Differential equation analysis in biomedical science and engineering : ordinary differential equation applications with R

✍ Scribed by William E. Schiesser

• Publisher: Wiley
• Year: 2014
• Tongue: English
• Leaves: 439
• Edition: 1
• Category: Library

✦ Synopsis

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-worldODE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reprodu. �Read more...

Abstract:

Features a foundation of mathematical and computational tools to formulate and solve ordinary differential equation problems across various fields. This 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 more. �Read more...

✦ Table of Contents

Content: Cover
Title Page
Contents
Preface
Chapter 1 Introduction to Ordinary Differential Equation Analysis: Bioreactor Dynamics
1.1 Introduction
1.2 A 7 x 7 ODE System for a Bioreactor
1.3 In-Line ODE Routine
1.4 Numerical and Graphical Outputs
1.5 Separate ODE Routine
1.6 Alternative Forms of ODE Coding
1.7 ODE Integrator Selection
1.8 Euler Method
1.9 Accuracy and Stability Constraints
1.10 Modified Euler Method as a Runge-Kutta Method
1.11 Modified Euler Method as an Embedded Method
1.12 Classic Fourth-Order Runge-Kutta Method as an Embedded Method
1.13 RKF45 Method
References. Chapter 2 Diabetes Glucose Tolerance Test2.1 Introduction
2.2 Mathematical Model
2.2.1 Glucose Balance
2.2.2 Insulin Balance
2.3 Computer Analysis of the Mathematical Model
2.3.1 ODE Integration by lsoda
2.3.2 ODE Integration by RKF45
2.3.3 ODE Integration with RKF45 in a Separate Routine
2.3.4 h Refinement
2.3.5 p Refinement
2.4 Conclusions
References
Chapter 3 Apoptosis
3.1 Introduction
3.2 Mathematical Model
3.3 Main Program
3.4 ODE Routine
3.5 Base Case Output
3.6 Base Case with Variation in ICs
3.7 Variation in ODEs
3.8 Selection of Units. 3.9 Model Solution with RKF453.10 Conclusion
Reference
Chapter 4 Dynamic Neuron Model
4.1 Introduction
4.2 The Dynamic Neuron Model
4.3 ODE Numerical Integration
4.3.1 Explicit Euler Integration
4.3.2 Numerical and Graphical Solutions
4.3.3 Evaluation and Plotting of the ODE Derivative Vector
4.3.4 p Refinement
4.4 Conclusions
References
Chapter 5 Stem Cell Differentiation
5.1 Introduction
5.2 Model Equations
5.3 R Routines
5.3.1 Main Program
5.3.2 ODE Routine
5.3.3 Numerical and Graphical Output
5.3.4 Analysis of the Terms in the ODEs
5.3.5 Stable States
5.4 Summary. ReferenceChapter 6 Acetylcholine Neurocycle
6.1 Introduction
6.2 ODE Model
6.3 Numerical Solution of the Model
6.3.1 ODE Routine
6.3.2 Main Program
6.4 Model Output
6.4.1 Equilibrium Solution
6.4.2 Nonequilibrium Solutions
6.4.3 Analysis of the Terms in the ODEs
6.5 ODE/PDE Model
Appendix A1: IC Vector by a Differential Levenberg Marquardt Method
A1.1 ODE Jacobian Matrix
A1.2 Newton's Method
A1.3 Steepest Descent Method
A1.4 The Levenberg Marquardt Method
A1.5 Differential Newton's Method
A1.6 Differential Steepest Descent Method
A1.7 Differential Levenberg Marquardt Method. A1.8 Solution for the IC Vector of the 8 x 8 ODE SystemReferences
Chapter 7 Tuberculosis with Differential Infectivity
7.1 Introduction
7.2 Mathematical Model
7.3 R Routines for the ODE Model
7.3.1 ODE Routine
7.3.2 Main Program
7.4 Model Output
7.5 Conclusions
References
Chapter 8 Corneal Curvature
8.1 Introduction
8.2 Model Equations
8.3 Method of Lines Solution
8.4 R Routines
8.4.1 Main Program
8.4.2 ODE Routine
8.5 Numerical Solution
8.6 Error Analysis of the Numerical Solution
8.7 Library Routines for Differentiation in Space
8.8 Summary
References.

✦ Subjects

Биологические дисциплины;Матметоды и моделирование в биологии;