Differential Equation Analysis Set

Included in this set: Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R. With the needed mathematical and computational tools, this book provides a solid foundation in formulating and solving real-world PDE numerical and analytical problems in various fields from applied mathematics, engineering, and computer science to biology and medicine, includes supporting documentation and step-by-step guidance, and features R codes that can be easily and conveniently used by readers. Topical coverage includes: introduction to PDEs and chemotaxis; pattern formation; Belousov-Zhabotinskii reaction system; Hodgkin-Huxley and Fitzhugh-Nagumo models; spatiotemporal effects of anesthesia during surgery; developing retinal vasculature; temprtature distributions in cryosurgery; multisection membrane separation system; and origin of PDEs and reaction-diffusion equations. Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R. This book provides readers with the necessary knowledge to reproduce and extend the numerical solutions with reasonable effort and is a valuable resource dealing with a vast class of differential and nonlinear algebraic equations. The investigated problems include ODEs supplemented with initial and boundary conditions. The studied equations describe a wide variety of fascinating phenomena such as apoptosis, cellular differentiation, and many others. Topical coverage includes: introduction to ODE analysis and bioreactor dynamics; diabetes glucose tolerance test; apoptosis (programmed cell death); dynamic neuron model; stem cell differentiation; acetylecholine neurocycle; tuberculosis with differential infectivity; corneal curvature; and stiff ODE integration.