Ebook: Applied Mathematical Modelling of Engineering Problems
- Tags: Mathematical Modeling and Industrial Mathematics, Calculus of Variations and Optimal Control, Optimization, Systems Theory Control
- Series: Applied Optimization 81
- Year: 2003
- Publisher: Springer US
- Edition: 1
- Language: English
- pdf
The subject of the book is the "know-how" of applied mathematical modelling: how to construct specific models and adjust them to a new engineering environment or more precise realistic assumptions; how to analyze models for the purpose of investigating real life phenomena; and how the models can extend our knowledge about a specific engineering process.
Two major sources of the book are the stock of classic models and the authors' wide experience in the field. The book provides a theoretical background to guide the development of practical models and their investigation. It considers general modelling techniques, explains basic underlying physical laws and shows how to transform them into a set of mathematical equations. The emphasis is placed on common features of the modelling process in various applications as well as on complications and generalizations of models.
The book covers a variety of applications: mechanical, acoustical, physical and electrical, water transportation and contamination processes; bioengineering and population control; production systems and technical equipment renovation. Mathematical tools include partial and ordinary differential equations, difference and integral equations, the calculus of variations, optimal control, bifurcation methods, and related subjects.
Content:
Front Matter....Pages i-xxi
Some Basic Models Of Physical Systems....Pages 1-28
Models Of Continuum Mechanical Systems....Pages 29-84
Variational Models and Structural Stability....Pages 85-104
Integral Models Of Physical Systems....Pages 105-138
Modelling in Bioengineering....Pages 139-182
Modelling Of Technological Renovation In Production Systems....Pages 183-240
Appendix....Pages 241-259
Back Matter....Pages 261-286
Content:
Front Matter....Pages i-xxi
Some Basic Models Of Physical Systems....Pages 1-28
Models Of Continuum Mechanical Systems....Pages 29-84
Variational Models and Structural Stability....Pages 85-104
Integral Models Of Physical Systems....Pages 105-138
Modelling in Bioengineering....Pages 139-182
Modelling Of Technological Renovation In Production Systems....Pages 183-240
Appendix....Pages 241-259
Back Matter....Pages 261-286
....