Differential Equation Analysis In Biomedical Science And Engineering
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Differential Equation Analysis In Biomedical Science And Engineering
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Author : William E. Schiesser
language : en
Publisher: John Wiley & Sons
Release Date : 2014-03-31
Differential Equation Analysis In Biomedical Science And Engineering written by William E. Schiesser and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-31 with Mathematics categories.
Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the computed numerical solutions and is a valuable resource for dealing with a broad class of linear and nonlinear partial differential equations. The author’s primary focus is on models expressed as systems of PDEs, which generally result from including spatial effects so that the PDE dependent variables are functions of both space and time, unlike ordinary differential equation (ODE) systems that pertain to time only. As such, the book emphasizes details of the numerical algorithms and how the solutions were computed. Featuring computer-based mathematical models for solving real-world problems in the biological and biomedical sciences and engineering, the book also includes: R routines to facilitate the immediate use of computation for solving differential equation problems without having to first learn the basic concepts of numerical analysis and programming for PDEs Models as systems of PDEs and associated initial and boundary conditions with explanations of the associated chemistry, physics, biology, and physiology Numerical solutions of the presented model equations with a discussion of the important features of the solutions Aspects of general PDE computation through various biomedical science and engineering applications Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R is an excellent reference for researchers, scientists, clinicians, medical researchers, engineers, statisticians, epidemiologists, and pharmacokineticists who are interested in both clinical applications and interpretation of experimental data with mathematical models in order to efficiently solve the associated differential equations. The book is also useful as a textbook for graduate-level courses in mathematics, biomedical science and engineering, biology, biophysics, biochemistry, medicine, and engineering.
Differential Equation Analysis In Biomedical Science And Engineering
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Author : William E. Schiesser
language : en
Publisher: John Wiley & Sons
Release Date : 2014-02-24
Differential Equation Analysis In Biomedical Science And Engineering written by William E. Schiesser and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-24 with Mathematics categories.
Features a solid foundation of mathematical and computational tools to formulate and solve real-world ODE problems across various fields With a step-by-step approach to solving ordinary differential equations (ODEs), Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R successfully applies computational techniques for solving real-world ODE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the computed numerical solutions and is a valuable resource for dealing with a broad class of linear and nonlinear ordinary differential equations. The author’s primary focus is on models expressed as systems of ODEs, which generally result by neglecting spatial effects so that the ODE dependent variables are uniform in space. Therefore, time is the independent variable in most applications of ODE systems. As such, the book emphasizes details of the numerical algorithms and how the solutions were computed. Featuring computer-based mathematical models for solving real-world problems in the biological and biomedical sciences and engineering, the book also includes: R routines to facilitate the immediate use of computation for solving differential equation problems without having to first learn the basic concepts of numerical analysis and programming for ODEs Models as systems of ODEs with explanations of the associated chemistry, physics, biology, and physiology as well as the algebraic equations used to calculate intermediate variables Numerical solutions of the presented model equations with a discussion of the important features of the solutions Aspects of general ODE computation through various biomolecular science and engineering applications Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R is an excellent reference for researchers, scientists, clinicians, medical researchers, engineers, statisticians, epidemiologists, and pharmacokineticists who are interested in both clinical applications and interpretation of experimental data with mathematical models in order to efficiently solve the associated differential equations. The book is also useful as a textbook for graduate-level courses in mathematics, biomedical science and engineering, biology, biophysics, biochemistry, medicine, and engineering.
Method Of Lines Pde Analysis In Biomedical Science And Engineering
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Author : William E. Schiesser
language : en
Publisher: John Wiley & Sons
Release Date : 2016-04-13
Method Of Lines Pde Analysis In Biomedical Science And Engineering written by William E. Schiesser and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-13 with Mathematics categories.
Presents the methodology and applications of ODE and PDE models within biomedical science and engineering With an emphasis on the method of lines (MOL) for partial differential equation (PDE) numerical integration, Method of Lines PDE Analysis in Biomedical Science and Engineering demonstrates the use of numerical methods for the computer solution of PDEs as applied to biomedical science and engineering (BMSE). Written by a well-known researcher in the field, the book provides an introduction to basic numerical methods for initial/boundary value PDEs before moving on to specific BMSE applications of PDEs. Featuring a straightforward approach, the book’s chapters follow a consistent and comprehensive format. First, each chapter begins by presenting the model as an ordinary differential equation (ODE)/PDE system, including the initial and boundary conditions. Next, the programming of the model equations is introduced through a series of R routines that primarily implement MOL for PDEs. Subsequently, the resulting numerical and graphical solution is discussed and interpreted with respect to the model equations. Finally, each chapter concludes with a review of the numerical algorithm performance, general observations and results, and possible extensions of the model. Method of Lines PDE Analysis in Biomedical Science and Engineering also includes: Examples of MOL analysis of PDEs, including BMSE applications in wave front resolution in chromatography, VEGF angiogenesis, thermographic tumor location, blood-tissue transport, two fluid and membrane mass transfer, artificial liver support system, cross diffusion epidemiology, oncolytic virotherapy, tumor cell density in glioblastomas, and variable grids Discussions on the use of R software, which facilitates immediate solutions to differential equation problems without having to first learn the basic concepts of numerical analysis for PDEs and the programming of PDE algorithms A companion website that provides source code for the R routines Method of Lines PDE Analysis in Biomedical Science and Engineering is an introductory reference for researchers, scientists, clinicians, medical researchers, mathematicians, statisticians, chemical engineers, epidemiologists, and pharmacokineticists as well as anyone interested in clinical applications and the interpretation of experimental data with differential equation models. The book is also an ideal textbook for graduate-level courses in applied mathematics, BMSE, biology, biophysics, biochemistry, medicine, and engineering.
