Features a solid foundation of mathematical and computationaltools to formulate and solve real-world PDE problems across variousfields
With a step-by-step approach to solving partial differentialequations (PDEs), Differential Equation Analysis in BiomedicalScience and Engineering: Partial Differential Equation Applicationswith R successfully applies computational techniques forsolving real-world PDE problems that are found in a variety offields, including chemistry, physics, biology, and physiology. Thebook provides readers with the necessary knowledge to reproduce andextend the computed numerical solutions and is a valuable resourcefor dealing with a broad class of linear and nonlinear partialdifferential equations.
The author’s primary focus is on models expressed assystems of PDEs, which generally result from including spatialeffects so that the PDE dependent variables are functions of bothspace and time, unlike ordinary differential equation (ODE) systemsthat pertain to time only. As such, the book emphasizes details ofthe numerical algorithms and how the solutions were computed.Featuring computer-based mathematical models for solving real-worldproblems in the biological and biomedical sciences and engineering,the book also 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 forPDEs
- Models as systems of PDEs and associated initial and boundaryconditions with explanations of the associated chemistry, physics,biology, and physiology
- Numerical solutions of the presented model equations with adiscussion of the important features of the solutions
- Aspects of general PDE computation through various biomedicalscience and engineering applications
Differential Equation Analysis in Biomedical Science andEngineering: Partial 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 9.30(h) x 0.90(d)|
About the Author
WILLIAM E. SCHIESSER, PHD, ScD(hon.) is Emeritus McCann Professor of Engineering andProfessor of Mathematics at Lehigh University. The author orcoauthor of thirteen books, Dr. Schiesser’s researchinterests include numerical software; ordinary, differentialalgebraic, and partial differential equations; and computationalmathematics.
Table of Contents
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