Download e-book for iPad: Advanced Calculus: A Differential Forms Approach by Harold M. Edwards

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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 booklet written for mathematicians, lecturers of arithmetic, and hugely encouraged scholars, Harold Edwards has taken a daring and strange method of the presentation of complex calculus. He starts off with a lucid dialogue of differential types and quick strikes to the basic 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 wanting a refreshingly casual and versatile reintroduction to the topic. For these types 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 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 greater dimensions utilizing the calculus of differential kinds, and the strategy of Lagrange multipliers in a basic yet easy-to-use formula. There are copious routines to aid consultant the reader in trying out realizing. The chapters should be learn in virtually any order, together with starting with the ultimate bankruptcy that includes the various extra conventional subject matters of complex calculus classes. furthermore, it really is perfect 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 scholar lucky adequate to have passed through this e-book could have an organization snatch of the character of contemporary arithmetic and an outstanding framework to proceed to extra complicated studies.

The most crucial feature…is that it truly is fun—it is enjoyable to learn the routines, it really is enjoyable to learn the reviews revealed within the margins, it truly is enjoyable just to decide a random spot within the e-book and start examining. this is often the way in which arithmetic might be offered, with an pleasure and liveliness that exhibit why we're drawn to the subject.

—The American Mathematical per month (First assessment)

An inviting, strange, high-level advent to vector calculus, established solidly on differential kinds. exceptional exposition: casual yet subtle, down-to-earth yet basic, geometrically rigorous, enjoyable yet critical. extraordinary diversified functions, actual and mathematical.

—The American Mathematical per 30 days (1994) in response to the second one Edition

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Additional info for Advanced Calculus: A Differential Forms Approach

Sample text

Unfortunately there is no such convenient notation for indicating orientations of 2 -dimensional integrals. 2 lies in describing precisely what is meant by a 'finely divided polygonal approximation to the domain of integration'. 2 for integrals in which the domain of integration is a simple domain for which a 'finely divided polygonal approximation' can be described explicitly. Consider first the case of an integral R A dx dy in which A dx dy is a (variable) 2-form on the xy-plane and in which the domain of integration R is a rectangle I R = {a :::; x :::; b, c :::; y :::; d} in the xy-plane oriented counterclockwise.

D 0 t H-"1" 31 This completes the definition of the integral of a 2-form A(x, y) dx dy over an oriented rectangle R. The integral fn A dx dy either is a number, defined above, or it does not exist. Only minor modifications are necessary to define the integral of a 3-form over an oriented rectangular parallelopiped or the integral of a 1-form over an oriented interval. The integral of a 2-form over a more general oriented domain D of the plane-for example, over the disk D = {(x, y): x 2 y 2 ::::; 1} oriented counterclockwise-can be defined by the simple trick of taking a rectangle R containing the domain D, setting the integrand equal to zero outside D, and proceeding as before.

Meanwhile this fact gives a very useful conceptual interpretation of the algebraic operations by which pullbacks are defined. This conceptual interpretation will frequently be used to explain ideas, but it will not be used to define concepts or to prove theorems until Chapter 6. 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.

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

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