Exploring Modeling with Data and Differential Equations Using R

ISBN-13: 9781032259482 / Angielski / Twarda / 2022 / 376 str.

John Zobitz

Opis

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

Recenzje

"What quantitative skills does the modern biologist need? Some might say just enough to run prepackaged programs and collaborate with the experts. In other words, enough to get into trouble.  The ambitious new book "Exploring Modeling with Data and Differential Equations in R" by John Zobitz shows that another path is possible.  Biologists with a background in calculus can see the foundational methods in mathematical modeling, statistics and programming put to work through the carefully chosen examples that build in this well-organized book.  The philosophy is well-expressed by the first word of the title "Exploring", and the actual code and the graphs it produces are invitations to explore data with models, and not to hold the "math" at arms length.  The student or researcher who works through this friendly guide will have the tools and confidence needed to get into the kind of good trouble that leads to insight and discovery."
-Fred Adler, Professor of Mathematics and Director of the School of Biological Sciences University of Utah

“It will be so exciting to teach from this book, with its thorough incorporation of computing and data sets. From the start, the topics interweave standard differential equations concepts (analytical solutions, Euler’s method, qualitative approaches, single equations, systems of equations, stability analysis, and more) with an introduction to the R programming language, probability, and statistics. There is significant time spent on stochastic differential equations and on determining model parameter values based on data. These are timely, as current-day mathematical modelers frequently incorporate stochastic effects into their models, and connecting with real data sets is absolutely crucial. Exploring Modeling with Data and Differential Equations Using R works well as a main text or supplement for a course in Differential Equations or Mathematical Modeling. Alternately, it is a resource for those learning new methods while pursuing independent research projects.”
- Meredith Greer, Professor of Mathematics, Bates College

Spis treści

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

O autorze

John Zobitz is a Professor of Mathematics and Data Science at Augsburg University in Minneapolis, Minnesota. His scholarship in environmental data science includes ecosystem models parameterized with datasets from environmental observation networks. He is a member of the Mathematical Association of America (MAA) and previous president of the North Central Section of the MAA. He has served on the editorial board of MAA Notes. He was a recipient of the Fulbright-Saastamoinen Foundation Grant in Health and Environmental Sciences at the University of Eastern Finland in Kuopio, Finland. In addition, he is an affiliated member of the Ecological Forecasting Network and regularly taught at Fluxcourse, an annual summer course for measurements and modeling of ecosystem biogeochemical fluxes.