Exploring Modeling With Data and Differential Equations Using R

List of contents

1. Models of rates with data 2. Introduction to R 3. Modeling With Rates of Change 4. Euler’s Method 5. Phase lines and equilibrium solutions 6. Coupled Systems of Equations 7. Exact Solutions to Differential Equations 8. Linear Regression and Curve Fitting 9. Probability and Likelihood Functions 10. Cost Functions & Bayes’ Rule 11. Sampling Distributions and the Bootstrap Method 12. The Metropolis-Hastings Algorithm 13. Markov Chain Monte Carlo Parameter Estimation 14. Information Criteria 15. Systems of linear differential equations 16. Systems of nonlinear equations 17. Local Linearization and the Jacobian 18. What are eigenvalues? 19. Qualitative Stability Analysis 20. Bifurcation 21. Stochastic Biological Systems 22. Simulating and Visualizing Randomness 23. Random Walks 24. Diffusion and Brownian Motion 25. Simulating Stochastic Differential Equations 26. Statistics of a Stochastic Differential Equation 27. Solutions to Stochastic Differential Equations

Summary

This book provides a unique introduction to differential equations with applications to the biological and other natural sciences. Additionally, model parameterization and simulation of stochastic differential equations are explored, providing additional tools for model analysis and evaluation

Product details

• Authors: John Zobitz
• Publisher: Taylor & Francis Ltd.
• Languages: English
• Product format: Hardback
• Released: 29.11.2022
• EAN: 9781032259482
• ISBN: 978-1-0-3225948-2
• No. of pages: 356
• Subjects: Natural sciences, medicine, IT, technology > Biology > Agriculture, horticulture; forestry, fishing, food; MATHEMATICS / Probability & Statistics / General, SCIENCE / Life Sciences / Biology, TECHNOLOGY & ENGINEERING / Environmental / General, environmental science, engineering & technology, Biology, life sciences, Probability & statistics, Agricultural science, Probability and statistics, Environmental science, engineering and technology