Showing posts with label differential equations. Show all posts
Showing posts with label differential equations. Show all posts

Dynamical Symmetry Review

Dynamical Symmetry
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Amazing read! Five stars! This book will assuredly stimulate new levels of thinking for the reader in various aspects of dynamical symmetry and it points to discoveries yet to be made in better understanding the some principals of physics therein. ...And makes important discoveries of its own in the process. Each reader should see if they can infer and verify for themselves the import of powerful new implications based upon Maxwell's original equations set forth towards the end of the book.Algebraic Theory of Molecules (Topics in Physical Chemistry Series)

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Whenever systems are governed by continuous chains of causes and effects, their behavior exhibits the consequences of dynamical symmetries, many of them far from obvious. Dynamical Symmetry introduces the reader to Sophus Lie's discoveries of the connections between differential equations and continuous groups that underlie this observation. It develops and applies the mathematical relations between dynamics and geometry that result. Systematic methods for uncovering dynamical symmetries are described, and put to use. Much material in the book is new and some has only recently appeared in research journals.
Though Lie groups play a key role in elementary particle physics, their connection with differential equations is more often exploited in applied mathematics and engineering. Dynamical Symmetry bridges this gap in a novel manner designed to help readers establish new connections in their own areas of interest. Emphasis is placed on applications to physics and chemistry. Applications to many of the other sciences illustrate both general principles and the ubiquitousness of dynamical symmetries.

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A First Course in Differential Equations (Undergraduate Texts in Mathematics) Review

A First Course in Differential Equations (Undergraduate Texts in Mathematics)
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Yeah, it's an ok book, but it's got a lot of typos and doesn't follow the curriculum of many Dif Equ classes. The first chapter is packed with tons of real applications and whatnot to distract you from actually getting to solve some Dif Equ's. By the time you get to chapter 4 it's pretty basic though, still doesn't cover everything in other classes (and covers some stuff not in other classes.

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This concise and up-to-date textbook is designed for the standard sophomore course in differential equations. It treats the basic ideas, models, and solution methods in a user friendly format that is accessible to engineers, scientists, economists, and mathematics majors. It emphasizes analytical, graphical, and numerical techniques, and it provides the tools needed by students to continue to the next level in applying the methods to more advanced problems. There is a strong connection to applications with motivations in mechanics and heat transfer, circuits, biology, economics, chemical reactors, and other areas. Moreover, the text contains a new, elementary chapter on systems of differential equations, both linear and nonlinear, that introduces key ideas without matrix analysis. Two subsequent chapters treat systems in a more formal way. Briefly, the topics include: First-order equations: separable, linear, autonomous, and bifurcation phenomena; Second-order linear homogeneous and non-homogeneous equations; Laplace transforms; and Linear and nonlinear systems, and phase plane properties.

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The Finite Element Method and Applications in Engineering Using ANSYS® Review

The Finite Element Method and Applications in Engineering Using ANSYS®
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This book is far superior to any other ANSYS FE book. It has something like 40 examples and the cd includes the batch input files. Other books on the subject (see Moaeveni) lack the # of example problems or batch file processing tutorials. Great for beginers and intermediate users who want to get the most out of ANSYS.

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This user-friendly book provides the reader with a theoretical and practical knowledge of the finite element method (FEM) and with the skills required to analyze engineering problems with ANSYS. A self-contained, introductory text, it minimizes the need for additional reference material, covering the fundamental topics in FEM as well as advanced topics concerning modeling and analysis with ANSYS. Extensive examples from various engineering disciplines are presented in a step-by-step fashion, focusing on the use of ANSYS through both the Graphics User Interface (GUI) and the ANSYS Parametric Design Language (APDL). It includes a CD-ROM with the "input" files for the example problems.

