Mathematics for the Life Sciences

Author: Glenn Ledder
Publisher: Springer Science & Business Media
ISBN: 1461472768
Format: PDF, ePub, Docs
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​​ ​​ 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 make full use of the remainder of the book, which includes two chapters on probability and its applications to inferential statistics and three chapters on discrete and continuous dynamical systems. The biological content of the book is self-contained and includes many basic biology topics such as the genetic code, Mendelian genetics, population dynamics, predator-prey relationships, epidemiology, and immunology. The large number of problem sets include some drill problems along with a large number of case studies. The latter are divided into step-by-step problems and sorted into the appropriate section, allowing readers to gradually develop complete investigations from understanding the biological assumptions to a complete analysis.

Introduction to Mathematical Biology

Author: Ching Shan Chou
Publisher: Springer
ISBN: 3319296388
Format: PDF, Docs
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This book is based on a one semester course that the authors have been teaching for several years, and includes two sets of case studies. The first includes chemostat models, predator-prey interaction, competition among species, the spread of infectious diseases, and oscillations arising from bifurcations. In developing these topics, readers will also be introduced to the basic theory of ordinary differential equations, and how to work with MATLAB without having any prior programming experience. The second set of case studies were adapted from recent and current research papers to the level of the students. Topics have been selected based on public health interest. This includes the risk of atherosclerosis associated with high cholesterol levels, cancer and immune interactions, cancer therapy, and tuberculosis. Readers will experience how mathematical models and their numerical simulations can provide explanations that guide biological and biomedical research. Considered to be the undergraduate companion to the more advanced book "Mathematical Modeling of Biological Processes" (A. Friedman, C.-Y. Kao, Springer – 2014), this book is geared towards undergraduate students with little background in mathematics and no biological background.

Mathematics for the Life Sciences

Author: Erin N. Bodine
Publisher:
ISBN: 9780691150727
Format: PDF, Kindle
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"This is the book I always wanted to write, a masterful and thorough introduction to the basic mathematical, statistical, and computational tools one needs to address biological problems, punctuated with solid and motivational applications to biology. The book is a seamless and authoritative treatment, with broad scope, that makes an ideal text for an introductory course."--Simon A. Levin, editor of "The Princeton Guide to Ecology" "This book presents mathematics as the Esperanto of science, which it truly is. The authors provide salient topics in understandable form, selecting examples that capture the interest of biologists. "Mathematics for the Life Sciences" is as useful as it is stimulating."--Rita Colwell, University of Maryland Institute for Advanced Computer Studies "This book does an admirable job of covering the mathematical topics that are essential for studying and analyzing biological systems. By bringing them together in a single coherent and well-written volume, the authors have produced a text that will truly serve undergraduate students in biology. The exercises are particularly well done."--Alan Hastings, University of California, Davis "This is a thorough, self-contained introductory textbook for training undergraduate students in basic mathematical and statistical methods that are important in biological sciences. Students are introduced to topics ranging from probability and statistics to matrix theory and calculus, with a brief introduction to modeling using difference and differential equations. Two unique features of this textbook are the inclusion of real-world biological data to motivate particular methods and the use of MATLAB for computational purposes."--Linda J. S. Allen, Texas Tech University "This spectacular book develops the reader's ability to quantitatively analyze problems arising in biology, and illustrates the great utility of mathematical models and computing to provide answers to key questions. The biological examples and student projects are excellent."--Carlos Castillo-Chavez, Arizona State University "This is a good introductory text for life sciences undergraduates who do not have a strong background in mathematics and need to familiarize themselves with core math concepts and their applications to biology. The problems and examples are well chosen, and the book is written in a style that is clear and makes it easy for students to use on their own."--Joceline Lega, University of Arizona There are no other books quite like this one on the market. Other texts on the subject do not have nearly the amount of statistics and probability that this one has, nor do they do as much to help build practical MATLAB skills. The abundance of data-driven examples, exercises, and student projects also sets this book apart from its competitors."Trachette L. Jackson, University of Michigan

Modeling Life

Author: Alan Garfinkel
Publisher: Springer
ISBN: 3319597310
Format: PDF, ePub, Mobi
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This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?

Mathematical Foundations of Neuroscience

Author: G. Bard Ermentrout
Publisher: Springer Science & Business Media
ISBN: 0387877088
Format: PDF, ePub, Mobi
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This book applies methods from nonlinear dynamics to problems in neuroscience. It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the mathematical and computational methods for analyzing them. The authors take a very broad approach and use many different methods to solve and understand complex models of neurons and circuits. They explain and combine numerical, analytical, dynamical systems and perturbation methods to produce a modern approach to the types of model equations that arise in neuroscience. There are extensive chapters on the role of noise, multiple time scales and spatial interactions in generating complex activity patterns found in experiments. The early chapters require little more than basic calculus and some elementary differential equations and can form the core of a computational neuroscience course. Later chapters can be used as a basis for a graduate class and as a source for current research in mathematical neuroscience. The book contains a large number of illustrations, chapter summaries and hundreds of exercises which are motivated by issues that arise in biology, and involve both computation and analysis. Bard Ermentrout is Professor of Computational Biology and Professor of Mathematics at the University of Pittsburgh. David Terman is Professor of Mathematics at the Ohio State University.

