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The Nature of Mathematical Modeling
356 pages, 1998
This book first covers exact and approximate logical ways( ordinary discriminational and difference equations, partial discriminational equations, variational principles, stochastic processes); numerical styles( finite differences for ODEs and PDEs, finite rudiments, cellular automata); model conclusion grounded on compliances( function fitting, data transforms, network infrastructures, hunt ways, viscosity estimation); as well as the special part of the time in modeling( filtering and state estimation, hidden Markov processes, direct and nonlinear time series).
Each of the motifs in the book would be the good subject of a devoted textbook, but only by presenting the material in this way, it is possible to make so important material accessible to so numerous people.
Each chapter presents a terse summary of the core results in an area, furnishing exposure to what they can( and can not) do, enough background to use them to break typical problems, and pointers to pierce the literature for particular operations.
Neil Gershenfeld's book, The Nature of Mathematical Modeling, gives you a comprehensive understanding of mathematical modeling. It's not just about equations and numbers, but also about how these models can be used to solve real-world problems. You'll see how math can be applied in various fields, from physics to economics.
One key point Gershenfeld emphasizes is the importance of accuracy in mathematical modeling. He explains that even a small error can lead to significant consequences, especially in fields like engineering or finance. So, it's crucial to check and double-check your models.
Gershenfeld also explores the role of computers in mathematical modeling. He shows how computers can help us create more complex models and solve problems that would be impossible to tackle by hand. So, if you're interested in computer science, you'll find this book particularly useful.
The Nature of Mathematical Modeling isn't just about theory. Gershenfeld also discusses the practical application of these models. He provides numerous examples of how mathematical models have been used to solve real-world problems, which can inspire you to apply these techniques in your own work or studies.
Finally, Gershenfeld highlights the interdisciplinary nature of mathematical modeling. He shows how it can be used in various fields, from physics to economics. This means that no matter what your area of interest or expertise, you can benefit from understanding mathematical modeling.