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Modeling and Simulation of Systems Using MATLAB and Simulink Review

Modeling and Simulation of Systems Using MATLAB and Simulink
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Firstly, the cd does not contain any MatLab code or Simulink sample models, it just contains very simple powerpoint presentations. I personally was not impressed by any of the information presented there. The text does discuss mathematical modelling using Matlab and some code is presented in the book. It assumes you know at least introductory Matlab, and the this is one of my beef's with the text; it is not an introductory Matlab text. In addition, the simulink component is just touched very briefly on towards the text's end. The book can be used to gain an appreciation of modelling, but additional references will have to be obtained to enhance one's competency in Matlab and Simulink.

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Not only do modeling and simulation help provide a better understanding of how real-world systems function, they also enable us to predict system behavior before a system is actually built and analyze systems accurately under varying operating conditions. Modeling and Simulation of Systems Using MATLAB and Simulink provides comprehensive, state-of-the-art coverage of all the important aspects of modeling and simulating both physical and conceptual systems. Various real-life examples show how simulation plays a key role in understanding real-world systems. The author also explains how to effectively use MATLAB and Simulink software to successfully apply the modeling and simulation techniques presented.After introducing the underlying philosophy of systems, the book offers step-by-step procedures for modeling different types of systems using modeling techniques, such as the graph-theoretic approach, interpretive structural modeling, and system dynamics modeling. It then explores how simulation evolved from pre-computer days into the current science of today. The text also presents modern soft computing techniques, including artificial neural networks, fuzzy systems, and genetic algorithms, for modeling and simulating complex and nonlinear systems. The final chapter addresses discrete systems modeling. Preparing both undergraduate and graduate students for advanced modeling and simulation courses, this text helps them carry out effective simulation studies. In addition, graduate students should be able to comprehend and conduct simulation research after completing this book.AncillariesAccompanying CD-ROM includes simulation code in MATLAB and Simulink, enabling quick and useful insight into real-world systems. A solutions manual is available for qualifying instructors.

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Foundations of Fluid Mechanics with Applications: Problem Solving Using Mathematica (Modeling and Simulation in Science, Engineering and Technology) Review

Foundations of Fluid Mechanics with Applications: Problem Solving Using Mathematica (Modeling and Simulation in Science, Engineering and Technology)
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This book presents the basic concepts of continuum mechanics. The material is presented in a tensor invariant form with a large number of problems with solutions. The book integrates the use of the computer algebra system Mathematica, and contains a large number of programs on the disk that will help clarify the concepts of continuum mechanics.(taken from the author)
Cheers

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This reference presents theory, methods and computations for fluid mechanics with Mathematica program examples.

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Differential Equations: A Modeling Approach Review

Differential Equations: A Modeling Approach
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While Ledder tries an innovative approach to teaching differential equations in his book, the attempt fails miserably. The book goes into detail explaining things at the conceptual level, but it leaves much of the technical math explanation to the reader in "instant exercises" and then does not actually cover examples that help solve the vast majority of the highly technical problems seen in the end of each chapter and on any exams you will take with your professor (the section on partial differential equations is most guilty of this). Furthermore, the material it does cover on its own is usually done in vague, unclear terms (with a couple notable exceptions involving linear systems). The modeling bits are somewhat interesting, but this book is not very useful in terms of learning to solve and manipulate the differential equations yourself. Unless you plan on learning all of the material in class, this book will have very little use for you.

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Introduction to Modeling for Biosciences Review

Introduction to Modeling for Biosciences
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This book is an ideal starting point for undergraduates, postgraduates and even researchers who want to learn the mathematical and computational techniques needed for the modelling of biological systems. The authors cover a wide range of techniques, from analytic approaches (deterministic equations, Markov Chains, master equation) to simulation based ones (agent based models and stochastic simulation algorithms). In particular, I found this book very useful in reviewing various stochastic algorithms needed to simulate biological systems (such as agent based models and Gillespie algorithms), but also in providing Java implementation for the algorithms. The authors' style is clear and this is very helpful for beginners.

