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Mathematical Systems Theory

Mathematical Systems Theory




G.J. Olsder

Mathematical Systems Theory

A system is part of reality which we think to be a separated unit within this reality. The reality outside the system is called the surroundings. The interaction between system and surroundings is realized via quantities, which are called input and output. Quite often one wants, through a proper choice of the input, the system to behave in a desired way.

Mathematical Systems Theory is concerned with the study and control of input/output phenomena. The emphasis is on the dynamic behaviour of these phenomena, i.e. how do characteristic features change in time and what are the relationships.

These course notes are intended for use at the undergraduate level and form the basis for other courses such as optimal control and filter theory.

Contents: 1. Introduction - 2. Some Modelling Principles - 3. Linear Differential Systems - 4 System Properties - 5. State and Output Feedback - 6. Input/Output Representations - 7. Linear Difference Systems - 8. Extensions and Some Related Topics - 9. MATLAB Exercises - Bibliography - Index

In the International Journal of Robust Nonlinear Control (2006, 16, 87-88) Christian Commault wrote in his review of this book:

'In conclusion, this book may find a very useful place in the literature on linear system theory because of its qualities of presentation and writing, its concision and its good trade-off between rigour and accessibility. It can be considered as an appealing entrance in system theory which will encourage students, and also new researchers in the field, to pursue by the study of more complete books as, for example, those cited before.'

http://www.vssd.nl/hlf/a003.htm










Euro 25.00


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Mathematical systems theory

Mathematical systems theory




G.J. Olsder

A system is part of reality which we think to be a separated unit within this reality. The reality outside the system is called the surroundings. The interaction between system and surroundings is realized via quantities, which are called input and output. Quite often one wants, through a proper choice of the input, the system to behave in a certain way. Mathematical Systems Theory is concerned with the study and control of input/output phenomena. The emphasis is on the dynamic behaviour of these phenomena: how do characteristic features change in time and what are the relationships? These course notes are intended for use at the under­graduate level and form the basis for other courses such as optimal control and filter theory. Contents: 1. Introduction - 2. Some Modelling Principles - 3. Linear Differential Systems - 4 System Properties - 5. State and Output Feedback - 6. Input/Output Representations - 7. Linear Difference Systems - 8. Extensions and Some Related Topics - 9. MATLAB Exercises - Bibliography - Index In the International Journal of Robust Nonlinear Control (2006, 16, 87-88) Christian Commault wrote in his review of the 3rd edition of this book: 'In conclusion, this book may find a very useful place in the literature on linear system theory because of its qualities of presentation and writing, its concision and its good trade-off between rigour and accessibility. It can be considered as an appealing entrance in system theory which will encourage students, and also new researchers in the field, to pursue by the study of more complete books as, for example, those cited before.' URL http://www.vssd.nl/hlf/a003.htm








Euro 18.00


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Numerical Methods for Ordinary Differential Equations

Numerical Methods for Ordinary Differential Equations



A big advantage of numerical mathematics is that a numerical solution can be obtained for problems, where an analytical solution does not exist. An additional advantage is, that a numerical method only uses evaluation of standard functions and the operations: addition, subtraction, multiplication and division. Because these are just the operations a computer can perform, numerical mathematics and computers form a perfect combination. An analytical method gives the solution as a mathematical formula, which is an advantage. From this we can gain insight in the behavior and the properties of the solution, and with a numerical solution (that gives the function as a table) this is not the case. On the other hand some form of visualization may be used to gain insight in the behavior of the solution. To draw a graph of a function with a numerical method is usually a more useful tool than to evaluate the analytical solution at a great number of points. In this book we discuss several numerical methods for solving ordinary differential equations. We emphasize those aspects that play an important role in practical problems. In this introductory text we confine ourselves to ordinary differential equations with the exception of the last chapter in which we discuss the heat equation, a parabolic partial differential equation. The techniques discussed in the introductory chapters, for e.g. interpolation, numerical quadrature and the solution of nonlinear equations, may also be used outside the context of differential equations. They have been included to make the book self contained as far as the numerical aspects are concerned. Contents: Preface | 1. Introduction | 2. Interpolation | 3. Numerical differentiation | 4. Nonlinear equations | 5. Numerical quadrature | 6. Numerical time integration of initial value problems | 7. The finite difference method for boundary value problems | 8. The instationary equation | Literature | Index URL http://www.vssd.nl/hlf/a026.htm








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Numerical Methods in Scientific Computing

Numerical Methods in Scientific Computing




J. van Kan

Numerical Methods in Scientific Computing
This is a book about numerically solving partial differential equations occurring in technical and physical contexts and the authors have set themselves a more ambitious target than to just talk about the numerics. The aim is to show the place of numerical solutions in the general modeling process, which must inevitably lead to considerations about modeling itself. Partial differential equations usually are a consequence of applying first principles to a technical or physical problem at hand. That means, that most of the time the physics also have to be taken into account, especially for validation of the numerical solution obtained.
This book in other words is especially aimed at engineers and scientists who have 'real world' problems. It will concern itself less with pesky mathematical detail. For the interested reader though, we have included sections on mathematical theory to provide the necessary mathematical background.

Contents:
1 Modeling
2 A Crash Course in PDE's
3 Finite Difference Methods
4 Finite Volume Methods
5 Minimization Problems in Physics
6 The Numerical Solution of Minimization Problems
7 The Weak Formulation and Galerkin's Method
8 Extension of the FEM
9 Solution of large systems of equations
10 The heat- or diffusion equation
11 The wave equation
12 The transport equation
13 Moving boundary problems

http://www.vssd.nl/hlf/a002.htm









Euro 26.00


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