John Zobitz

Exploring Modeling with Data and Differential Equations Using R

• Gebundenes Buch

Produktbeschreibung

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

Produktdetails

• Verlag: Taylor & Francis Ltd
• Seitenzahl: 380
• Erscheinungstermin: 29. November 2022
• Englisch
• Abmessung: 240mm x 161mm x 25mm
• Gewicht: 748g
• ISBN-13: 9781032259482
• ISBN-10: 1032259485
• Artikelnr.: 64689543

Autorenporträt

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.

Inhaltsangabe

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