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Mathematical modeling can be a useful tool for researchers in the biological scientists.Yet in biological modeling there is no one modeling technique that is suitable for all problems. Instead, different problems call for different approaches. Furthermore, it can be helpful to analyze the same system using a variety of approaches, to be able to exploit the advantages and drawbacks of each. In practice, it is often unclear which modeling approaches will be most suitable for a particular biological question, a problem which requires researchers to know a reasonable amount about a number of techniques, rather than become experts on a single one."Introduction to Modeling for Biosciences" addresses this issue by presenting a broad overview of the most important techniques used to model biological systems.In addition to providing an introduction into the use of a wide range of software tools and modeling environments, this helpful text/reference describes the constraints and difficulties that each modeling technique presents in practice, enabling the researcher to quickly determine which software package would be most useful for their particular problem.Topics and features: introduces a basic array of techniques to formulate models of biological systems, and to solve them; intersperses the text with exercises throughout the book; includes practical introductions to the Maxima computer algebra system, the PRISM model checker, and the Repast Simphony agent modeling environment; discusses agent-based models, stochastic modeling techniques, differential equations and Gillespie's stochastic simulation algorithm; contains appendices on Repast batch running, rules of differentiation and integration, Maxima and PRISM notation, and some additional mathematical concepts; supplies source code for many of the example models discussed, at the associated website http://www.cs.kent.ac.uk/imb/.This unique and practical guide leads the novice modeler through realistic and concrete modeling projects, highlighting and commenting on the process of abstracting the real system into a model.Students and active researchers in the biosciences will also benefit from the discussions of the high-quality, tried-and-tested modeling tools described in the book.Dr. David J. Barnes is a lecturer in computer science at the University of Kent, UK, with a strong background in the teaching of programming.Dr. Dominique Chu is a lecturer in computer science at the University of Kent, UK.He is an internationally recognized expert in agent-based modeling, and has also in-depth research experience in stochastic and differential equation based modeling.

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First Course in Differential Equations with Modeling Applications Review

First Course in Differential Equations with Modeling Applications
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I think before reading all other reviews of Zill's text, one must consider who did the 'panning'. Was it an instructor who used it to teach the class or a disgrunteled student who was unhappy about taking the class in the first place or unhappy with the grade received? This text is a little easier to read than most. It could be more thorough, but that would not be necessary for an undergraduate class. Professionally, I would prefer numerical methods come earlier, but I have no other criticism. I use it to teach DE and the good students all seem to like it while those who are failing would not like anything associated with the course. I don't necessarily cover the topics in the same order as the chapters are laid out, but the book is versatile enough that it doesn't cause any problems.

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This edition places emphasis on modelling and using technology in problem solving, and features applications. Step-by-step solutions are provided for every example, and this work aims to show students how the mathematical concepts have relevant, everyday applications.

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Differential Equations: Modeling with MATLAB Review

Differential Equations: Modeling with MATLAB
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If you're looking for a book to learn how to model differential equations with MATLAB, don't buy this book. No examples in MATLAB are given, only references to what commands in 'DELAB' (The author's MATLAB interface) can be used to solve problems. I purchased and returned this book.

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Utilizing MATLAB's computational and graphical tools right from the start, this analysis of differential equations helps users probe a variety of mathematical models, encouraging them to develop problem-solving skills and independent judgment as they derive mathematical models, select approaches to their analysis, and find answers to the original physical questions. Providing immediate graphic and numeric support, it demonstrates how physical problems motivate the central ideas and techniques of differential equations, showing how they model physical phenomena by examining ideas from four perspectives: geometric, analytic, numeric, and physical.Introduces qualitative analysis and numerical methods for scalar equations and systems early on, without sacrificing coverage of the most important traditional analytical methods. Fully integrates MATLAB into the text and exercises, and uses mathematical models of physical problems throughout to emphasize the interplay between the physical problem and the analytic, graphical, and numeric information available from the differential equation model. Seamlessly integrates over 1,400 exercises, open-ended chapter projects, and motivational 'Thought Questions'.For scientists and engineers.

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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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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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