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  • © 1981

Applications of Functional Analysis in Engineering

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Part of the book series: Mathematical Concepts and Methods in Science and Engineering (MCSENG, volume 22)

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  • ISBN: 978-1-4684-3926-7
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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xv
  2. Physical Space. Abstract Spaces

    • J. L. Nowinski
    Pages 1-5
  3. Basic Vector Algebra

    • J. L. Nowinski
    Pages 7-15
  4. Inner Product of Vectors. Norm

    • J. L. Nowinski
    Pages 17-24
  5. Euclidean Spaces of Many Dimensions

    • J. L. Nowinski
    Pages 33-43
  6. Infinite-Dimensional Euclidean Spaces

    • J. L. Nowinski
    Pages 45-57
  7. Abstract Spaces. Hilbert Space

    • J. L. Nowinski
    Pages 59-75
  8. Function Space

    • J. L. Nowinski
    Pages 77-96
  9. Some Geometry of Function Space

    • J. L. Nowinski
    Pages 97-112
  10. Bounds and Inequalities

    • J. L. Nowinski
    Pages 123-166
  11. The Method of the Hypercircle

    • J. L. Nowinski
    Pages 167-203
  12. The Method of Orthogonal Projections

    • J. L. Nowinski
    Pages 205-221
  13. The Rayleigh-Ritz and Trefftz Methods

    • J. L. Nowinski
    Pages 223-240
  14. Function Space and Variational Methods

    • J. L. Nowinski
    Pages 241-260
  15. Distributions. Sobolev Spaces

    • J. L. Nowinski
    Pages 261-274
  16. Back Matter

    Pages 275-304

About this book

Functional analysis owes its OrIgms to the discovery of certain striking analogies between apparently distinct disciplines of mathematics such as analysis, algebra, and geometry. At the turn of the nineteenth century, a number of observations, made sporadically over the preceding years, began to inspire systematic investigations into the common features of these three disciplines, which have developed rather independently of each other for so long. It was found that many concepts of this triad-analysis, algebra, geometry-could be incorporated into a single, but considerably more abstract, new discipline which came to be called functional analysis. In this way, many aspects of analysis and algebra acquired unexpected and pro­ found geometric meaning, while geometric methods inspired new lines of approach in analysis and algebra. A first significant step toward the unification and generalization of algebra, analysis, and geometry was taken by Hilbert in 1906, who studied the collection, later called 1 , composed of infinite sequences x = Xb X 2, ... , 2 X , ... , of numbers satisfying the condition that the sum Ik"= 1 X 2 converges. k k The collection 12 became a prototype of the class of collections known today as Hilbert spaces.

Keywords

  • Finite
  • Hilbert space
  • algebra
  • class
  • collections
  • differential operator
  • distribution
  • function
  • functional
  • functional analysis
  • geometry
  • mathematics
  • mechanics

Authors and Affiliations

  • University of Delaware, Newark, USA

    J. L. Nowinski

Bibliographic Information

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • ISBN: 978-1-4684-3926-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 109.00
Price excludes VAT (USA)