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Exploring Modeling with Data and Differential Equations Using R 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. This unified framework sits "at the intersection" of different mathematical subject areas, Data Science, statistics, and the natural sciences. The text throughout emphasizes data science workflows using the R statistical software program and the tidyverse constellation of packages. Only knowledge of calculus is needed the text’s integrated framework is a stepping stone for further advanced study in mathematics or as a comprehensive introduction to modeling for quantitative natural scientists.
The primary tools we will use to analyze models for this book are R and RStudio. These programs are powerful ones to learn! Admittedly learning a new software may be challenging however I think it is worth it. With R you will have enormous flexibility to efficiently utilize data, design effective visualizations, and process statistical models. The program RStudio is called an Integrated Development Environment for the statistical software language R.
Packages are one way that R gets some awesome versatility. Packages are contributed, specialized code produced by users (just like you!), and shared with the world. Packages are similar to apps on your phone, which rather than obtaining them from the app store can be found in two different places:
• CRAN4, which stands for Comprehensive R Archive Network. This is the clearing house for many contributed packages - and allows for easy cross-platform functionality.
• Github. This is another place where people can share code and packages (including myself!). The code here has not been vetted through CRAN for compatibility, but if you trust the person sharing the code, it should work.
For this textbook I have written a collection of functions and data that we will use. This package name is called demodelr (Differential Equations and Models in R).
The text will introduce you to:
- modeling with systems of differential equations and developing analytical, computational, and visual solution techniques.
- the R programming language, the tidyverse syntax, and developing data science workflows.
- qualitative techniques to analyze a system of differential equations.
- data assimilation techniques (simple linear regression, likelihood or cost functions, and Markov Chain, Monte Carlo Parameter Estimation) to parameterize models from data.
- simulating and evaluating outputs for stochastic differential equation models.
An associated R package provides a framework for computation and visualization of results