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Author: James P. Keener
Publisher:
Published: 2021
Total Pages:
ISBN-13: 9781470464141
DOWNLOAD EBOOKDownload or read book Biology in Time and Space written by James P. Keener and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: James P. Keener
Publisher: American Mathematical Soc.
Published: 2021-06-02
Total Pages: 308
ISBN-13: 1470454289
DOWNLOAD EBOOKHow do biological objects communicate, make structures, make measurements and decisions, search for food, i.e., do all the things necessary for survival? Designed for an advanced undergraduate audience, this book uses mathematics to begin to tell that story. It builds on a background in multivariable calculus, ordinary differential equations, and basic stochastic processes and uses partial differential equations as the framework within which to explore these questions.
Download or read book Biology in Time and Space: A Partial Differential Equation Modeling Approach written by James P. Keener and published by American Mathematical Soc.. This book was released on 2021-06-02 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: How do biological objects communicate, make structures, make measurements and decisions, search for food, i.e., do all the things necessary for survival? Designed for an advanced undergraduate audience, this book uses mathematics to begin to tell that story. It builds on a background in multivariable calculus, ordinary differential equations, and basic stochastic processes and uses partial differential equations as the framework within which to explore these questions.
Author: Jacek Banasiak
Publisher: Springer Science & Business
Published: 2014-04-19
Total Pages: 295
ISBN-13: 3319051407
DOWNLOAD EBOOKThis monograph presents new tools for modeling multiscale biological processes. Natural processes are usually driven by mechanisms widely differing from each other in the time or space scale at which they operate and thus should be described by appropriate multiscale models. However, looking at all such scales simultaneously is often infeasible, costly, and provides information that is redundant for a particular application. Hence, there has been a growing interest in providing a more focused description of multiscale processes by aggregating variables in a way that is relevant to the purpose at hand and preserves the salient features of the dynamics. Many ad hoc methods have been devised, and the aim of this book is to present a systematic way of deriving the so-called limit equations for such aggregated variables and ensuring that the coefficients of these equations encapsulate the relevant information from the discarded levels of description. Since any approximation is only valid if an estimate of the incurred error is available, the tools the authors describe allow for proving that the solutions to the original multiscale family of equations converge to the solution of the limit equation if the relevant parameter converges to its critical value. The chapters are arranged according to the mathematical complexity of the analysis, from systems of ordinary linear differential equations, through nonlinear ordinary differential equations, to linear and nonlinear partial differential equations. Many chapters begin with a survey of mathematical techniques needed for the analysis. All problems discussed in this book belong to the class of singularly perturbed problems; that is, problems in which the structure of the limit equation is significantly different from that of the multiscale model. Such problems appear in all areas of science and can be attacked using many techniques. Methods of Small Parameter in Mathematical Biology will appeal to senior undergraduate and graduate students in applied and biomathematics, as well as researchers specializing in differential equations and asymptotic analysis.
Download or read book Methods of Small Parameter in Mathematical Biology written by Jacek Banasiak and published by Springer Science & Business. This book was released on 2014-04-19 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents new tools for modeling multiscale biological processes. Natural processes are usually driven by mechanisms widely differing from each other in the time or space scale at which they operate and thus should be described by appropriate multiscale models. However, looking at all such scales simultaneously is often infeasible, costly, and provides information that is redundant for a particular application. Hence, there has been a growing interest in providing a more focused description of multiscale processes by aggregating variables in a way that is relevant to the purpose at hand and preserves the salient features of the dynamics. Many ad hoc methods have been devised, and the aim of this book is to present a systematic way of deriving the so-called limit equations for such aggregated variables and ensuring that the coefficients of these equations encapsulate the relevant information from the discarded levels of description. Since any approximation is only valid if an estimate of the incurred error is available, the tools the authors describe allow for proving that the solutions to the original multiscale family of equations converge to the solution of the limit equation if the relevant parameter converges to its critical value. The chapters are arranged according to the mathematical complexity of the analysis, from systems of ordinary linear differential equations, through nonlinear ordinary differential equations, to linear and nonlinear partial differential equations. Many chapters begin with a survey of mathematical techniques needed for the analysis. All problems discussed in this book belong to the class of singularly perturbed problems; that is, problems in which the structure of the limit equation is significantly different from that of the multiscale model. Such problems appear in all areas of science and can be attacked using many techniques. Methods of Small Parameter in Mathematical Biology will appeal to senior undergraduate and graduate students in applied and biomathematics, as well as researchers specializing in differential equations and asymptotic analysis.
