Showing posts with label applied math. Show all posts
Showing posts with label applied math. Show all posts

Mathematical Modeling of Physical Systems: An Introduction (Engineering & Technology) Review

Mathematical Modeling of Physical Systems: An Introduction (Engineering and Technology)
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This book has a really nice, diversified selection of topics, and is quite readable. However, out of the three parts I looked at carefully, it is clear that one (the example on Global Positioning System) has a mathematical mistake (equations 3.13a,b,c), when solving a set of equations simultaneously in which all reference to y and z squared terms was lost on the right side of the equation. I think the book does well in explaining the big ideas, but one had better check all the details of the calculations before accepting them.

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Mathematical Modeling of Physical Systems provides a concise and lucid introduction to mathematical modeling for students and professionals approaching the topic for the first time. It is based on the premise that modeling is as much an art as it is a science--an art that can be mastered only by sustained practice. To provide that practice, the text contains approximately 100 worked examples and numerous practice problems drawn from civil and biomedical engineering, as well as from economics, physics, and chemistry. Problems range from classical examples, such as Euler's treatment of the buckling of the strut, to contemporary topics such as silicon chip manufacturing and the dynamics of the human immunodeficiency virus (HIV). The required mathematics are confined to simple treatments of vector algebra, matrix operations, and ordinary differential equations. Both analytical and numerical methods are explained in enough detail to function as learning tools for the beginner or as refreshers for the more informed reader. Ideal for third-year engineering, mathematics, physics, and chemistry students, Mathematical Modeling of Physical Systems will also be a welcome addition to the libraries of practicing professionals.

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Modeling Biological Systems:: Principles and Applications Review

Modeling Biological Systems:: Principles and Applications
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This book is a complete dissapointment.
It does not offer any real scientific physical models which then can be transformed in an algorithm and being simulated but is is merely a conglomerate of several statistical procedures commonly used in Biology for interpreting data (maybe copied by the author and collected from other books, as nothing that he presents is new!). This book does not offer any scientific, fundamental insight in how to really model and simulate properly complex biological systems, it is also written in a very unscientific, popular style. The mathematical level corresponds to High-School and as the author says in the preface: "The process of modeling biological systems is certainly not a science, but neither is it as unconstrained as the creation of a work of pure art that is evaluated solely on its esthetic content". I think that nonsense speaks for itself. This author should rather write novels instead of cobbling something together that gets the label "scientific" on the cover.
The book is not trash, the author does have collected some of the simplest "models" there are to describe collections of data in statistical terms, but this has NOTHING to do with proper scientific numerical and mathematical modeling and even less with scientific Computing in the field of biological complex systems, e.g. how to simulate membranes, proteins using Quantum Chemistry or Molecular dynamics techniques.
All in all I judge this book as a complete waste of money and as completely superfluous.

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This is the second edition of a textbook currently published by Springer for a course in mathematical modeling and computer simulation for biologists at the advanced undergraduate and introductory graduate level. The audience for this edition is similar to that of the previous one: advanced level courses in computational biology, as well as researchers retooling themselves. This new edition includes a CD-ROM with real examples of models as teaching tools.

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Differential Equations: A Modeling Perspective Review

Differential Equations: A Modeling Perspective
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A terrible book to learn DEs from. Just finished a course using it, they expect you to know how to solve problems with poor examples or any examples at all. This book expects you to figure everything out on your own. Also, it is useless to study from, as there are only 1 or 2 questions that actually have answers in the back of the book. It is simply cryptic, and one has to waste more time than is really neccesary to be able to figure it out. Buy another book.

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This effective and practical new edition continues to focus on differential equations as a powerful tool in constructing mathematical models for the physical world. It emphasizes modeling and visualization of solutions throughout. Each chapter introduces a model and then goes on to look at solutions of the differential equations involved using an integrated analytical, numerical, and qualitative approach. The authors present the material in a way that's clear and understandable to students at all levels. Throughout the text the authors convey their enthusiasm and excitement for the study of ODEs.

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Mathematical Modeling, Third Edition Review

Mathematical Modeling, Third Edition
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In this book you'll find, fully explained, subjects that are only mentioned briefly in other texts on modeling. I liked the chapter (chapter five) on Eigenvalue Methods for the analysis of dynamic models. I wished I had it four years ago when I was taking a course on modeling at the University of Washington. It really shows you how to do it. The same can be said about chapters 2 and 3 on optimization and chapters 7 and 8 on probability models (I liked specially the one on Markov Chains). I'm using it for teaching those techniques. The pseuodocode it includes is particularly helpful when you take the methods presented in the book to the computer. However, I would not recomend it to be used on its own as the only text in a course. It is a nice complement to texts like Gurney and Nisbet's Ecological Dynamics that presents many particular models in detail, while Meerschaert makes enphasis on general techniques. It's also a step up the ladder from "abc-of-modeling-techniques" texts like Vandermeer's Elementary Mathemathical Ecology. With 20/20 hindsight, if I had to learn modeling from the begining (or, if I had to teach it as I'm doing now) I would choose these titles as a step-by-step system, coupled with some Math packages like MathCad or Matlab.

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A First Course in Mathematical Modeling Review

A First Course in Mathematical Modeling
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From discrete to continuous modelling, with many proyects and examples, I like very spacially this book for the undergraduate level. The presentation is very clear, but rigurous, making experience the reader through the models. It focuses on the interpretation and ends with some tools for modelbuilding. For a start of mathematical model understanding of reality this book is specially good, clear and completely well written. Good job Mr. Giordano and Weir! See also: Mesterton-Gibbons:An aproach to Mathematical Modelling, Fowler: Mathematical Models in the Sciences, Beltrami: Mathematics for Dynamical Modeling, Morrison: The Art of Modeling Dynamical Systams and Giordano: Differential Equations a Modeling Aproach.

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Differential Equations Computing and Modeling (4th Edition) Review

Differential Equations Computing and Modeling (4th Edition)
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This book has several problems.
1. There are numerous typos in the text as well as in the solutions printed in the back of the book (and in the solutions manual). It can be very frustrating to puzzle over a problem for a long time only to find you were right and the book was wrong.
2. Several important techniques are only explained as short paragraphs in the exercise section (ie Euler Equation substitution, Reduction of Order, and others). You are left to try and figure out how to apply the vague instructions by looking at the solutions manual or asking someone else. I found this to be the biggest problem with the book.
3. The end of each example or concept is marked by a small red box in the margin of the page. These boxes are easy to miss so the distinction between example and theory, as well as between different aspects of the theory will become blurred unless you pay close attention to when the red boxes appear. Consequently results derived from theory and results derived from specific examples tend to blend together.
4. Often the authors add length to problems by providing the given values in non-SI units and the constants of nature in SI units. While this isn't a serious problem with the book, it would make the book needlessly annoying if you were using it for self study.
For the class that required this book I ended up checking out a different textbook on differential equations from the library to learn from. I only used this one for the questions we were assigned. If you have any choice in the matter I would recommend getting a different book.

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This practical book reflects the new technological emphasis that permeates differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB; it does not concentrate on traditional manual methods but rather on new computer-based methods that lead to a wider range of more realistic applications. The book starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the book. For mathematicians and those in the field of computer science and engineering.

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