Principles of Mathematics in Operations Research (Free PDF)

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The aim of this book is to provide an overview of mathematical concepts and their relationships not only for graduate students in the fields of Operations Research, Management Science and Industrial Engineering but also for practitioners and academicians who seek to refresh their mathematical skills.

The contents, which could broadly be divided into two as linear algebra and real analysis, may also be more specifically categorized as linear algebra, convex analysis, linear programming, real and functional analysis. The book has been designed to include fourteen chapters so that it might assist a 14- week graduate course, one chapter to be covered each week.

The introductory chapter aims to introduce or review the relationship between Operations Research and mathematics, to offer a view of mathematics as a language and to expose the reader to the art of proof-making. The chapters in Part 1, linear algebra, aim to provide input on preliminary linear algebra, orthogonality, eigen values and vectors, positive definiteness, condition numbers, convex sets and functions, linear programming and duality theory. The chapters in Part 2, real analysis, aim to raise awareness of number systems, basic topology, continuity, differentiation, power series and special functions, and Laplace and z-transforms.

1. Introduction
2. Preliminary Linear Algebra
3. Orthogonality
4. Eigen Values and Vectors
5. Positive Definiteness
6. Computational Aspects
7. Convex Sets
8. Linear Programming
9. Number Systems
10. Basic Topology
11. Continuity
12. Differentiation
13. Power Series and Special Functions
14. Special Transformations

Author Details
"Levent Kandiller"

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