The Nature of Mathematical Modeling

从NASA的人那里看system engineering，感觉像是在讨论数学建模的问题，于是找了本数学建模的本质——CAE的方法论也在数学建模那里！

《The Nature of Mathematical Modeling》

解析解，数值解，有限单元，偏微分方程等等。这都是CAE的概念！

This is a book about the nature of mathematical modeling and about the kinds of techniques that are useful for modeling (both natural and otherwise). It is oriented towards simple, efficient implementations on computers. 大家的目的算是一致了！

The text has three parts. 解析解的问题The first covers exact and approximate analytical techniques (ordinary differential and difference equations, partial differential equations, variational principles, stochastic processes); 数值分析的问题the second, numerical methods (finite differences for ODEs and PDEs, finite elements, cellular automata); and the third, 实验解的问题model inference based on observations (function fitting, data transforms, network architectures, search techniques, density estimation, filtering and state estimation, linear and nonlinear time series).

这个分类本质上跟altair的那本the practice of

Each of these essential topics would be the worthy subject of a dedicated text, but such a narrow treatment obscures the connections among old and new approaches to modeling. By covering so much material so compactly, this book helps bring it to a much broader audience. Each chapter presents a concise summary of the core results in an area, providing an accessible introduction to what they can (and cannot) do, enough background to use them to solve typical problems, and then pointers into the specialized research literature. The text is complemented by a Website and extensive worked problems that introduce extensions and applications. This essential book will be of great value to anyone seeking to develop quantitative and qualitative descriptions of complex phenomena, from physics to finance.

Professor Neil Gershenfeld leads the Physics and Media Group at the MIT Media Lab and codirects the Things That Think research consortium. His laboratory investigates the relationship between the content of information and its physical representation, from building molecular quantum computers to building musical instruments for collaborations ranging from Yo-Yo Ma to Penn & Teller. He has a BA in Physics from Swarthmore College, was a technician at Bell Labs, received a PhD in Applied Physics from Cornell University, and he was a Junior Fellow of the Harvard Society of Fellows.