William E. Schiesser - Differential Equation Analysis in Biomedical Science and Engineering : Partial Differential Equation Applications with R read online MOBI, EPUB, FB2
9781118705186 English 1118705181 Cataloging much-needed mathematical and computational tools, Differential Equation Analysis in Biomedical Science and Engineering Partial Differential Equation Applications with R provides a solid foundation in formulating and solving real-world PDE numerical and analytical problems in various fields, from applied mathematics, engineering, and computer science to biology and medicine. Addressing the fact that the details of the numerical algorithms and how the solution was computed are usually missing, the text includes supporting documentation and step-by-step guidance, and features R codes that can be easily and conveniently used by students, researchers, and scientists., Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fieldsWith 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 PDEsModels as systems of PDEs and associated initial and boundary conditions with explanations of the associated chemistry, physics, biology, and physiologyNumerical solutions of the presented model equations with a discussion of the important features of the solutionsAspects 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., Models in biological and biomedical sciences are normally presented as a system of ordinary or partial differential equations (ODEs/PDEs) based in the chemical, physical, or physiological principles they are describing. A numerical solution is then presented with a discussion of the important features of that solution. However, this book addresses the fact that the details of the numerical algorithms and how the solution was computed are usually missing. Most importantly, the computer code for the numerical solution is not provided so readers cannot delve into the model itself. Researchers do not have the time, interest, or in many instances, the ability to sort through a lot of advanced mathematical theory to develop the models needed to solve specific problems. However, this book alleviates the problem of forcing readers to understand and program a model from theoretical concepts and instead puts readers on a path to solving real problems from the start. 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 vast class of differential and nonlinear algebraic equations. The investigated problems include PDEs supplemented with initial and boundary conditions. The studied equations describe a wide variety of fascinating phenomena such as chemotaxis, retinal vasculature, and many others. For all of these problems, the author developed a valuable library of routines, all of which are provided within the book. Using the routines, readers can make their own numerical experiments and construct their own codes to solve many other models. In addition, the book features a collection of case studies, all of which will be of great interest to the biomolecular science and engineering (BMSE) fields. 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; temprtature distributions in cryosurgery; multisection membrane separation system; and origin of PDEs and reaction-diffusion equations.
9781118705186 English 1118705181 Cataloging much-needed mathematical and computational tools, Differential Equation Analysis in Biomedical Science and Engineering Partial Differential Equation Applications with R provides a solid foundation in formulating and solving real-world PDE numerical and analytical problems in various fields, from applied mathematics, engineering, and computer science to biology and medicine. Addressing the fact that the details of the numerical algorithms and how the solution was computed are usually missing, the text includes supporting documentation and step-by-step guidance, and features R codes that can be easily and conveniently used by students, researchers, and scientists., Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fieldsWith 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 PDEsModels as systems of PDEs and associated initial and boundary conditions with explanations of the associated chemistry, physics, biology, and physiologyNumerical solutions of the presented model equations with a discussion of the important features of the solutionsAspects 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., Models in biological and biomedical sciences are normally presented as a system of ordinary or partial differential equations (ODEs/PDEs) based in the chemical, physical, or physiological principles they are describing. A numerical solution is then presented with a discussion of the important features of that solution. However, this book addresses the fact that the details of the numerical algorithms and how the solution was computed are usually missing. Most importantly, the computer code for the numerical solution is not provided so readers cannot delve into the model itself. Researchers do not have the time, interest, or in many instances, the ability to sort through a lot of advanced mathematical theory to develop the models needed to solve specific problems. However, this book alleviates the problem of forcing readers to understand and program a model from theoretical concepts and instead puts readers on a path to solving real problems from the start. 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 vast class of differential and nonlinear algebraic equations. The investigated problems include PDEs supplemented with initial and boundary conditions. The studied equations describe a wide variety of fascinating phenomena such as chemotaxis, retinal vasculature, and many others. For all of these problems, the author developed a valuable library of routines, all of which are provided within the book. Using the routines, readers can make their own numerical experiments and construct their own codes to solve many other models. In addition, the book features a collection of case studies, all of which will be of great interest to the biomolecular science and engineering (BMSE) fields. 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; temprtature distributions in cryosurgery; multisection membrane separation system; and origin of PDEs and reaction-diffusion equations.