Publication Date



Vidale-Wolfe marketing model, ODE reading project, optimal control, Green's theorem


Economics | Marketing | Mathematics | Physical Sciences and Mathematics | Science and Mathematics Education


The Vidale-Wolfe marketing model is a first-order, linear, non-homogeneous ordinary differential equation (ODE) where the forcing term is proportional to advertising expenditure. With an initial response in sales as the initial condition, the solution of the initial value problem is straightforward for a first undergraduate ODE course. The model serves as an excellent example of many relevant topics for those students whose interests lie in economics, finance, or marketing. Its inclusion in the curriculum is particularly rewarding at an institution without a physics program. The model is not new, but it was novel to us when a group of students chose it for an exploratory project that we designed in order to help students acquire the ability to interpret and communicate mathematical results. In addition to describing the project in this work, we discuss the Vidale-Wolfe model and show how it can lead one to use Green's theorem in a real situation.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.