Differential Models: An Introduction with Mathcad

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Differential equations are often used in mathematical models for technological processes or devices. However, the design of a differential mathematical model is crucial and difficult in engineering.

As a hands-on approach to learn how to pose a differential mathematical model the authors have selected 9 examples with important practical application and treat them as following:
- Problem-setting and physical model formulation
- Designing the differential mathematical model
- Integration of the differential equations
- Visualization of results

Each step of the development of a differential model is enriched by respective Mathcad 11 commands, todays necessary linkage of engineering significance and high computing complexity.

To support readers of the book with respect to changes that might occur in future versions of Mathcad (Mathcad 12 for example), updates of examples, codes etc. can be downloaded from the following web page www.thermal.ru. Readers can work with Mathcad-sheets of the book without any Mathcad by help Mathcad Application Server Technology.

Author(s): Prof. Dr. Alexander Pavlovich Solodov, Ass. Prof. Dr.-Ing. Valery Fedorovich Ochkov (auth.)
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2005

Language: English
Pages: 232
Tags: Appl.Mathematics/Computational Methods of Engineering;Theoretical and Applied Mechanics;Mathematical Methods in Physics;Ordinary Differential Equations;Partial Differential Equations;Mechanics, Fluids, Thermodynamics

Differential Mathematical Models....Pages 1-35
Integrable Differential Equations....Pages 37-46
Dynamic Model of Systems with Heat Generation....Pages 47-60
Stiff Differential Equations....Pages 61-78
Heat Transfer near the Stagnation Point at Cross Tube Flow....Pages 79-94
The Falkner-Skan Equation of Boundary Layer....Pages 95-121
Rayleigh’s Equation: Hydrodynamical Instability....Pages 123-136
Kinematic Waves of Concentration in Ion-Exchange Filter....Pages 137-150
Kinematic Shock Waves....Pages 151-180
Numerical Modeling of the CPU-Board Temperature Field....Pages 181-201
Temperature Waves....Pages 203-218