By Harold M. Edwards
In a booklet written for mathematicians, academics of arithmetic, and hugely influenced scholars, Harold Edwards has taken a daring and strange method of the presentation of complicated calculus. He starts with a lucid dialogue of differential varieties and quick strikes to the basic theorems of calculus and Stokes’ theorem. the result's actual arithmetic, either in spirit and content material, and a thrilling selection for an honors or graduate path or certainly for any mathematician short of a refreshingly casual and versatile reintroduction to the topic. For these kinds of capability readers, the writer has made the process paintings within the most sensible culture of artistic mathematics.
This reasonable softcover reprint of the 1994 variation provides the varied set of themes from which complicated calculus classes are created in attractive unifying generalization. the writer emphasizes using differential types in linear algebra, implicit differentiation in greater dimensions utilizing the calculus of differential types, and the tactic of Lagrange multipliers in a common yet easy-to-use formula. There are copious routines to aid consultant the reader in trying out knowing. The chapters will be learn in virtually any order, together with starting with the ultimate bankruptcy that includes many of the extra conventional themes of complicated calculus classes. furthermore, it truly is excellent for a path on vector research from the differential types element of view.
The expert mathematician will locate right here a pleasant instance of mathematical literature; the coed lucky adequate to have passed through this booklet could have a company snatch of the character of contemporary arithmetic and an effective framework to proceed to extra complicated studies.
The most vital feature…is that it really is fun—it is enjoyable to learn the routines, it's enjoyable to learn the reviews revealed within the margins, it's enjoyable just to choose a random spot within the booklet and start interpreting. this can be the way in which arithmetic can be provided, with an pleasure and liveliness that express why we're attracted to the subject.
—The American Mathematical per 30 days (First assessment)
An inviting, strange, high-level advent to vector calculus, dependent solidly on differential varieties. really good exposition: casual yet refined, down-to-earth yet normal, geometrically rigorous, enjoyable yet critical. awesome assorted purposes, actual and mathematical.
—The American Mathematical per thirty days (1994) in line with the second one Edition
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Extra resources for Advanced Calculus: A Differential Forms Approach (Modern Birkhäuser Classics)
Advanced Calculus: A Differential Forms Approach (Modern Birkhäuser Classics) by Harold M. Edwards