Modern Mathematical Methods In Technology

Modern Mathematical Methods In Technology

1st Edition - January 1, 1975

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  • Author: S. Fenyo
  • eBook ISBN: 9780444601902

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Modern Mathematical Methods in Technology deals with applied mathematics and its finite methods. The book explains the linear algebra, optimization theory, and elements of the theory of graphs. This book explains the matrix theory and analysis, as well as the applications of matrix calculus. It discusses the linear mappings, basic matrix operations, hypermatrices, vector systems, and other algebraic concepts. In addition, it presents the sequences, series, continuity, differentiation, and integration of matrices, as well as the analytical matrix functions. The book discusses linear optimization, linear programming problems, and their solution. It also describes transportation problems and their solution by Hungarian method, as well as convex optimization and the Kuhn-Tucker theorem. The book discusses graphs including sub-, complete, and complementary graphs. It also presents the Boolean algebra and Ford-Fulkerson theorem. This book is invaluable to Math practitioners and non-practitioners.

Table of Contents

  • Editorial Note


    Chapter 1 Linear Algebra

    101. Matrix Theory

    101.01. Linear mappings

    101.02. Matrices

    101.03. Basic matrix operations

    101.04. Hypermatrices

    101.05. Linearly independent vectors

    101.06. Orthogonal and biorthogonal systems of vectors

    101.07. The inverse of a matrix

    101.08. The dyadic decomposition of matrices

    101.09. The rank of a vector system

    101.10. The rank of a matrix

    101.11. The minimal decomposition of a matrix

    101.12. A few theorems on products of matrices

    101.13. The dyadic decomposition of certain important matrices

    101.14. Eigenvalues and eigenvectors of matrices

    101.15. Symmetric and hermitian matrices

    101.16. Matrix polynomials

    101.17. The characteristic polynomial of a matrix. The Cayley-Hamilton theorem

    101.18. The minimum polynomial of a matrix

    101.19. The biorthogonal minimal decomposition of a square matrix

    102. Matrix Analysis

    102.01. Sequences, series, continuity, differentiation and integration of matrices

    102.02. Power series of matrices

    102.03. Analytical matrix functions

    102.04. Decomposition of rational matrices

    103. A Few Applications of Matrix Calculus

    103.01. The theory of systems of linear equations

    103.02. Linear integral equations

    103.03. Linear systems of differential equations

    103.04. The motion of a particle

    103.05. The stability of linear systems

    103.06. Bending of a supported beam

    103.07. Application of matrix techniques to linear electrical networks

    103.08. The application of matrices to the theory of four-pole devices

    Chapter 2 Optimization Theory

    201. Linear Optimization

    201.01. The problem

    201.02 Geometrical approaches

    201.03. Minimum vectors for a linear programming problem

    201.04. Solution of the linear programming problem

    201.05. Dual linear programming problems

    201.06. Transportation problems and their solution by the Hungarian method

    202. Convex Optimization

    202.01. The problem

    202.02. Definitions and lemmas

    202.03. The Kuhn-Tucker theorem

    202.04. Convex optimization with differentiable functions

    Chapter 3 Elements of the Theory of Graphs

    301.01. Introduction

    301.02. The idea of a graph

    301.03. Sub-graphs and complete graphs; complementary graphs

    301.04. Chains, paths and cycles

    301.05. Components and blocks of a graph

    301.06. Trees and spanning trees of a graph

    301.061. An application

    301.07. Fundamental systems of cycles and sheaves

    301.08. Graphs on surfaces

    301.09. Duality

    301.10. Boolean algebra

    301.101. Incidence matrices

    301.102. Cycle matrices

    301.103. Sheaf matrices

    301.104. Vectors spaces generated by graphs

    301.11. Directed graphs

    301.111. Matrices associated with directed graphs

    301.12. The application of graph theory to the theory of electric networks

    301.13. The Ford-Fulkerson theorem



Product details

  • No. of pages: 334
  • Language: English
  • Copyright: © North Holland 1975
  • Published: January 1, 1975
  • Imprint: North Holland
  • eBook ISBN: 9780444601902

About the Author

S. Fenyo

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