The Local Brewery: A Project for Use in Differential Equations Courses

We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer. The project aims to expose the students to the modeling process by creating and solving a mathematical model and effectively communicating their findings in a technical report. The students are required to produce a simple first-order differential equation and find the solution, given varying initial conditions. The students are also required to analyze a more complex, nonlinear ODE system model of the fermentation process. In dealing with the nonlinear system of equations, we provide the students a Mathematica file to reduce the time spent developing the model, but allow for more time to interpret the model. We also share some perspectives on the implementation of the project, provide alternative implementations, and possible extensions to the project.本研究介绍了一项面向常微分方程（ordinary differential equations, ODE）课程的建模项目，该项目依托一阶微分方程与一阶微分方程组，对啤酒发酵过程开展建模工作。本项目旨在通过构建与求解数学模型，以及以技术报告形式高效呈现研究成果，帮助学生完整体验并掌握建模全流程。学生需构建一个简单的一阶微分方程，并针对不同初始条件求解该方程的解析解。此外，学生还需对更为复杂的啤酒发酵过程非线性ODE系统模型开展分析工作。在处理该非线性方程组时，我们为学生提供了Mathematica文件，以减少其在模型构建上耗费的时间，从而留出更多时间用于模型解读。本文还分享了该项目的实施思路、可选实施方案，以及该项目的潜在拓展方向。