Exploring Mathematical Modeling In Biology Through Case Studies And Experimental Activities

Author : Rebecca Sanft,Anne Walter
Publisher : Academic Press
Page : 260 pages
File Size : 53,8 Mb
Release : 2020-04-15
Category : Science
ISBN : 9780128195956

Get Book

Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities by Rebecca Sanft,Anne Walter Pdf

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

Author : Rebecca Sanft,Anne Walter
Publisher : Academic Press
Page : 262 pages
File Size : 42,8 Mb
Release : 2020-03-30
Category : Science
ISBN : 9780128195963

Get Book

Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities by Rebecca Sanft,Anne Walter Pdf

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

Author : Ching Shan Chou,Avner Friedman
Publisher : Springer
Page : 172 pages
File Size : 55,8 Mb
Release : 2016-04-27
Category : Mathematics
ISBN : 9783319296388

Get Book

Introduction to Mathematical Biology by Ching Shan Chou,Avner Friedman Pdf

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.

Author : H.T. Banks,H.T. Tran
Publisher : CRC Press
Page : 298 pages
File Size : 47,8 Mb
Release : 2009-01-12
Category : Mathematics
ISBN : 1420073389

Get Book

Mathematical and Experimental Modeling of Physical and Biological Processes by H.T. Banks,H.T. Tran Pdf

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.

Author : Olfa Boubaker
Publisher : Academic Press
Page : 396 pages
File Size : 42,8 Mb
Release : 2020-06-30
Category : Science
ISBN : 9780128226216

Get Book

Control Theory in Biomedical Engineering by Olfa Boubaker Pdf

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

Author : Edward Beltrami
Publisher : Academic Press
Page : 224 pages
File Size : 51,5 Mb
Release : 2002
Category : Computers
ISBN : 0120855615

Get Book

Mathematical Models for Society and Biology by Edward Beltrami Pdf

Mathematical Modeling for Society and Biology engagingly relates mathematics to compelling real-life problems in biology and contemporary society. It shows how mathematical tools can be used to gain insight into these modern, common problems to provide effective, real solutions. Beltrami's creative, non-threatening approach draws on a wealth of interesting examples pertaining to current social and biological issues. Central ideas appear again in different contexts throughout the book, showing the general unity of the modeling process. The models are strikingly novel and based on issues of real concern. Most have never appeared in book form. Through the relevance of these models mathematics becomes not just figures and numbers, but a means to a more refined understanding of the world.

Author : Sarah P. Otto,Troy Day
Publisher : Princeton University Press
Page : 745 pages
File Size : 45,6 Mb
Release : 2011-09-19
Category : Science
ISBN : 9781400840915

Get Book

A Biologist's Guide to Mathematical Modeling in Ecology and Evolution by Sarah P. Otto,Troy Day Pdf

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

Author : Avner Friedman,Chiu-Yen Kao
Publisher : Springer
Page : 154 pages
File Size : 55,8 Mb
Release : 2014-09-19
Category : Mathematics
ISBN : 9783319083148

Get Book

Mathematical Modeling of Biological Processes by Avner Friedman,Chiu-Yen Kao Pdf

This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.

Author : Nathan C Ryan,Dorothy Wallace
Publisher : World Scientific Publishing Company
Page : 272 pages
File Size : 50,9 Mb
Release : 2017-08-17
Category : Science
ISBN : 9789813222793

Get Book

Applications of Calculus to Biology and Medicine by Nathan C Ryan,Dorothy Wallace Pdf

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.

Author : Glenn Ledder
Publisher : Springer Science & Business Media
Page : 431 pages
File Size : 42,7 Mb
Release : 2013-08-29
Category : Mathematics
ISBN : 9781461472766

Get Book

Mathematics for the Life Sciences by Glenn Ledder Pdf

​ ​​ 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.

Author : Alan Garfinkel,Jane Shevtsov,Yina Guo
Publisher : Springer
Page : 445 pages
File Size : 48,9 Mb
Release : 2017-09-06
Category : Mathematics
ISBN : 9783319597317

Get Book

Modeling Life by Alan Garfinkel,Jane Shevtsov,Yina Guo Pdf

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?

Author : Andreas Kremling
Publisher : CRC Press
Page : 379 pages
File Size : 51,7 Mb
Release : 2013-11-12
Category : Mathematics
ISBN : 9781466567900

Get Book

Systems Biology by Andreas Kremling Pdf

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

Author : Valeria Zazzu,Maria Brigida Ferraro,Mario R. Guarracino
Publisher : Springer
Page : 199 pages
File Size : 46,9 Mb
Release : 2015-11-26
Category : Mathematics
ISBN : 9783319234977

Get Book

Mathematical Models in Biology by Valeria Zazzu,Maria Brigida Ferraro,Mario R. Guarracino Pdf

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.

Author : Fiona Palmer
Publisher : Unknown
Page : 0 pages
File Size : 53,6 Mb
Release : 2022-09-13
Category : Electronic
ISBN : 1639873546

Get Book

Mathematical Biology: Modeling and Analysis by Fiona Palmer Pdf

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.

Author : Mazen Shahin
Publisher : Unknown
Page : 390 pages
File Size : 42,6 Mb
Release : 2014
Category : Electronic books
ISBN : OCLC:1047848256

Get Book

Explorations of Mathematical Models in Biology with MATLAB by Mazen Shahin Pdf