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.
Зміст
Preface ix
1. Introduction to Partial Differentiation Equation Analysis:
Chemotaxis 1
2. Pattern Formation 43
3. Belousov-Zhabotinskii Reaction System 103
4. Hodgkin-Huxley and Fitzhugh-Nagumo Models 127
5. Anesthesia Spatiotemporal Distribution 163
6. Influenza with Vaccination and Diffusion 207
7. Drug Release Tracking 243
8. Temperature Distributions in Cryosurgery 287
Index 323
Про автора
WILLIAM E. SCHIESSER, PHD, Sc D
(hon.) is Emeritus Mc Cann Professor of Engineering and
Professor of Mathematics at Lehigh University. The author or
coauthor of thirteen books, Dr. Schiesser’s research
interests include numerical software; ordinary, differential
algebraic, and partial differential equations; and computational
mathematics.
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