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Exploring Mathematical Modeling In Biology Through Case Studies And Experimental Activities
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Book Synopsis Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities by : Rebecca Sanft
Download or read book Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities written by Rebecca Sanft and published by Academic Press. This book was released on 2020-03-30 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring Mathematical Modeling in Biology through Case Studies and Experimental Activities provides supporting materials for courses taken by students majoring in mathematics, computer science or in the life sciences. The book's cases and lab exercises focus on hypothesis testing and model development in the context of real data. The supporting mathematical, coding and biological background permit readers to explore a problem, understand assumptions, and the meaning of their results. The experiential components provide hands-on learning both in the lab and on the computer. As a beginning text in modeling, readers will learn to value the approach and apply competencies in other settings. Included case studies focus on building a model to solve a particular biological problem from concept and translation into a mathematical form, to validating the parameters, testing the quality of the model and finally interpreting the outcome in biological terms. The book also shows how particular mathematical approaches are adapted to a variety of problems at multiple biological scales. Finally, the labs bring the biological problems and the practical issues of collecting data to actually test the model and/or adapting the mathematics to the data that can be collected. Presents a single volume on mathematics and biological examples, with data and wet lab experiences suitable for non-experts Contains three real-world biological case studies and one wet lab for application of the mathematical models Includes R code templates throughout the text, which are also available through an online repository, along with the necessary data files to complete all projects and labs
Book Synopsis Mathematical and Experimental Modeling of Physical and Biological Processes by : H.T. Banks
Download or read book Mathematical and Experimental Modeling of Physical and Biological Processes written by H.T. Banks and published by CRC Press. This book was released on 2009-01-12 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through several case study problems from industrial and scientific research laboratory applications, Mathematical and Experimental Modeling of Physical and Biological Processes provides students with a fundamental understanding of how mathematics is applied to problems in science and engineering. For each case study problem, the authors discuss why a model is needed and what goals can be achieved with the model. Exploring what mathematics can reveal about applications, the book focuses on the design of appropriate experiments to validate the development of mathematical models. It guides students through the modeling process, from empirical observations and formalization of properties to model analysis and interpretation of results. The authors also describe the hardware and software tools used to design the experiments so faculty/students can duplicate them. Integrating real-world applications into the traditional mathematics curriculum, this textbook deals with the formulation and analysis of mathematical models in science and engineering. It gives students an appreciation of the use of mathematics and encourages them to further study the applied topics. Real experimental data for projects can be downloaded from CRC Press Online.
Book Synopsis Introduction to Mathematical Biology by : Ching Shan Chou
Download or read book Introduction to Mathematical Biology written by Ching Shan Chou and published by Springer. This book was released on 2016-04-27 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Models for Society and Biology by : Edward Beltrami
Download or read book Mathematical Models for Society and Biology written by Edward Beltrami and published by Academic Press. This book was released on 2013-06-19 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Models for Society and Biology, 2e, is a useful resource for researchers, graduate students, and post-docs in the applied mathematics and life science fields. Mathematical modeling is one of the major subfields of mathematical biology. A mathematical model may be used to help explain a system, to study the effects of different components, and to make predictions about behavior. Mathematical Models for Society and Biology, 2e, draws on current issues to engagingly relate how to use mathematics to gain insight into problems in biology and contemporary society. For this new edition, author Edward Beltrami uses mathematical models that are simple, transparent, and verifiable. Also new to this edition is an introduction to mathematical notions that every quantitative scientist in the biological and social sciences should know. Additionally, each chapter now includes a detailed discussion on how to formulate a reasonable model to gain insight into the specific question that has been introduced. Offers 40% more content – 5 new chapters in addition to revisions to existing chapters Accessible for quick self study as well as a resource for courses in molecular biology, biochemistry, embryology and cell biology, medicine, ecology and evolution, bio-mathematics, and applied math in general Features expanded appendices with an extensive list of references, solutions to selected exercises in the book, and further discussion of various mathematical methods introduced in the book
Book Synopsis Control Theory in Biomedical Engineering by : Olfa Boubaker
