In the Little Mathematics Library series we now come to *Systems of*

*Linear Inequalities* by *A. S. Solodovnikov*.

The book tells about the relation of systems of linear

inequalities to convex polyhedra, gives a description of the

set of all solutions of a system of linear inequalities,

analyses the questions of compatibility and

incompatibility; finally, it gives an insight into linear

programming as one of the topics in the theory of

systems of linear inequalities. The last section but one

gives a proof of duality theorem of lienar programming.

The book is intended for senior pupils and all amateur

mathematicians.

The book was translated the Russian by Vladimir Shokurov and was

first published by Mir in 1979.

PDF | Cover | Bookmarks | OCR | 7.3MB | 130 pp | 600 dpi

You can get the book here.

You can get the Magnet/Torrent links here.

Contents

1. Some Facts from Analytic Geometry 8

2. Visualization of Systems of Linear Inequalities In Two or Three Unknowns 17

3. The Convex Hull of a System of Points 22

4. A Convex Polyhedral Cone 25

5. The Feasible Region of a System of Linear Inequalities in Two Unknowns 31

6. The Feasible Region of a System in Three Unknowns 44

7. Systems of Linear Inequalities in Any Number of Unknowns 52

8. The Solution of a System of Linear Inequalities by successive Reduction of the Number of Unknowns 57

9. Incompatible Systems 64

10. A Homogeneous System of Linear Inequalities. The Fundamental Set of Solutions 69

11. The Solution of a Nonhomogeneous System of Inequalities 81

12. A Linear Programming Problem 84

13. The Simplex Method 91

14. The Duality Theorem in Linear Programming 101

15. Transportation Problem 107

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