Partial Differential Equation Analysis In Biomedical Engineering
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Author : W. E. Schiesser
language : en
Publisher:
Release Date : 2013
Partial Differential Equation Analysis In Biomedical Engineering written by W. E. Schiesser and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Biomedical engineering categories.
Gives graduate students and researchers an introductory overview of partial differential equation analysis of biomedical engineering systems through detailed examples.
Time Delay Ode Pde Models
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Author : W.E. Schiesser
language : en
Publisher: CRC Press
Release Date : 2019-11-25
Time Delay Ode Pde Models written by W.E. Schiesser and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-25 with Mathematics categories.
Time delayed (lagged) variables are an inherent feature of biological/physiological systems. For example, infection from a disease may at first be asymptomatic, and only after a delay is the infection apparent so that treatment can begin.Thus, to adequately describe physiological systems, time delays are frequently required and must be included in the equations of mathematical models. The intent of this book is to present a methodology for the formulation and computer implementation of mathematical models based on time delay ordinary differential equations (DODEs) and partial differential equations (DPDEs). The DODE/DPDE methodology is presented through a series of example applications, particularly in biomedical science and engineering (BMSE). The computer-based implementation of the example models is explained with routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The DPDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The example applications can first be executed to confirm the reported solutions, then extended by variation of the parameters and the equation terms, and even the forumulation and use of alternative DODE/DPDE models. • Introduces time delay ordinary and partial differential equations (DODE/DPDEs) and their numerical computer-based integration (solution) • Illustrates the computer implementation of DODE/DPDE models with coding (programming) in R, a quality, open-source scientific programming system readily available from the Internet • Applies DODE/DPDE models to biological/physiological systems through a series of examples • Provides the R routines for all of the illustrative applications through a download link • Facilitates the use of the models with reasonable time and effort on modest computers
Partial Differential Equation Analysis In Biomedical Engineering
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Author : W. E. Schiesser
language : en
Publisher: Cambridge University Press
Release Date : 2013
Partial Differential Equation Analysis In Biomedical Engineering written by W. E. Schiesser 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 2013 with Mathematics categories.
Gives graduate students and researchers an introductory overview of partial differential equation analysis of biomedical engineering systems through detailed examples.
Differential Equation Analysis Set
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Author : William E. Schiesser
language : en
Publisher: Wiley
Release Date : 2014-05-05
Differential Equation Analysis Set written by William E. Schiesser and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-05 with Mathematics categories.
Included in this set: Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R With the needed mathematical and computational tools, this book provides a solid foundation in formulating and solving real-world PDE problems in various fields from applied mathematics, engineering, and computer science to biology and medicine, includes supporting documentation and step-by-step guidance, and features R codes that can be easily and conveniently used by readers. Topical coverage includes: introduction to PDEs and chemotaxis; pattern formation; Belousov-Zhabotinskii reaction system; Hodgkin-Huxley and Fitzhugh-Nagumo models; spatiotemporal effects of anesthesia during surgery; developing retinal vasculature; temperature distributions in cryosurgery; multisection membrane separation system; and origin of PDE reaction-diffusion equations. Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R This book provides readers with the necessary knowledge to reproduce and extend the numerical solutions with reasonable effort and is a valuable resource dealing with a broad class of differential and nonlinear algebraic equations. The investigated problems include ODEs and associated initial conditions. The studied equations describe a wide variety of basic phenomena such as apoptosis, stem cell differentiation, and many others. Topical coverage includes: introduction to ODE analysis and bioreactor dynamics; diabetes glucose tolerance test; apoptosis; dynamic neuron model; stem cell differentiation; acetylcholine neurocycle; tuberculosis with differential infectivity; corneal curvature; and stiff ODE integration.
Ordinary Differential Equations For Engineers
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Author : Ali Ümit Keskin
language : en
Publisher: Springer
Release Date : 2018-09-01
Ordinary Differential Equations For Engineers written by Ali Ümit Keskin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-01 with Technology & Engineering categories.
This monograph presents teaching material in the field of differential equations while addressing applications and topics in electrical and biomedical engineering primarily. The book contains problems with varying levels of difficulty, including Matlab simulations. The target audience comprises advanced undergraduate and graduate students as well as lecturers, but the book may also be beneficial for practicing engineers alike.
Differential Equations For Engineers
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Author : Wei-Chau Xie
language : en
Publisher: Cambridge University Press
Release Date : 2010-04-26
Differential Equations For Engineers written by Wei-Chau Xie 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 2010-04-26 with Technology & Engineering categories.
Xie presents a systematic introduction to ordinary differential equations for engineering students and practitioners. Mathematical concepts and various techniques are presented in a clear, logical, and concise manner. Various visual features are used to highlight focus areas. Complete illustrative diagrams are used to facilitate mathematical modeling of application problems. Readers are motivated by a focus on the relevance of differential equations through their applications in various engineering disciplines. Studies of various types of differential equations are determined by engineering applications. Theory and techniques for solving differential equations are then applied to solve practical engineering problems. A step-by-step analysis is presented to model the engineering problems using differential equations from physical principles and to solve the differential equations using the easiest possible method. This book is suitable for undergraduate students in engineering.
Mathematical Modelling In Biomedicine
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Author : Y. Cherruault
language : en
Publisher: Springer Science & Business Media
Release Date : 1986-02-28
Mathematical Modelling In Biomedicine written by Y. Cherruault 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 1986-02-28 with Mathematics categories.
Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then is that they can't see the problem. one day, perhaps you will find the final question. G.K. Chesterton. The Scandal of Father Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, cod ing theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.