Advanced Calculus: A Differential Forms Approach - download pdf or read online

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, lecturers of arithmetic, and hugely stimulated scholars, Harold Edwards has taken a daring and weird method of the presentation of complicated calculus. He starts off with a lucid dialogue of differential kinds and quick 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 some of these capability readers, the writer has made the technique paintings within the top culture of artistic mathematics.

This cheap softcover reprint of the 1994 version offers the various set of themes from which complex calculus classes are created in appealing unifying generalization. the writer emphasizes using differential varieties in linear algebra, implicit differentiation in greater dimensions utilizing the calculus of differential kinds, and the strategy of Lagrange multipliers in a common yet easy-to-use formula. There are copious workouts to aid advisor the reader in checking out figuring out. The chapters might be learn in virtually any order, together with starting with the ultimate bankruptcy that includes many of the extra conventional subject matters of complicated calculus classes. additionally, it's perfect for a path on vector research from the differential varieties element of view.

The specialist mathematician will locate the following a pleasant instance of mathematical literature; the coed lucky sufficient to have passed through this booklet could have a company snatch of the character of contemporary arithmetic and a high-quality framework to proceed to extra complex studies.

The most crucial feature…is that it's fun—it is enjoyable to learn the routines, it really is enjoyable to learn the reviews published within the margins, it's enjoyable just to choose a random spot within the ebook and start analyzing. 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 overview)

An inviting, strange, high-level advent to vector calculus, dependent solidly on differential kinds. amazing exposition: casual yet refined, down-to-earth yet basic, geometrically rigorous, interesting yet severe. notable diversified functions, actual and mathematical.

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

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Extra resources for Advanced Calculus: A Differential Forms Approach

Sample text

Where c = Yo < Y1 < Y2 < · · · points Pi;, one in each of the mn rectangles Rii = < Xm-1 < Xm = < Yn-1 < Yn = b d {(x, y): Xi-1 :::; X :::; Xi, Yi-1 :::; Y :::; Y;} · The approximating sum is then tThis sum is a number once A. R are given and all the choices a are made. It is helpful to imagine that a computer has been programmed to compute this number I:(a) whenever it is provided with the choices a. See Appendix 1. (1) [A(Pi;)][oriented area of Ri;] 2: i,j = m n 2: 2: A(Pi;)(Xi - Xi_t)(y; - Yi-1).

3 Flow from a source (spatial flow). Find the 2-form describing flow in space from a source at (0, 0, 0), again assuming that the flow is outward at all points with a magnitude depending only on r, and assuming that there are no sources between spheres about the origin. ] 4 Linear flows. A linear flow is described by a (variable) 0-form assigning numbers to oriented points. Find the 0-form describing flow from a source at 0 on the line. How would a 0-form be described in general? What is a constant 0-form?

2 Flow from a source (planar flow). Find the 1-form describing a planar flow from a source at (0, 0), assuming the flow is outward at all points (x, y) and has magnitude inversely proportional to the radius r = r(x, y) = V x2 + y2 (so that the flow is radially symmetric and the total flow Chapter 2 f Integrals 24 across a circle of radius r about the origin is independent of r; that is, so there is no source between two circles of different radius). The magnitude of a flow is measured by the rate of flow across a line perpendicular to the direction of flow.

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


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