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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Calculus and Analysis in Euclidean Space (Paperback, Softcover reprint of the original 1st ed. 2016)
Loot Price: R2,056
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Calculus and Analysis in Euclidean Space (Paperback, Softcover reprint of the original 1st ed. 2016)
Series: Undergraduate Texts in Mathematics
Expected to ship within 10 - 15 working days
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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.
General
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