Master your Minecraft
 
 

Special Offers see all

Enter to WIN a $100 Credit

Subscribe to PowellsBooks.news
for a chance to win.
Privacy Policy

Tour our stores


    Recently Viewed clear list


    Best Books of the Year | December 10, 2014

    Mary Jo Schimelpfenig: IMG Best Fantasy/Sci-Fi of 2014



    Here are the books that knocked my socks off in 2014. All of them would make great gifts; each of them was truly something that evoked that... Continue »

    spacer

Applied Algebra and Functional Analysis

by

Applied Algebra and Functional Analysis Cover

 

Synopses & Reviews

Publisher Comments:

"A valuable reference." — American Scientist. Excellent graduate-level treatment of set theory, algebra and analysis for applications in engineering and science. Fundamentals, algebraic structures, vector spaces and linear transformations, metric spaces, normed spaces and inner product spaces, linear operators, more. A generous number of exercises have been integrated into the text. 1981 edition.

Book News Annotation:

Reprint of the work originally published by Prentice-Hall in 1981.
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Synopsis:

Graduate-level treatment of set theory, algebra and analysis for applications in engineering and science. Vector spaces and linear transformations, metric spaces, normed spaces and inner product spaces, more. Exercises. 1981 edition.


Table of Contents

PREFACE

CHAPTER 1: FUNDAMENTAL CONCEPTS

  1.1 Sets

  1.2 Functions

  1.3 Relations and Equivalence Relations

  1.4 Operations on Sets

  1.5 Mathematical Systems Considered in This Book

  1.6 References and Notes

    References

CHAPTER 2: ALGEBRAIC STRUCTURES

  2.1 Some Basic Structures of Algebra

    A. Semigroups and Groups

    B. Rings and Fields

    C. "Modules, Vector Spaces, and Algebras"

    D. Overview

  2.2 Homomorphisms

  2.3 Application to Polynomials

  2.4 References and Notes

    References

CHAPTER 3: VECTOR SPACES AND LINEAR TRANSFORMATIONS

  3.1 Linear Spaces

  3.2 Linear Subspaces and Direct Sums

  3.3 "Linear Independence, Bases, and Dimension"

  3.4 Linear Transformations

  3.5 Linear Functionals

  3.6 Bilinear Functionals

  3.7 Projections

  3.8 Notes and References

    References

CHAPTER 4: FINITE-DIMENSIONAL VECTOR SPACES AND MATRICES

  4.1 Coordinate Representation of Vectors

  4.2 Matrices

    A. Representation of Linear Transformations by Matrices

    B. Rank of a Matrix

    C. Properties of Matrices

  4.3 Equivalence and Similarity

  4.4 Determinants of Matrices

  4.5 Eigenvalues and Eigenvectors

  4.6 Some Canonical Forms of Matrices

  4.7 "Minimal Polynomials, Nilpotent Operators and the Jordan Canonical Form"

    A. Minimal Polynomials

    B. Nilpotent Operators

    C. The Jordan Canonical Form

  4.8 Bilinear Functionals and Congruence

  4.9 Euclidean Vector Spaces

    A. Euclidean Spaces : Definition and Properties

    B. Orthogonal Bases

  4.10 Linear Transformations on Euclidean Vector Spaces

    A. Orthogonal Transformations

    B. Adjoint Transformations

    C. Self-Adjoint Transformations

    D. Some Examples

    E. Further Properties of Orthogonal Transformations

  4.11 Applications to Ordinary Differential Equations

    A. Initial-Value Problem : Definition

    B. Initial-Value Problem : Linear Systems

  4.12 Notes and References

    References

CHAPTER 5: METRIC SPACES

  5.1 Definition of Metric Spaces

  5.2 Some Inequalities

  5.3 Examples of Important Metric Spaces

  5.4 Open and Closed Sets

  5.5 Complete Metric Spaces

  5.6 Compactness

  5.7 Continuous Functions

  5.8 Some Important Results in Applications

  5.9 Equivalent and Homeomorphic Metric Spaces. Topological Spaces

  5.10 Applications

    A. Applications of the Contraction Mapping Principle

    B. Further Applications to Ordinary Differential Equations

  5.11 References and Notes

    References

CHAPTER 6: NORMED SPACES AND INNER PRODUCT SPACES

  6.1 Normed Linear Spaces

  6.2 Linear Subspaces

  6.3 Infinite Series

  6.4 Convex Sets

  6.5 Linear Functionals

  6.6 Finte-Dimensional Spaces

  6.7 Geometric Aspects of Linear Functionals

  6.8 Extension of Linear Functionals

  6.9 Dual Space and Second Dual Space

  6.10 Weak Convergence

  6.11 Inner Product Spaces

  6.12 Orthogonal Complements

  6.13 Fourier Series

  6.14 The Riesz Representation Theorem

  6.15 Some Applications

    A. Approximation of Elements in Hilbert Space (Normal Equations)

    B. Random Variables

    C. Estimation of Random Variables

  6.16 Notes and References

    References

CHAPTER 7: LINEAR OPERATORS

  7.1 Bounded Linear Transformations

  7.2 Inverses

  7.3 Conjugate and Adjoint Operators

  7.4 Hermitian Operators

  7.5 "Other Linear Operators: Normal Operators, Projections, Unitary Operators, and Isometric Operators"

  7.6 The Spectrum of an Operator

  7.7 Completely Continuous Operators

  7.8 The Spectral Theorem for Completely Continuous Normal Operators

  7.9 Differentiation of Operators

  7.10 Some Applications

    A. Applications to Integral Equations

    B. An Example from Optimal Control

    C. Minimization of Functionals: Method of Steepest Descent

  7.11 References and Notes

    References

    Index

Product Details

ISBN:
9780486675985
Author:
Michel, Anthony M.
Author:
Herget, Charles J.
Author:
Michel, Anthony M.
Author:
Michel, Anthony N.
Author:
Mathematics
Publisher:
Dover Publications
Location:
New York :
Subject:
Mathematics
Subject:
Mathematical Analysis
Subject:
Algebra
Subject:
Algebra - General
Subject:
General Mathematics
Subject:
Applied Algebra
Subject:
Functional Analysis
Subject:
Algebraic structures
Subject:
Mathematics - Algebra
Subject:
Appli
Subject:
ed Algebra
Subject:
Set Theory
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
92-596
Publication Date:
20111131
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
512
Dimensions:
8.5 x 5.38 in 1.14 lb

Other books you might like

  1. Language, Logic and Experience: The... New Trade Paper $17.95
  2. The Works of Mencius Used Trade Paper $8.95
  3. The Republic Used Trade Paper $3.95
  4. Challenging Problems in Geometry Used Trade Paper $8.50
  5. Tensors, Differential Forms, and... Used Trade Paper $9.50
  6. Challenging Mathematical Problems... New Trade Paper $14.95

Related Subjects

Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General

Applied Algebra and Functional Analysis Used Trade Paper
0 stars - 0 reviews
$6.50 In Stock
Product details 512 pages Dover Publications - English 9780486675985 Reviews:
"Synopsis" by , Graduate-level treatment of set theory, algebra and analysis for applications in engineering and science. Vector spaces and linear transformations, metric spaces, normed spaces and inner product spaces, more. Exercises. 1981 edition.


spacer
spacer
  • back to top

FOLLOW US ON...

     
Powell's City of Books is an independent bookstore in Portland, Oregon, that fills a whole city block with more than a million new, used, and out of print books. Shop those shelves — plus literally millions more books, DVDs, and gifts — here at Powells.com.