Download or read book Control Theory in Biomedical Engineering written by Olfa Boubaker and published by Academic Press. This book was released on 2020-06-30 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control Theory in Biomedical Engineering: Applications in Physiology and Medical Robotics highlights the importance of control theory and feedback control in our lives and explains how this theory is central to future medical developments. Control theory is fundamental for understanding feedback paths in physiological systems (endocrine system, immune system, neurological system) and a concept for building artificial organs. The book is suitable for graduate students and researchers in the control engineering and biomedical engineering fields, and medical students and practitioners seeking to enhance their understanding of physiological processes, medical robotics (legs, hands, knees), and controlling artificial devices (pacemakers, insulin injection devices). Control theory profoundly impacts the everyday lives of a large part of the human population including the disabled and the elderly who use assistive and rehabilitation robots for improving the quality of their lives and increasing their independence. Gives an overview of state-of-the-art control theory in physiology, emphasizing the importance of this theory in the medical field through concrete examples, e.g., endocrine, immune, and neurological systems Takes a comprehensive look at advances in medical robotics and rehabilitation devices and presents case studies focusing on their feedback control Presents the significance of control theory in the pervasiveness of medical robots in surgery, exploration, diagnosis, therapy, and rehabilitation
Book Synopsis A Biologist's Guide to Mathematical Modeling in Ecology and Evolution by : Sarah P. Otto
Download or read book A Biologist's Guide to Mathematical Modeling in Ecology and Evolution written by Sarah P. Otto and published by Princeton University Press. This book was released on 2011-09-19 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available
Book Synopsis Applications of Calculus to Biology and Medicine by : Nathan C Ryan
Download or read book Applications of Calculus to Biology and Medicine written by Nathan C Ryan and published by World Scientific Publishing Company. This book was released on 2017-08-17 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biology majors and pre-health students at many colleges and universities are required to take a semester of calculus but rarely do such students see authentic applications of its techniques and concepts. Applications of Calculus to Biology and Medicine: Case Studies from Lake Victoria is designed to address this issue: it prepares students to engage with the research literature in the mathematical modeling of biological systems, assuming they have had only one semester of calculus. The text includes projects, problems and exercises: the projects ask the students to engage with the research literature, problems ask the students to extend their understanding of the materials and exercises ask the students to check their understanding as they read the text. Students who successfully work their way through the text will be able to engage in a meaningful way with the research literature to the point that they would be able to make genuine contributions to the literature. Request Inspection Copy Contents: Background:Lake VictoriaWhat is Calculus?Population Modeling:Introduction to Population ModelingLogistic GrowthHarvesting a Population with Logistic GrowthEuler's MethodModeling Interlude: The Modeling ProcessResearch Interlude: Reading a Research PaperBrief Introduction to SageProjects for Population ModelingDrug Modeling:Introduction to PharmacokineticsTwo Models for Lead in the BodyMethods of Drug AdministrationEuler's Method for Systems of Differential EquationsModeling Interlude: Sensitivity AnalysisResearch Interlude: Writing a Research PaperProjects for Pharmacokinetic ModelingPredator Prey Modeling:Undamped Lotka-Volterra EquationsDamped Lotka-Volterra EquationsPredator SatiationIsoclinesSpecies FormationTop PredatorsModeling Interlude: Potential Problems with ModelsResearch Interlude: Making FiguresProjects for Predatory-Prey ModelsInfectious Disease Modeling:SIR Model for Infectious DiseasesMalariaHIV/AIDSProjects for Infectious Disease ModelsClassroom Tested Projects Readership: Undergraduates in biomathematics, mathematical biology, mathematical modeling, applied mathematics, and dynamical systems.
Download or read book Modeling Life written by Alan Garfinkel and published by Springer. This book was released on 2017-09-06 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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?
Book Synopsis Dynamic Models in Biology by : Stephen P. Ellner
Download or read book Dynamic Models in Biology written by Stephen P. Ellner and published by Princeton University Press. This book was released on 2011-09-19 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: From controlling disease outbreaks to predicting heart attacks, dynamic models are increasingly crucial for understanding biological processes. Many universities are starting undergraduate programs in computational biology to introduce students to this rapidly growing field. In Dynamic Models in Biology, the first text on dynamic models specifically written for undergraduate students in the biological sciences, ecologist Stephen Ellner and mathematician John Guckenheimer teach students how to understand, build, and use dynamic models in biology. Developed from a course taught by Ellner and Guckenheimer at Cornell University, the book is organized around biological applications, with mathematics and computing developed through case studies at the molecular, cellular, and population levels. The authors cover both simple analytic models--the sort usually found in mathematical biology texts--and the complex computational models now used by both biologists and mathematicians. Linked to a Web site with computer-lab materials and exercises, Dynamic Models in Biology is a major new introduction to dynamic models for students in the biological sciences, mathematics, and engineering.
