Analysis In Euclidean Space
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Author |
: Kenneth Hoffman |
Publisher |
: Courier Dover Publications |
Total Pages |
: 449 |
Release |
: 2019-07-17 |
ISBN-10 |
: 9780486833651 |
ISBN-13 |
: 0486833658 |
Rating |
: 4/5 (51 Downloads) |
Synopsis Analysis in Euclidean Space by : Kenneth Hoffman
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.
Author |
: Jerry Shurman |
Publisher |
: Springer |
Total Pages |
: 505 |
Release |
: 2016-11-26 |
ISBN-10 |
: 9783319493145 |
ISBN-13 |
: 3319493140 |
Rating |
: 4/5 (45 Downloads) |
Synopsis Calculus and Analysis in Euclidean Space by : Jerry Shurman
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.
Author |
: Elias M. Stein |
Publisher |
: Princeton University Press |
Total Pages |
: 312 |
Release |
: 2016-06-02 |
ISBN-10 |
: 9781400883899 |
ISBN-13 |
: 140088389X |
Rating |
: 4/5 (99 Downloads) |
Synopsis Introduction to Fourier Analysis on Euclidean Spaces (PMS-32), Volume 32 by : Elias M. Stein
The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.
Author |
: Kenneth Hoffman |
Publisher |
: |
Total Pages |
: 438 |
Release |
: 1969 |
ISBN-10 |
: OCLC:33384564 |
ISBN-13 |
: |
Rating |
: 4/5 (64 Downloads) |
Synopsis Analysis in Euclidean Space by : Kenneth Hoffman
Author |
: Joaquim Bruna |
Publisher |
: Wspc (Europe) |
Total Pages |
: 0 |
Release |
: 2022 |
ISBN-10 |
: 1800611714 |
ISBN-13 |
: 9781800611719 |
Rating |
: 4/5 (14 Downloads) |
Synopsis Analysis in Euclidean Space by : Joaquim Bruna
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.
Author |
: Claus Müller |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 227 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461205814 |
ISBN-13 |
: 1461205816 |
Rating |
: 4/5 (14 Downloads) |
Synopsis Analysis of Spherical Symmetries in Euclidean Spaces by : Claus Müller
This self-contained book offers a new and direct approach to the theories of special functions with emphasis on spherical symmetry in Euclidean spaces of arbitrary dimensions. Based on many years of lecturing to mathematicians, physicists and engineers in scientific research institutions in Europe and the USA, the author uses elementary concepts to present the spherical harmonics in a theory of invariants of the orthogonal group. One of the highlights is the extension of the classical results of the spherical harmonics into the complex - particularly important for the complexification of the Funk-Hecke formula which successfully leads to new integrals for Bessel- and Hankel functions with many applications of Fourier integrals and Radon transforms. Numerous exercises stimulate mathematical ingenuity and bridge the gap between well-known elementary results and their appearance in the new formations.
Author |
: Kenneth Hoffman |
Publisher |
: |
Total Pages |
: |
Release |
: 1967 |
ISBN-10 |
: OCLC:16398012 |
ISBN-13 |
: |
Rating |
: 4/5 (12 Downloads) |
Synopsis Analysis in Euclidean Space by : Kenneth Hoffman
Author |
: Frank Jones |
Publisher |
: Jones & Bartlett Learning |
Total Pages |
: 626 |
Release |
: 2001 |
ISBN-10 |
: 0763717088 |
ISBN-13 |
: 9780763717087 |
Rating |
: 4/5 (88 Downloads) |
Synopsis Lebesgue Integration on Euclidean Space by : Frank Jones
"'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" --
Author |
: Pertti Mattila |
Publisher |
: Cambridge University Press |
Total Pages |
: 360 |
Release |
: 1999-02-25 |
ISBN-10 |
: 0521655951 |
ISBN-13 |
: 9780521655958 |
Rating |
: 4/5 (51 Downloads) |
Synopsis Geometry of Sets and Measures in Euclidean Spaces by : Pertti Mattila
This book studies the geometric properties of general sets and measures in euclidean space.
Author |
: Gregory L. Naber |
Publisher |
: Courier Corporation |
Total Pages |
: 276 |
Release |
: 2012-08-29 |
ISBN-10 |
: 9780486153445 |
ISBN-13 |
: 0486153444 |
Rating |
: 4/5 (45 Downloads) |
Synopsis Topological Methods in Euclidean Spaces by : Gregory L. Naber
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.