Mathematical Modeling

Author: Stefan Heinz
Publisher: Springer Science & Business Media
ISBN: 9783642203114
Format: PDF, Docs
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The whole picture of Mathematical Modeling is systematically and thoroughly explained in this text for undergraduate and graduate students of mathematics, engineering, economics, finance, biology, chemistry, and physics. This textbook gives an overview of the spectrum of modeling techniques, deterministic and stochastic methods, and first-principle and empirical solutions. Complete range: The text continuously covers the complete range of basic modeling techniques: it provides a consistent transition from simple algebraic analysis methods to simulation methods used for research. Such an overview of the spectrum of modeling techniques is very helpful for the understanding of how a research problem considered can be appropriately addressed. Complete methods: Real-world processes always involve uncertainty, and the consideration of randomness is often relevant. Many students know deterministic methods, but they do hardly have access to stochastic methods, which are described in advanced textbooks on probability theory. The book develops consistently both deterministic and stochastic methods. In particular, it shows how deterministic methods are generalized by stochastic methods. Complete solutions: A variety of empirical approximations is often available for the modeling of processes. The question of which assumption is valid under certain conditions is clearly relevant. The book provides a bridge between empirical modeling and first-principle methods: it explains how the principles of modeling can be used to explain the validity of empirical assumptions. The basic features of micro-scale and macro-scale modeling are discussed – which is an important problem of current research.

Dynamic Modeling of Environmental Systems

Author: Michael Deaton
Publisher: Springer Science & Business Media
ISBN: 1461213002
Format: PDF, Docs
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A primer on modeling concepts and applications that is specifically geared toward the environmental field. Sections on modeling terminology, the uses of models, the model-building process, and the interpretation of output provide the foundation for detailed applications. After an introduction to the basics of dynamic modeling, the book leads students through an analysis of several environmental problems, including surface-water pollution, matter-cycling disruptions, and global warming. The scientific and technical context is provided for each problem, and the methods for analyzing and designing appropriate modeling approaches is provided. While the mathematical content does not exceed the level of a first-semester calculus course, the book gives students all of the background, examples, and practice exercises needed both to use and understand environmental modeling. It is suitable for upper-level undergraduate and beginning-graduate level environmental professionals seeking an introduction to modeling in their field.

Mathematics and Technology

Author: Christiane Rousseau
Publisher: Springer Science & Business Media
ISBN: 0387692169
Format: PDF, Kindle
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This book introduces the student to numerous modern applications of mathematics in technology. The authors write with clarity and present the mathematics in a clear and straightforward way making it an interesting and easy book to read. Numerous exercises at the end of every section provide practice and reinforce the material in the chapter. An engaging quality of this book is that the authors also present the mathematical material in a historical context and not just the practical one. Mathematics and Technology is intended for undergraduate students in mathematics, instructors and high school teachers. Additionally, its lack of calculus centricity as well as a clear indication of the more difficult topics and relatively advanced references make it suitable for any curious individual with a decent command of high school math.

Modeling and Simulation

Author: Hans-Joachim Bungartz
Publisher: Springer Science & Business Media
ISBN: 3642395244
Format: PDF, ePub, Docs
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Die Autoren führen auf anschauliche und systematische Weise in die mathematische und informatische Modellierung sowie in die Simulation als universelle Methodik ein. Es geht um Klassen von Modellen und um die Vielfalt an Beschreibungsarten. Aber es geht immer auch darum, wie aus Modellen konkrete Simulationsergebnisse gewonnen werden können. Nach einem kompakten Repetitorium zum benötigten mathematischen Apparat wird das Konzept anhand von Szenarien u. a. aus den Bereichen „Spielen – entscheiden – planen" und „Physik im Rechner" umgesetzt.

Modeling the Dynamics of Life Calculus and Probability for Life Scientists

Author: Frederick R. Adler
Publisher: Cengage Learning
ISBN: 0840064187
Format: PDF, ePub
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Designed to help life sciences students understand the role mathematics has played in breakthroughs in epidemiology, genetics, statistics, physiology, and other biological areas, MODELING THE DYNAMCICS OF LIFE: CALCULUS AND PROBABILTY FOR LIFE SCIENTISTS, Third Edition, provides students with a thorough grounding in mathematics, the language, and ’the technology of thought’ with which these developments are created and controlled. The text teaches the skills of describing a system, translating appropriate aspects into equations, and interpreting the results in terms of the original problem. The text helps unify biology by identifying dynamical principles that underlie a great diversity of biological processes. Standard topics from calculus courses are covered, with particular emphasis on those areas connected with modeling such as discrete-time dynamical systems, differential equations, and probability and statistics. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.