By Harold M. Edwards
In a booklet written for mathematicians, lecturers of arithmetic, and hugely stimulated scholars, Harold Edwards has taken a daring and weird method of the presentation of complicated calculus. He starts with a lucid dialogue of differential varieties and speedy strikes to the basic theorems of calculus and Stokes’ theorem. the result's real arithmetic, either in spirit and content material, and an exhilarating selection for an honors or graduate path or certainly for any mathematician wanting a refreshingly casual and versatile reintroduction to the topic. For most of these capability readers, the writer has made the method paintings within the most sensible culture of inventive mathematics.
This cheap softcover reprint of the 1994 variation provides the various set of themes from which complex calculus classes are created in appealing unifying generalization. the writer emphasizes using differential kinds in linear algebra, implicit differentiation in better dimensions utilizing the calculus of differential kinds, and the strategy of Lagrange multipliers in a common yet easy-to-use formula. There are copious routines to aid consultant the reader in trying out realizing. The chapters should be learn in nearly any order, together with starting with the ultimate bankruptcy that comprises a few of the extra conventional issues of complex calculus classes. furthermore, it's excellent for a direction on vector research from the differential types element of view.
The specialist mathematician will locate right here a pleasant instance of mathematical literature; the coed lucky adequate to have passed through this e-book may have a company grab of the character of recent arithmetic and an outstanding framework to proceed to extra complex studies.
The most crucial feature…is that it's fun—it is enjoyable to learn the workouts, it's enjoyable to learn the reviews revealed within the margins, it's enjoyable just to decide a random spot within the ebook and start interpreting. this can be the way in which arithmetic will be awarded, with an pleasure and liveliness that express why we're drawn to the subject.
—The American Mathematical per month (First evaluate)
An inviting, strange, high-level creation to vector calculus, dependent solidly on differential varieties. brilliant exposition: casual yet refined, down-to-earth yet common, geometrically rigorous, exciting yet critical. extraordinary diversified functions, actual and mathematical.
—The American Mathematical per 30 days (1994) in keeping 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