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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.
Auteur
WILLIAM E. SCHIESSER, PhD, ScD (hon.) is Emeritus McCann
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.
Résumé
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:
Contenu
Preface ix
Introduction to Ordinary Differential Equation Analysis: Bioreactor Dynamics 1
Diabetes Glucose Tolerance Test 79
Apoptosis 145
Dynamic Neuron Model 191
Stem Cell Differentiation 217
Acetylcholine Neurocycle 241
Tuberculosis with Differential Infectivity 321
Corneal Curvature 337
Appendix A1: Stiff ODE Integration 375
Index 417