Book Synopsis Systems Biology by : Andreas Kremling
Download or read book Systems Biology written by Andreas Kremling and published by CRC Press. This book was released on 2013-11-12 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawing on the latest research in the field, Systems Biology: Mathematical Modeling and Model Analysis presents many methods for modeling and analyzing biological systems, in particular cellular systems. It shows how to use predictive mathematical models to acquire and analyze knowledge about cellular systems. It also explores how the models are sy
Book Synopsis Mathematical Models in Biology by : Valeria Zazzu
Download or read book Mathematical Models in Biology written by Valeria Zazzu and published by Springer. This book was released on 2015-11-26 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy. The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content useful as it addresses existing challenges in identifying the gaps between mathematical modeling and biological research. The shared solutions will aid and promote further collaboration between life sciences and mathematics.
Book Synopsis Mathematics for the Life Sciences by : Glenn Ledder
Download or read book Mathematics for the Life Sciences written by Glenn Ledder and published by Springer Science & Business Media. This book was released on 2013-08-29 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Course in Mathematical Biology by : Gerda de Vries
Download or read book A Course in Mathematical Biology written by Gerda de Vries and published by SIAM. This book was released on 2006-07-01 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the only book that teaches all aspects of modern mathematical modeling and that is specifically designed to introduce undergraduate students to problem solving in the context of biology. Included is an integrated package of theoretical modeling and analysis tools, computational modeling techniques, and parameter estimation and model validation methods, with a focus on integrating analytical and computational tools in the modeling of biological processes. Divided into three parts, it covers basic analytical modeling techniques; introduces computational tools used in the modeling of biological problems; and includes various problems from epidemiology, ecology, and physiology. All chapters include realistic biological examples, including many exercises related to biological questions. In addition, 25 open-ended research projects are provided, suitable for students. An accompanying Web site contains solutions and a tutorial for the implementation of the computational modeling techniques. Calculations can be done in modern computing languages such as Maple, Mathematica, and MATLAB?.
Book Synopsis Mathematical Biology: Modeling and Analysis by : Fiona Palmer
Download or read book Mathematical Biology: Modeling and Analysis written by Fiona Palmer and published by . This book was released on 2022-09-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical biology also known as biomathematics is the sub-field of biology which uses analysis, abstractions and mathematical models to study the principles that influence structure, development and behavior of living organisms. It uses techniques and tools of mathematics to understand complex, non-linear mechanisms in biology. It aims to create models and representations of biological processes which can be used in practical as well as theoretical research. Tools and techniques of applied mathematics are commonly used for creating such models. Some of the areas of research in this field are algebraic biology, complex systems biology, computational neuroscience, abstract relational biology and evolutionary biology. This book explores all the important aspects of this field in the present day scenario. It also strives to provide a fair idea about mathematical biology and to help develop a better understanding of the latest developments within the field. In this book, using case studies and examples, constant effort has been made to make the understanding of the difficult concepts of this discipline as easy and informative as possible, for the readers.
Book Synopsis Mathematical Modeling of Biological Systems, Volume II by : Andreas Deutsch
Download or read book Mathematical Modeling of Biological Systems, Volume II written by Andreas Deutsch and published by Springer Science & Business Media. This book was released on 2007-10-12 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume II of this two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. Highlighted throughout are mathematical and computational apporaches to examine central problems in the life sciences, ranging from the organization principles of individual cells to the dynamics of large populations. The chapters are thematically organized into the following main areas: epidemiology, evolution and ecology, immunology, neural systems and the brain, and innovative mathematical methods and education. The work will be an excellent reference text for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.
Book Synopsis Mathematical Modeling of Biological Systems by : Harvey J. Gold
Download or read book Mathematical Modeling of Biological Systems written by Harvey J. Gold and published by John Wiley & Sons. This book was released on 1977 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modeling process - an overview. Dimension and similarity. Probability models. Dynamic processes. Interacting dynamic processes. Feedback control and stability of biological systems. Curve fiting: estimating the parameters. Computing.
Book Synopsis A Course in Mathematical Biology by : Gerda de Vries
Download or read book A Course in Mathematical Biology written by Gerda de Vries and published by SIAM. This book was released on 2006-07-01 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the only book that teaches all aspects of modern mathematical modeling and that is specifically designed to introduce undergraduate students to problem solving in the context of biology. Included is an integrated package of theoretical modeling and analysis tools, computational modeling techniques, and parameter estimation and model validation methods, with a focus on integrating analytical and computational tools in the modeling of biological processes. Divided into three parts, it covers basic analytical modeling techniques; introduces computational tools used in the modeling of biological problems; and includes various problems from epidemiology, ecology, and physiology. All chapters include realistic biological examples, including many exercises related to biological questions. In addition, 25 open-ended research projects are provided, suitable for students. An accompanying Web site contains solutions and a tutorial for the implementation of the computational modeling techniques. Calculations can be done in modern computing languages such as Maple, Mathematica, and MATLAB?.
