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By Kai Velten
Content material:
Chapter 1 rules of Mathematical Modeling (pages 1–46):
Chapter 2 Phenomenological versions (pages 47–115):
Chapter three Mechanistic types I: ODEs (pages 117–228):
Chapter four Mechanistic types II: PDEs (pages 229–316):
Read or Download Mathematical Modeling and Simulation: Introduction for Scientists and Engineers PDF
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Extra info for Mathematical Modeling and Simulation: Introduction for Scientists and Engineers
Example text
2. At the white box end of the spectrum, mathematical models can be applied to design, test, and optimize systems and processes on the computer before they are actually physically realized. g. 3) or virtual prototyping [7, 24, 25]. 9 below. Based on the method described there, what-if studies can be performed, that is, it can be investigated what happens with the temperature distribution if you change certain characteristics of the device virtually on the computer, and this can then be used to optimize the construction of the device so as to achieve certain desired characteristics of the temperature distribution.
First of all, statistics itself is a collection of mathematical models that can be used to describe data or to draw inferences from data [19]. Beyond this, statistical methods provide a necessary link between nonstatistical mathematical models and 33 34 1 Principles of Mathematical Modeling the real world. In mathematical modeling, one is always concerned with experimental data, not only to validate model predictions, but also to develop hypotheses about the system, which help to set up appropriate equations.
6. e. on the ‘‘Q’’ of a mathematical model (S, Q, M)) whether a stationary (time-independent) or instationary (time-dependent) model is appropriate. 3. Lumped – distributed. 6. e. on the ‘‘Q’’ of a mathematical model (S, Q, M)) whether a lumped (space-independent) or distributed (space-dependent) model is appropriate. 2) is an example of a lumped model since it does not use spatial coordinates. 9 is based on a distributed model. Direct – inverse. 2a. 7 Classification of Mathematical Models solves a so-called direct problem [3].