Calculus and Analysis in Euclidean Space (Undergraduate Texts in Mathematics) by Jerry Shurman (PDF)

Description

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 ofgeometric 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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Reasonable price for a book of this kind.

⭐There isn’t much I can say about the contents of this book that aren’t adequately described in the Preface. I learned the subject from the author and his notes (which later became this book), and I still believe they form the best introduction to the Jacobian matrix, the Inverse and Implicit Function Theorems, Differential Forms, and much more.

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