By Harold M. Edwards
In a e-book written for mathematicians, lecturers of arithmetic, and hugely inspired scholars, Harold Edwards has taken a daring and weird method of the presentation of complicated calculus. He starts with a lucid dialogue of differential kinds and speedy strikes to the elemental theorems of calculus and Stokes’ theorem. the result's actual arithmetic, either in spirit and content material, and an exhilarating selection for an honors or graduate direction or certainly for any mathematician wanting a refreshingly casual and versatile reintroduction to the topic. For some of these power readers, the writer has made the procedure paintings within the top culture of artistic mathematics.
This cheap softcover reprint of the 1994 variation offers the various set of themes from which complex 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 varieties, and the tactic of Lagrange multipliers in a basic yet easy-to-use formula. There are copious workouts to aid advisor the reader in trying out figuring out. The chapters might be learn in nearly any order, together with starting with the ultimate bankruptcy that comprises a few of the extra conventional themes of complicated calculus classes. furthermore, it really is excellent for a path on vector research from the differential kinds element of view.
The specialist mathematician will locate right here a pleasant instance of mathematical literature; the scholar lucky adequate to have undergone this booklet may have an organization seize of the character of contemporary arithmetic and an excellent framework to proceed to extra complicated studies.
The most crucial feature…is that it really is fun—it is enjoyable to learn the workouts, it really is enjoyable to learn the reviews revealed within the margins, it truly is enjoyable just to decide a random spot within the publication and start studying. this can be the way in which arithmetic can be offered, with an pleasure and liveliness that express why we're drawn to the subject.
—The American Mathematical per 30 days (First overview)
An inviting, strange, high-level creation to vector calculus, established solidly on differential kinds. awesome exposition: casual yet refined, down-to-earth yet normal, geometrically rigorous, enjoyable yet critical. notable varied purposes, actual and mathematical.
—The American Mathematical per 30 days (1994) in response to the second one Edition
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Additional resources for Advanced Calculus: A Differential Forms Approach (Modern Birkhäuser Classics)
Advanced Calculus: A Differential Forms Approach (Modern Birkhäuser Classics) by Harold M. Edwards