Author: T. A. Burton
Publisher: Routledge
Published: 2017-10-05
Total Pages: 292
ISBN-13: 135143103X
DOWNLOAD EBOOKFirst published in 1980. CRC Press is an imprint of Taylor & Francis.
Download or read book Modeling and Differential Equations in Biology written by T. A. Burton and published by Routledge. This book was released on 2017-10-05 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1980. CRC Press is an imprint of Taylor & Francis.
Author: Johannes Müller
Publisher: Springer
Published: 2015-08-13
Total Pages: 721
ISBN-13: 3642272517
DOWNLOAD EBOOKThis book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.
Download or read book Methods and Models in Mathematical Biology written by Johannes Müller and published by Springer. This book was released on 2015-08-13 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.
Author: Avner Friedman
Publisher: Springer
Published: 2014-09-19
Total Pages: 152
ISBN-13: 3319083147
DOWNLOAD EBOOKThis 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.
Download or read book Mathematical Modeling of Biological Processes written by Avner Friedman and published by Springer. This book was released on 2014-09-19 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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: T. A. Burton
Publisher: CRC Press
Published: 1980-09-01
Total Pages: 300
ISBN-13: 9780824771331
DOWNLOAD EBOOKPersistence in lotka-volterra models of food chains and competition; Mathematical models of humoral immune response; Mathematical models of dose and cell cycle effects in multifraction radiotherapy; Theorical and experimental investigations of microbial competition in continuous culture; A liapunov functional for a class of reaction-diffusion systems; Stochastic prey-predator relationships; Coexistence in predator-prey systems; Stability of some multispecies population models; Population dynamics in patchy environments; Limit cycles in a model of b-cell simulation; Optimal age-specific harvesting policy for a cintinuous time-population model; Models involving differential and integral equations appropriate for describing a temperature dependent predator-prey mite ecosystem on apples.
Download or read book Modeling and Differential Equations in Biology written by T. A. Burton and published by CRC Press. This book was released on 1980-09-01 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Persistence in lotka-volterra models of food chains and competition; Mathematical models of humoral immune response; Mathematical models of dose and cell cycle effects in multifraction radiotherapy; Theorical and experimental investigations of microbial competition in continuous culture; A liapunov functional for a class of reaction-diffusion systems; Stochastic prey-predator relationships; Coexistence in predator-prey systems; Stability of some multispecies population models; Population dynamics in patchy environments; Limit cycles in a model of b-cell simulation; Optimal age-specific harvesting policy for a cintinuous time-population model; Models involving differential and integral equations appropriate for describing a temperature dependent predator-prey mite ecosystem on apples.
Author: Shandelle M. Henson
Publisher: CRC Press
Published: 2022-12-29
Total Pages: 339
ISBN-13: 100080609X
DOWNLOAD EBOOKFeatures Minimal pre-requisites beyond a solid background in calculus, such as a calculus I course. Suitable for upper division mathematics and sciences students and graduate-level biology students. Provides sample MATLAB codes and instruction in Appendices.
Download or read book Mathematical Modeling in Biology written by Shandelle M. Henson and published by CRC Press. This book was released on 2022-12-29 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features Minimal pre-requisites beyond a solid background in calculus, such as a calculus I course. Suitable for upper division mathematics and sciences students and graduate-level biology students. Provides sample MATLAB codes and instruction in Appendices.
