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.
✔ Author(s): Jerry Shurman
✔ Title: Calculus and Analysis in Euclidean Space (Undergraduate Texts in Mathematics)
✔ Rating : 5 out of 5 base on (11 reviews)
✔ ISBN-10: 3319841300
✔ ISBN-13: 9783319841304
✔ Language: English
✔ Format ebook: PDF, EPUB, Kindle, Audio, HTML and MOBI
✔ Device compatibles: Android, iOS, PC and Amazon Kindle
Readers' opinions about Calculus and Analysis in Euclidean Space by Jerry Shurman
Thea Bell
This book completely captured my heart. The characters were so relatable, and their journeys resonated deeply with me. The writing was poetic and powerful, leaving me with a sense of awe. I'm grateful to have experienced this literary gem.
Melody Blake
I loved the powerful messages hidden within the story. The book tackled important social issues and made me ponder the world we live in. It's a must-read for everyone.
Violet Tyler
The plot was incredibly well-crafted, with twists and turns that kept me hooked until the very last page. It was impossible to predict what would happen next.
