euclidean Space by : Joaquim Bruna

Download or read book Analysis in Euclidean Space written by Joaquim Bruna. This book was released on 2022. Available in PDF, EPUB and Kindle. Book excerpt: Based on notes written during the author's many years of teaching, Analysis in Euclidean Space mainly covers Differentiation and Integration theory in several real variables, but also an array of closely related areas including measure theory, differential geometry, classical theory of curves, geometric measure theory, integral geometry, and others. With several original results, new approaches and an emphasis on concepts and rigorous proofs, the book is suitable for undergraduate students, particularly in mathematics and physics, who are interested in acquiring a solid footing in analysis and expanding their background. There are many examples and exercises inserted in the text for the student to work through independently. Analysis in Euclidean Space comprises 21 chapters, each with an introduction summarizing its contents, and an additional chapter containing miscellaneous exercises. Lecturers may use the varied chapters of this book for different undergraduate courses in analysis. The only prerequisites are a basic course in linear algebra and a standard first-year calculus course in differentiation and integration. As the book progresses, the difficulty increases such that some of the later sections may be appropriate for graduate study.

Topological Methods in Euclidean Spaces

2012-08-29 Mathematics
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Release : 2012-08-29
Genre : Mathematics
Kind : eBook
Book Rating : 444/5 ( reviews)

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Book Synopsis Topological Methods in Euclidean Spaces by : Gregory L. Naber

Download or read book Topological Methods in Euclidean Spaces written by Gregory L. Naber. This book was released on 2012-08-29. Available in PDF, EPUB and Kindle. Book excerpt: Extensive development of such topics as elementary combinatorial techniques, Sperner's Lemma, the Brouwer Fixed Point Theorem, and the Stone-Weierstrass Theorem. New section of solutions to selected problems.

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