Author: Frederic Y M Wan
Publisher: World Scientific Publishing Company
Published: 2017-08-16
Total Pages: 400
ISBN-13: 9813143355
DOWNLOAD EBOOKBroadly speaking, there are two general approaches to teaching mathematical modeling: 1) the case study approach, and 2) the method based approach (that teaches mathematical techniques with applications to relevant mathematical models). This text emphasizes instead the scientific issues for modeling different phenomena. For the natural or harvested growth of a fish population, we may be interested in the evolution of the population, whether it reaches a steady state (equilibrium or cycle), stable or unstable with respect to a small perturbation from equilibrium, or whether a small change in the environment would cause a catastrophic change, etc. Each scientific issue requires an appropriate model and a different set of mathematical tools to extract information from the model. Models examined are chosen to help explain or justify empirical observations such as cocktail drug treatments are more effective and regenerations after injuries or illness are fast-tracked (compared to original developments). Volume I of this three-volume set limits its scope to phenomena and scientific issues that are modeled by ordinary differential equations (ODE). Scientific issues such as signal and wave propagation, diffusion, and shock formation involving spatial dynamics to be modeled by partial differential equations (PDE) will be treated in Vol. II. Scientific issues involving randomness and uncertainty are examined in Vol. III. Request Inspection Copy Contents: Mathematical Models and the Modeling CycleGrowth of a Population:Evolution and EquilibriumStability and BifurcationInteracting Populations:Linear InteractionsNonlinear Autonomous InteractionsHIV Dynamics and Drug TreatmentsIndex Theory, Bistability and FeedbackOptimization:The Economics of GrowthOptimization over a Planning PeriodModifications of the Basic ProblemBoundary Value Problems are More ComplexConstraints and Control:"Do Your Best" and the Maximum PrincipleChlamydia TrachomatisGenetic Instability and CarcinogenesisMathematical Modeling RevisitedAppendices:First Order ODEBasic Numerical MethodsAssignments Readership: Undergraduates in mathematical biology, mathematical modeling of dynamical systems, optimization and control, viral dynamics (infectious diseases), oncology.
Download or read book Dynamical System Models in the Life Sciences and Their Underlying Scientific Issues written by Frederic Y M Wan and published by World Scientific Publishing Company. This book was released on 2017-08-16 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Broadly speaking, there are two general approaches to teaching mathematical modeling: 1) the case study approach, and 2) the method based approach (that teaches mathematical techniques with applications to relevant mathematical models). This text emphasizes instead the scientific issues for modeling different phenomena. For the natural or harvested growth of a fish population, we may be interested in the evolution of the population, whether it reaches a steady state (equilibrium or cycle), stable or unstable with respect to a small perturbation from equilibrium, or whether a small change in the environment would cause a catastrophic change, etc. Each scientific issue requires an appropriate model and a different set of mathematical tools to extract information from the model. Models examined are chosen to help explain or justify empirical observations such as cocktail drug treatments are more effective and regenerations after injuries or illness are fast-tracked (compared to original developments). Volume I of this three-volume set limits its scope to phenomena and scientific issues that are modeled by ordinary differential equations (ODE). Scientific issues such as signal and wave propagation, diffusion, and shock formation involving spatial dynamics to be modeled by partial differential equations (PDE) will be treated in Vol. II. Scientific issues involving randomness and uncertainty are examined in Vol. III. Request Inspection Copy Contents: Mathematical Models and the Modeling CycleGrowth of a Population:Evolution and EquilibriumStability and BifurcationInteracting Populations:Linear InteractionsNonlinear Autonomous InteractionsHIV Dynamics and Drug TreatmentsIndex Theory, Bistability and FeedbackOptimization:The Economics of GrowthOptimization over a Planning PeriodModifications of the Basic ProblemBoundary Value Problems are More ComplexConstraints and Control:"Do Your Best" and the Maximum PrincipleChlamydia TrachomatisGenetic Instability and CarcinogenesisMathematical Modeling RevisitedAppendices:First Order ODEBasic Numerical MethodsAssignments Readership: Undergraduates in mathematical biology, mathematical modeling of dynamical systems, optimization and control, viral dynamics (infectious diseases), oncology.
Author: Ulrich Langer
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2019-09-23
Total Pages: 261
ISBN-13: 3110548488
DOWNLOAD EBOOKThis volume provides an introduction to modern space-time discretization methods such as finite and boundary elements and isogeometric analysis for time-dependent initial-boundary value problems of parabolic and hyperbolic type. Particular focus is given on stable formulations, error estimates, adaptivity in space and time, efficient solution algorithms, parallelization of the solution pipeline, and applications in science and engineering.
Download or read book Space-Time Methods written by Ulrich Langer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-09-23 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to modern space-time discretization methods such as finite and boundary elements and isogeometric analysis for time-dependent initial-boundary value problems of parabolic and hyperbolic type. Particular focus is given on stable formulations, error estimates, adaptivity in space and time, efficient solution algorithms, parallelization of the solution pipeline, and applications in science and engineering.
