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Titlebook: Mathematics for the Life Sciences; Calculus, Modeling, Glenn Ledder Textbook 20131st edition Springer Science+Business Media, LLC 2013 cal

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发表于 2025-3-21 18:52:13 | 显示全部楼层 |阅读模式
书目名称Mathematics for the Life Sciences
副标题Calculus, Modeling,
编辑Glenn Ledder
视频video
概述Many examples and exercises.Emphasis on mathematical modeling and dynamical systems approach.Most topics presented in a biological context rather than a math context.Includes supplementary material: .
丛书名称Springer Undergraduate Texts in Mathematics and Technology
图书封面Titlebook: Mathematics for the Life Sciences; Calculus, Modeling,  Glenn Ledder Textbook 20131st edition Springer Science+Business Media, LLC 2013 cal
描述​ ​​ .Mathematics for the Life Sciences  provides  present and future biologists with the mathematical concepts and tools needed to understand and use mathematical models and read advanced mathematical biology books.  It presents mathematics in biological contexts, focusing on the central mathematical ideas, and providing detailed explanations.  The author assumes no mathematics background beyond algebra and precalculus.  Calculus is presented as a one-chapter primer that is suitable for readers who have not studied the subject before, as well as readers who have taken a calculus course and need a review.  This primer is followed by a novel chapter on mathematical modeling that begins with discussions of biological data and the basic principles of modeling.  The remainder of the chapter introduces the reader to topics in mechanistic modeling (deriving models from biological assumptions) and empirical modeling (using data to parameterize and select models).  The modeling chapter contains a thorough treatment of key ideas and techniques that are often neglected in mathematics books.  It also provides the reader with a sophisticated viewpoint and the essential background needed to mak
出版日期Textbook 20131st edition
关键词calculus; dynamical systems; mathematical biology textbook; mathematical modeling
版次1
doihttps://doi.org/10.1007/978-1-4614-7276-6
isbn_softcover978-1-4939-4452-1
isbn_ebook978-1-4614-7276-6Series ISSN 1867-5506 Series E-ISSN 1867-5514
issn_series 1867-5506
copyrightSpringer Science+Business Media, LLC 2013
The information of publication is updating

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发表于 2025-3-21 22:45:06 | 显示全部楼层
Mathematical Modelingture that is seldom taught in mathematics courses. Models can be derived from mechanistic principles or based on empirical data; there are some commonalities between these types of modeling as well as important differences. The first two sections present the concepts of mathematical modeling. Three
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Working with Probability. Chapter 4 follows with seven sections that are grouped into three themes. The first four sections treat inferential statistics, beginning with an introductory section that introduces the central question of whether a test population is the same as or different from a general population. This is fo
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Dynamics of Single Populationsvia simple examples and simulations, and two additional sections present the principal graphical methods: cobweb analysis for discrete equations and phase line analysis for continuous equations. The final section uses the graphical methods as motivation for the development of the linearized stabilit
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Discrete Dynamical Systemscomputer simulations. The simulations lead to the discovery of an asymptotic growth rate and stage structure, which we can determine by ad hoc methods for systems of only two or three components. The second section presents the matrix algebra that is needed as background for a more mathematical stud
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Continuous Dynamical Systems the mathematics of continuous dynamical systems. Only autonomous systems are considered. After two sections that introduce a lead poisoning model and Michaelis–Menten kinetics as examples and study them with a combination of nondimensionalization and asymptotic ideas, the heart of the chapter consi
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ution, the form of the reaction rate, which is discontinuous as a function of the dependent variable, precludes bifurcation of non-trivial steady solutions from the branch of trivial solutions. A constructive approach to the existence theory for non-trivial global solution branches is developed. The
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Glenn Ledder math­ ematical questions posed by such equations and the important role they play in many areas of science and technology. Examples of current inter­ est are biological and chemical pattern formation, semiconductor design, environmental problems such as solute transport in groundwater flow, phase t
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