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Differential Equations And Mathematical Biology

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Differential Equations And Mathematical Biology

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Author : D.S. Jones
language : en
Publisher: Chapman and Hall/CRC
Release Date : 2003-02-26

Differential Equations And Mathematical Biology written by D.S. Jones and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-02-26 with Mathematics categories.

The conjoining of mathematics and biology has brought about significant advances in both areas, with mathematics providing a tool for modelling and understanding biological phenomena and biology stimulating developments in the theory of nonlinear differential equations. The continued application of mathematics to biology holds great promise and in fact may be the applied mathematics of the 21st century. Differential Equations and Mathematical Biology provides a detailed treatment of both ordinary and partial differential equations, techniques for their solution, and their use in a variety of biological applications. The presentation includes the fundamental techniques of nonlinear differential equations, bifurcation theory, and the impact of chaos on discrete time biological modelling. The authors provide generous coverage of numerical techniques and address a range of important applications, including heart physiology, nerve pulse transmission, chemical reactions, tumour growth, and epidemics. This book is the ideal vehicle for introducing the challenges of biology to mathematicians and likewise delivering key mathematical tools to biologists. Carefully designed for such multiple purposes, it serves equally well as a professional reference and as a text for coursework in differential equations, in biological modelling, or in differential equation models of biology for life science students.

Modeling Differential Equations In Biology

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Author : Clifford Henry Taubes
language : en
Publisher: Cambridge University Press
Release Date : 2008-01-17

Modeling Differential Equations In Biology written by Clifford Henry Taubes and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-17 with Mathematics categories.

Based on a very successful one-semester course taught at Harvard, this text teaches students in the life sciences how to use differential equations to help their research. It needs only a semester's background in calculus. Ideas from linear algebra and partial differential equations that are most useful to the life sciences are introduced as needed, and in the context of life science applications, are drawn from real, published papers. It also teaches students how to recognize when differential equations can help focus research. A course taught with this book can replace the standard course in multivariable calculus that is more usually suited to engineers and physicists.

Differential Equations And Mathematical Biology

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Author : D.S. Jones
language : en
Publisher: CRC Press
Release Date : 2009-11-09

Differential Equations And Mathematical Biology written by D.S. Jones and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-09 with Mathematics categories.

Deepen students' understanding of biological phenomenaSuitable for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, Differential Equations and Mathematical Biology, Second Edition introduces students in the physical, mathematical, and biological sciences to fundamental modeli

Parabolic Equations In Biology

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Author : Benoît Perthame
language : en
Publisher: Springer
Release Date : 2015-09-09

Parabolic Equations In Biology written by Benoît Perthame and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-09 with Mathematics categories.

This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.

Differential Equations And Mathematical Biology

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Author : D. S. Jones
language : en
Publisher: Springer
Release Date : 2012-01-24

Differential Equations And Mathematical Biology written by D. S. Jones and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-24 with Science categories.

Over the past decade, mathematics has made a considerable impact as a tool with which to model and understand biological phenomena. In return, biology has confronted the mathematician with a variety of challenging problems which have stimulated developments in the theory of nonlinear differential equations. This book is the outcome of the need to introduce undergraduates of mathematics, the physical and biological sciences to some of those developments. It is primarily directed towards students with a mathematical background up to and including that normally taught in a first-year physical science degree of a British university (sophomore year in a North American university) who are interested in the application of mathematics to biological and physical situations. Chapter 1 is introductory, showing how the study of first-order ordinary differential equations may be used to model the growth of a population, monitoring the administration of drugs and the mechanism by which living cells divide. In Chapter 2, a fairly comprehensive account of linear ordinary differential equations with constant coefficients is given. Such equations arise frequently in the discussion of the biological models encountered throughout the text. Chapter 3 is devoted to modelling biological pheno mena and in particular includes (i) physiology of the heart beat cycle, (ii) blood flow, (iii) the transmission of electrochemical pulses in the nerve, (iv) the Belousov-Zhabotinskii chemical reaction and (v) predator-prey models.

Differential Equations And Mathematical Biology

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Author : D. S. Jones
language : en
Publisher: Springer
Release Date : 2014-01-14

A Course In Mathematical Biology

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Author : Gerda de Vries
language : en
Publisher: SIAM
Release Date : 2006-07-01

A Course In Mathematical Biology written by Gerda de Vries and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-01 with Mathematics categories.

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?.

Delay Differential Equations And Applications To Biology

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Author : Fathalla A. Rihan
language : en
Publisher: Springer Nature
Release Date : 2021-08-19

Delay Differential Equations And Applications To Biology written by Fathalla A. Rihan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-19 with Mathematics categories.

This book discusses the numerical treatment of delay differential equations and their applications in bioscience. A wide range of delay differential equations are discussed with integer and fractional-order derivatives to demonstrate their richer mathematical framework compared to differential equations without memory for the analysis of dynamical systems. The book also provides interesting applications of delay differential equations in infectious diseases, including COVID-19. It will be valuable to mathematicians and specialists associated with mathematical biology, mathematical modelling, life sciences, immunology and infectious diseases.

Methods And Models In Mathematical Biology

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Author : Johannes Müller
language : en
Publisher: Springer
Release Date : 2015-08-13

Methods And Models In Mathematical Biology written by Johannes Müller and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-13 with Mathematics categories.

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.

Mathematical Biology Ii

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Author : James D. Murray
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-15

Mathematical Biology Ii written by James D. Murray and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-15 with Mathematics categories.

This richly illustrated third edition provides a thorough training in practical mathematical biology and shows how exciting mathematical challenges can arise from a genuinely interdisciplinary involvement with the biosciences. It has been extensively updated and extended to cover much of the growth of mathematical biology. From the reviews: ""This book, a classical text in mathematical biology, cleverly combines mathematical tools with subject area sciences."--SHORT BOOK REVIEWS

Differential Equations And Mathematical Biology

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