Differential Equation Analysis in Biomedical Science and Engineering : Partial Differential Equation Applications with R.
Title:
Differential Equation Analysis in Biomedical Science and Engineering : Partial Differential Equation Applications with R.
Author:
Schiesser, William E.
ISBN:
9781118705322
Personal Author:
Edition:
1st ed.
Physical Description:
1 online resource (344 pages)
Contents:
Cover -- Title Page -- Contents -- Preface -- Chapter 1 Introduction to Partial Differentiation Equation Analysis: Chemotaxis -- 1.1 Introduction -- 1.2 Linear Diffusion Model -- 1.3 Nonlinear Chemotaxis Model -- 1.4 Method of Lines Solution of 2-PDE Chemotaxis Model -- 1.4.1 Main Program -- 1.4.2 ODE Routine -- 1.5 Model Output -- 1.6 Computation of PDE Terms -- 1.7 Conclusions -- References -- Chapter 2 Pattern Formation -- 2.1 Introduction -- 2.2 Two PDE Model -- 2.2.1 ODE Routine -- 2.2.2 Main Program -- 2.2.3 Numerical Solution -- 2.3 Three PDE Model -- 2.3.1 ODE Routine -- 2.3.2 Main Program -- 2.3.3 Supplemental Routine -- 2.3.4 Numerical Solution -- 2.4 Conclusions -- References -- Chapter 3 Belousov-Zhabotinskii Reaction System -- 3.1 Introduction -- 3.2 The Belousov-Zhabotinskii Reaction System -- 3.2.1 ODE Routine -- 3.2.2 Main Program -- 3.2.3 Model Output -- 3.3 Conclusions -- Reference -- Chapter 4 Hodgkin-Huxley and Fitzhugh-Nagumo Models -- 4.1 Introduction -- 4.2 PDE Model -- 4.3 MOL Routines -- 4.3.1 ODE Routine -- 4.3.2 Main Program -- 4.4 Model Output -- 4.5 Discontinuous Initial Condition -- 4.6 Conclusions -- References -- Chapter 5 Anesthesia Spatiotemporal Distribution -- 5.1 Introduction -- 5.2 Two PDE Model -- 5.2.1 Main Program -- 5.2.2 ODE Routine -- 5.2.3 Other PDE Routines -- 5.2.4 Model Output -- 5.3 Conclusions -- 5.4 Model Extension -- 5.4.1 ODE Routine for the Extended Model -- 5.4.2 Main Program for the Extended Model -- 5.4.3 Output for the Extended Model -- Acknowledgment -- References -- Chapter 6 Influenza with Vaccination and Diffusion -- 6.1 Introduction -- 6.2 Five PDE Model -- 6.2.1 ODE Routine -- 6.2.2 Main Program -- 6.2.3 Model Output -- 6.3 Summary -- References -- Chapter 7 Drug Release Tracking -- 7.1 Introduction -- 7.2 Three PDE Model -- 7.2.1 ODE Routine.
7.2.2 Rate Functions -- 7.2.3 Main Program -- 7.3 Model Output -- 7.3.1 Base Case -- 7.3.2 Variation of Spatial Differentiation -- 7.3.3 Variation of Polymer Stress -- 7.4 Alternate Coordinate Systems -- 7.5 Summary -- References -- Chapter 8 Temperature Distributions in Cryosurgery -- 8.1 Introduction -- 8.2 PDE Model -- 8.3 Method of Lines Analysis -- 8.3.1 ODE Routine -- 8.3.2 Physical Property Routines -- 8.3.3 Main Program -- 8.4 Numerical Output -- 8.5 Variations in the Model -- 8.6 Summary -- References -- Index.
Abstract:
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.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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