Harold M. Edwards's Advanced Calculus: A Differential Forms Approach PDF

By Harold M. Edwards

ISBN-10: 0817637079

ISBN-13: 9780817637071

ISBN-10: 0817684115

ISBN-13: 9780817684112

ISBN-10: 0817684123

ISBN-13: 9780817684129

ISBN-10: 3764337079

ISBN-13: 9783764337070

In a e-book written for mathematicians, academics of arithmetic, and hugely influenced scholars, Harold Edwards has taken a daring and strange method of the presentation of complex calculus. He starts with a lucid dialogue of differential types and fast 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 path or certainly for any mathematician short of a refreshingly casual and versatile reintroduction to the topic. For these kind of capability readers, the writer has made the method paintings within the top culture of artistic mathematics.

This cheap softcover reprint of the 1994 version provides the various set of issues from which complicated calculus classes are created in appealing unifying generalization. the writer emphasizes using differential types in linear algebra, implicit differentiation in better dimensions utilizing the calculus of differential kinds, and the tactic of Lagrange multipliers in a normal yet easy-to-use formula. There are copious workouts to assist consultant the reader in trying out realizing. The chapters could 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. moreover, it's perfect for a path on vector research from the differential varieties aspect of view.

The specialist mathematician will locate the following a pleasant instance of mathematical literature; the scholar lucky sufficient to have undergone this publication could have a company clutch of the character of recent arithmetic and a great framework to proceed to extra complex studies.

The most crucial feature…is that it's fun—it is enjoyable to learn the routines, it truly is enjoyable to learn the reviews revealed within the margins, it really is enjoyable just to choose a random spot within the publication and start examining. this is often the best way arithmetic will be offered, with an pleasure and liveliness that exhibit why we're drawn to the subject.

—The American Mathematical per thirty days (First assessment)

An inviting, strange, high-level creation to vector calculus, dependent solidly on differential varieties. terrific exposition: casual yet subtle, down-to-earth yet normal, geometrically rigorous, interesting yet critical. impressive diversified purposes, actual and mathematical.

—The American Mathematical per 30 days (1994) in accordance with the second one Edition

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Extra resources for Advanced Calculus: A Differential Forms Approach

Sample text

Since both approximations can be improved by taking the polygonal approximation to S to consist of more and shorter segments, it would be expected that the approximating sum could be made arbitrarily close to the true value by refining the approximation in this way. That is, the amount of work required for the displacement S should be equal to the limiting value of the approximating sums as the approximating curve is taken to consist of more and shorter segments fitting the curveS more and more closely.

Exercises 1 Show that the pullback of dx dy dz under the composition ofthe maps u = r + 3s v= 2s+t w=r- s+t x = 2u + v y = 3u + v z= u+v+w is equal to the pullback of the pullback; that is, verify the theorem for this case. 5 / Summary 19 2 Do the same for the composition of the maps u = lOr- 1s v w = = + t + 5s- t r + s + 2t 3r x = 2u + v y = 13u- v z = -u + + + 1v - w w 2w. 3 For each of the following triples of points in the plane determine whether they are collinear or determine a counterclockwise orientation or determine a clockwise orientation.

Tn-1 < tn = b of the parameterizing time interval D and drawing the polygonal curve from (x(t 0 ), y(t 0 )) to (x(t1), y(t1)) to ... to (x(tn). y(tn)). The corresponding sum approximating fs (A dx + B dy) is n L i=l (A ~xi + B ~Yi) where ~Xi = x(ti)- x(ti-t), ~Yi = y(ti)- YCti-t) and where the functions A, B are evaluated at some point in the neighborhood of the line segment from (xCti-t), YCti-t)) to (x(ti), y(t;))-at the point (x(ti), y(ti)) where ti is a point in the ith interval ti-t ::; ti ::; ti, for instance.

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Advanced Calculus: A Differential Forms Approach by Harold M. Edwards


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