Features a solid foundation of mathematical and computationaltools to formulate and solve real-world ODE problems across variousfields
With a step-by-step approach to solving ordinary differentialequations (ODEs), Differential Equation Analysis in BiomedicalScience and Engineering: Ordinary Differential EquationApplications with R successfully applies computationaltechniques for solving real-world ODE problems that are found in avariety of fields, including chemistry, physics, biology, andphysiology. The book provides readers with the necessary knowledgeto reproduce and extend the computed numerical solutions and is avaluable resource for dealing with a broad class of linear andnonlinear ordinary differential equations.
The author’s primary focus is on models expressed assystems of ODEs, which generally result by neglecting spatialeffects so that the ODE dependent variables are uniform in space.Therefore, time is the independent variable in most applications ofODE systems. As such, the book emphasizes details of the numericalalgorithms and how the solutions were computed. Featuringcomputer-based mathematical models for solving real-world problemsin the biological and biomedical sciences and engineering, the bookalso includes:
- R routines to facilitate the immediate use of computation forsolving differential equation problems without having to firstlearn the basic concepts of numerical analysis and programming forODEs
- Models as systems of ODEs with explanations of the associatedchemistry, physics, biology, and physiology as well as thealgebraic equations used to calculate intermediate variables
- Numerical solutions of the presented model equations with adiscussion of the important features of the solutions
- Aspects of general ODE computation through variousbiomolecular science and engineering applications
Differential Equation Analysis in Biomedical Science andEngineering: Ordinary Differential Equation Applications with Ris an excellent reference for researchers, scientists, clinicians,medical researchers, engineers, statisticians, epidemiologists, andpharmacokineticists who are interested in both clinicalapplications and interpretation of experimental data withmathematical models in order to efficiently solve the associateddifferential equations. The book is also useful as a textbook forgraduate-level courses in mathematics, biomedical science andengineering, biology, biophysics, biochemistry, medicine, andengineering.
|Product dimensions:||6.10(w) x 9.40(h) x 1.10(d)|
About the Author
WILLIAM E. SCHIESSER, PhD, ScD (hon.) is Emeritus McCannProfessor of Engineering and Professor of Mathematics at LehighUniversity. The author or coauthor of thirteen books, Dr.Schiesser’s research interests include numerical software;ordinary, differential algebraic, and partial differentialequations; and computational mathematics.
Table of Contents
1. Introduction to Ordinary Differential Equation Analysis: Bioreactor Dynamics 1
2. Diabetes Glucose Tolerance Test 79
3. Apoptosis 145
4. Dynamic Neuron Model 191
5. Stem Cell Differentiation 217
6. Acetylcholine Neurocycle 241
7. Tuberculosis with Differential Infectivity 321
8. Corneal Curvature 337
Appendix A1: Stiff ODE Integration 375