Exploring Modeling with Data and Differential Equations Using R

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 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. It can be found here: https: //cran.r-project.org/web/packages/demodelr/index.html.

《使用 R 探索數據建模和微分方程》提供了一個獨特的微分方程介紹，並應用於生物學和其他自然科學領域。此外，還探討了模型參數化和隨機微分方程的模擬，為模型分析和評估提供了額外的工具。這個統一的框架位於不同數學學科、數據科學、統計學和自然科學的交叉點上。全文強調使用 R 統計軟件和 tidyverse 套件集進行數據科學工作流程。只需要了解微積分知識；本書的整合框架是進一步深入研究數學或作為量化自然科學建模的全面介紹的基礎。

本書將向您介紹以下內容：
- 使用微分方程系統進行建模，並開發分析、計算和視覺化解決方案技術。
- R 程序語言、tidyverse 語法和數據科學工作流程的開發。
- 使用定性技術分析微分方程系統。
- 使用數據同化技術（簡單線性回歸、似然函數或成本函數，以及馬爾可夫鏈、蒙特卡羅參數估計）從數據中參數化模型。
- 模擬和評估隨機微分方程模型的輸出。

相關的 R 套件提供了計算和結果可視化的框架。可以在這裡找到：https://cran.r-project.org/web/packages/demodelr/index.html。

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.

John Zobitz是明尼蘇達州明尼阿波利斯奧格斯堡大學的數學和數據科學教授。他在環境數據科學方面的學術研究包括使用環境觀測網絡的數據集參數化生態系統模型。他是美國數學協會（MAA）的成員，曾任MAA北中部分會的主席。他曾在MAA Notes的編輯委員會任職。他曾獲得富布萊特-薩斯塔蒙寧基金會在芬蘭庫奧皮奧的東芬蘭大學的健康和環境科學領域的獎學金。此外，他還是生態預測網絡的聯繫成員，並定期在Fluxcourse上教授，這是一個用於測量和建模生態系統生物地球化學通量的年度夏季課程。