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Advanced Calculus (Dover Books on Mathematics)

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Advanced Calculus (Dover Books on Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

"This book is a radical departure from all previous concepts of advanced calculus," declared the Bulletin of the American Mathematics Society, "and the nature of this departure merits serious study of the book by everyone interested in undergraduate education in mathematics." Classroom-tested in a Princeton University honors course, it offers students a unified introduction to advanced calculus.

Starting with an abstract treatment of vector spaces and linear transforms, the authors introduce a single basic derivative in an invariant form. All other derivatives — gradient, divergent, curl, and exterior — are obtained from it by specialization. The corresponding theory of integration is likewise unified, and the various multiple integral theorems of advanced calculus appear as special cases of a general Stokes formula. The text concludes by applying these concepts to analytic functions of complex variables.

Synopsis:

Starting with an abstract treatment of vector spaces and linear transforms, this introduction presents a corresponding theory of integration and concludes with applications to analytic functions of complex variables. 1959 edition.

Synopsis:

Classroom-tested in a Princeton University honors course, this text offers a unified introduction to advanced calculus. Starting with an abstract treatment of vector spaces and linear transforms, the authors present a corresponding theory of integration, concluding with a series of applications to analytic functions of complex variables. 1959 edition.

Table of Contents

I The Algebra of Vector Spaces
II Linear Transformations of Vector Spaces
III The Scalar Product
IV Vector Products in R3
V Endomorphisms
VI Vector-Valued Functions of a Scalar
VII Scalar-Valued Functions of a Vector
VIII Vector-Valued Functions of a Vector
IX Tensor Products and the standard Algebras
X Topology and Analysis
XI Differential Calculus of Forms
XII Integral Calculus of Forms
XIII Complex Structure
 

Product Details

ISBN:
9780486480909
Author:
Nickerson, H. K.
Publisher:
Dover Publications
Author:
Mathematics
Author:
Steenrod, N.E.
Author:
Spencer, D. C.
Author:
Nickerson, H.K
Subject:
Calculus
Subject:
Mathematics-Calculus
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
20110931
Binding:
TRADE PAPER
Language:
English
Pages:
560
Dimensions:
9.25 x 6.5 in 1.62 pd

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Advanced Calculus (Dover Books on Mathematics) New Trade Paper
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Product details 560 pages Dover Publications - English 9780486480909 Reviews:
"Synopsis" by ,
Starting with an abstract treatment of vector spaces and linear transforms, this introduction presents a corresponding theory of integration and concludes with applications to analytic functions of complex variables. 1959 edition.
"Synopsis" by ,
Classroom-tested in a Princeton University honors course, this text offers a unified introduction to advanced calculus. Starting with an abstract treatment of vector spaces and linear transforms, the authors present a corresponding theory of integration, concluding with a series of applications to analytic functions of complex variables. 1959 edition.
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