The first chapter introduces the reader to the basic concepts of mathematical
modeling. It introduces important concepts such as a model and types of modeling
and gives an idea of the classification and basic properties of mathematical models.
Special attention is paid to identifying differences between continuous, discrete, and
hybrid models.
The second chapter is devoted to the description of the Wolfram SystemModeler
environment. The basics of working in the Model Center for creating your own
model with components from the Modelica standard library, principles for creating
your own components, and rules for performing a computational experiment in the
Simulation Center are given.
The third chapter gives a general idea of the fundamental principles underlying
any mathematical model, such as the laws of conservation in classical mechanics or
variational principles. On these principles, the so-called basic models can be built,
which later serve as the foundation on which more complex hierarchical models are
built.
In the fourth, fifth, and sixth chapters, the reader is invited to explore methods
for solving single component, multicomponent, and hybrid problems using two
alternative approaches: direct programming of mathematical models in Modelica
[7] and component modeling technologies using standard libraries [5]. In the last
three chapters, illustrative examples of constructing models of dynamic systems are
given with increasing degree of complexity.
The knowledge acquired through this textbook can be used by students for
independent assignments and virtual laboratory work.
In preparing the tutorial, materials from the site of the software development
company Wolfram Research Inc. [8] were used.
References
1. Matlab, Simuink: https://www.mathworks.com/
2. Maple: https://www.maplesoft.com/
3. Rand Model Designer: https://www.mvstudium.com/
4. ISMA: https://drive.google.com/open?id=1xV25DkoYK_Qnp4oKIOob2lNbn3rVM9K5
5. Wolfram SystemModeler: https://www.wolfram.com/system-modeler/
6. Mathematica: https://www.wolfram.com/mathematica/
7. Modelica: https://www.modelica.org/
8. Wolfram Research Inc.: https://www.wolfram.com/
xii
Introduction
modeling. It introduces important concepts such as a model and types of modeling
and gives an idea of the classification and basic properties of mathematical models.
Special attention is paid to identifying differences between continuous, discrete, and
hybrid models.
The second chapter is devoted to the description of the Wolfram SystemModeler
environment. The basics of working in the Model Center for creating your own
model with components from the Modelica standard library, principles for creating
your own components, and rules for performing a computational experiment in the
Simulation Center are given.
The third chapter gives a general idea of the fundamental principles underlying
any mathematical model, such as the laws of conservation in classical mechanics or
variational principles. On these principles, the so-called basic models can be built,
which later serve as the foundation on which more complex hierarchical models are
built.
In the fourth, fifth, and sixth chapters, the reader is invited to explore methods
for solving single component, multicomponent, and hybrid problems using two
alternative approaches: direct programming of mathematical models in Modelica
[7] and component modeling technologies using standard libraries [5]. In the last
three chapters, illustrative examples of constructing models of dynamic systems are
given with increasing degree of complexity.
The knowledge acquired through this textbook can be used by students for
independent assignments and virtual laboratory work.
In preparing the tutorial, materials from the site of the software development
company Wolfram Research Inc. [8] were used.
References
1. Matlab, Simuink: https://www.mathworks.com/
2. Maple: https://www.maplesoft.com/
3. Rand Model Designer: https://www.mvstudium.com/
4. ISMA: https://drive.google.com/open?id=1xV25DkoYK_Qnp4oKIOob2lNbn3rVM9K5
5. Wolfram SystemModeler: https://www.wolfram.com/system-modeler/
6. Mathematica: https://www.wolfram.com/mathematica/
7. Modelica: https://www.modelica.org/
8. Wolfram Research Inc.: https://www.wolfram.com/
xii
Introduction