Calculus and Analysis in Euclidean Space

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Jerry Shurman is professor of mathematics at Reed College, Portland, OR, USA. He is also the co-author of GTM 228 "A First Course in Modular Forms."

Zusammenfassung

Concentrates on n-dimensional Euclidean space

Uses multivariable calculus to teach mathematics as a blend of reasoning, computing, and problem-solving, doing justice to the structure, the details, and the scope of the ideas

Contains figures, formulas, and words to guide the reader to do mathematics resourcefully by marshaling the skills of geometric intuition, algebraic manipulation, and incisive use of natural language

Includes supplementary material: [...]

Request lecturer material: [...]

Inhaltsverzeichnis

Preface.- 1 Results from One-Variable Calculus.- Part I Multivariable Differential Calculus.- 2 Euclidean Space.- 3 Linear Mappings and Their Matrices.- 4 The Derivative.- 5 Inverse and Implicit Functions.- Part II Multivariable Integral Calculus.- 6 Integration.- 7 Approximation by Smooth Functions.- 8 Parameterized Curves.- 9 Integration of Differential Forms.- Index.

Details

Erscheinungsjahr:	2016
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	505
Reihe:	Undergraduate Texts in Mathematics
Inhalt:	xiii 505 S. 1 s/w Illustr. 505 p. 1 illus.
ISBN-13:	9783319493121
ISBN-10:	3319493124
Sprache:	Englisch
Einband:	Gebunden
Autor:	Shurman, Jerry
Hersteller:	Springer-Verlag GmbH Springer International Publishing
Abbildungen:	87 schwarz-weiße und 94 farbige Abbildungen, 3 schwarz-weiße Tabellen, Bibliographie
Maße:	241 x 160 x 34 mm
Von/Mit:	Jerry Shurman
Erscheinungsdatum:	16.12.2016
Gewicht:	0,945 kg

preigu-id: 108143663