系统理论的数学方法MATHEMATICAL METHODS FOR SYSTEM THEORY
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作者： L.Menini著
出 版 社： 东南大学出版社
出版时间： 1998-12-1字数：版次： 1页数： 553印刷时间： 1998/03/01开本：印次： 1纸张： 胶版纸I S B N ： 9789810233341包装： 精装内容简介
This book covers selected topics in geometry, algebra, calculus and probability theory. It contains the basic mathematical notions required by a first course in system theory for engineering and applied mathematics students. It is the first book to provide a self-contained and precise account of all the major mathematical methods and concepts relevant to the study of system theory.
目录
Preface
Notations
1 Discrete Probability Spaces
1.1 Basic Notions of Discrete Probability Spaces
1.2 Hints on Continuous Probability Spaces
1.3 Some Useful Results
1.4 Applications
1.4.1 Geometric Distribution
1.4.2 Exponential Distribution
1.4.3 Binomial Distribution
1.4.4 Erlang Distribution
1.5 Problems
Bibliography
2 Basics of Abstract Algebra
2.1 Basic Notions of Semigroups
2.2 Groups of Order 1, 2, 3 and 4
2.2.1 Groups of Order 1
2.2.2 Groups of Order 2
2.2.3 Groups of Order 3
2.2.4 Groups of Order 4
2.3 Basic Notions of Binary Relations
2.4 Equivalence Relations
2.4.1 Equivalence Relations on a Singleton
2.4.2 Equivalence Relations on a Set Having Two Elements
2.4.3 Equivalence Relations on a Set Having Three Elements
2.5 Partially Ordered Sets
2.5.1 Partially Ordered Sets Having Two Elements
2.5.2 Partially Ordered Sets Having Three Elements
2.6 Problems
Bibliography
3 Graphs and Algorithms
3.1 Basic Notions
3.2 Representations of Graphs and Some Results
3.3 Problems
Bibliography
4 Geometry of ]Rn
4.1 Geometric Applications in IRn
4.2 Convex Sets
4.3 Extreme Points and Supporting Hyperplanes
4.4 Problems
Bibliography
5 Linear Algebraic Equations
5.1 Basic Notations
5.2 Linear Dependence and Independence of Vectors
5.3 Linear Equations
5.4 Problems
Bibliography
6 Difference and Differential Equations
6.1 Basic Definitions and Results
6.2 Linear Time-Invariant Difference and Differential Equations
6.3 Orbits of Planar Systems
6.3.1 Linear Time-Invariant Systems
6.3.2 Non-Linear Time-Invariant Systems
6.3.3 The Method of Isoclines
6.4 Bifurcation Points
6.5 Solution of Linear Time-Invariant Equations using z and La-place Transforms
6.6 Affine Time-Invariant Difference and Differential Equations
7 The z-Transform
8 The Laplace Transform
9 Norms
A Solutions of Selected Exercises
B Answers to Problems
Subject Index
