By Harold M. Edwards

In a e-book written for mathematicians, academics of arithmetic, and hugely encouraged scholars, Harold Edwards has taken a daring and weird method of the presentation of complex calculus. He starts off with a lucid dialogue of differential kinds and speedy 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 strength readers, the writer has made the process paintings within the top culture of artistic 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 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 workouts to aid advisor the reader in checking 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 complex calculus classes. furthermore, it's excellent for a direction on vector research from the differential types element of view.

The expert mathematician will locate the following a pleasant instance of mathematical literature; the scholar lucky sufficient to have passed through this publication can have a company seize of the character of recent arithmetic and a fantastic framework to proceed to extra complex studies.

*The most vital 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 truly is enjoyable just to choose a random spot within the publication and start analyzing. this is often the way in which arithmetic may be provided, with an pleasure and liveliness that express why we're attracted to the subject.*

**—The American Mathematical per month (First assessment) **

*An inviting, strange, high-level creation to vector calculus, dependent solidly on differential types. brilliant exposition: casual yet refined, down-to-earth yet basic, geometrically rigorous, wonderful yet critical. outstanding varied purposes, actual and mathematical.*

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

**Read Online or Download Advanced Calculus: A Differential Forms Approach PDF**

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**Additional info for Advanced Calculus: A Differential Forms Approach**

**Sample text**

Y, z) dx B(x. y, z) dy C(x. y, z) dz. * If S is any oriented curve, then an approximation to the amount of work required for the displacement S is found as follows: Approximate S by an oriented polygonal curve consisting of short straight-line displacements. The approximate amount of work required for each of these is found from (2), and the amount required for S is approximately equal to the sum of these values. The number found in this way is called an approximating sum; there are two approximations involved in the process: first, the approximation of the curve S by a polygonal curve, and second, the approximation of the amount of work required for each segment of the polygonal curve by (2).

All orientations fall into two classes such that two orientations in the same class agree. * Chapter 1 J Constant Forms 18 With this definition of orientation the 3-form dx dy dz can be described as the function 'oriented volume' assigning to oriented solids in xyz-space the number which is the volume of the solid if its orientation is right-handed and which is minus the volume if its orientation is lefthanded. If the solid consists of several oriented pieces then the oriented volume of the whole is defined to be the sum of the oriented volumes of the pieces.

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.