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 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; temperature distributions in cryosurgery; multisection membrane separation system; and origin of PDE 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 broad class of differential and nonlinear algebraic equations. The investigated problems include ODEs and associated initial conditions. The studied equations describe a wide variety of basic phenomena such as apoptosis, stem cell differentiation, and many others.

Topical coverage includes: introduction to ODE analysis and bioreactor dynamics; diabetes glucose tolerance test; apoptosis; dynamic neuron model; stem cell differentiation; acetylcholine neurocycle; tuberculosis with differential infectivity; corneal curvature; and stiff ODE integration.

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

Preface ix

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

Index 417

William E. Schiesser is Emeritus McCann Professor of Computational Biomedical Engineering and Chemical and Biomolecular Engineering at Lehigh University.