This Daily Study Group provides a comprehensive introduction to partial differential equations (PDEs)—their properties, solution methods and applications—through the powerful framework of Wolfram Language. The study group builds on lessons from an upcoming Wolfram U interactive course and begins with the historical development of PDE theory, highlighting its significance and modern relevance. As the sessions progress, we will explore the major classes of PDEs, including linear and nonlinear first-order PDEs, as well as well-known second-order PDEs such as the heat, wave and Laplace equations. We will also examine four famous PDEs from various fields: the Black–Scholes equation in finance, the Schrödinger equation in quantum mechanics, the Maxwell equations in electromagnetism and the Navier–Stokes equations in fluid dynamics.

In Daily Study Groups, the instructor guides each session by sharing short lessons with examples, polling the group to review key concepts, introducing practice problems and answering questions. A certificate of program completion will be awarded to participants who attend online sessions and pass the course quizzes. Study group sessions run daily, Monday through Friday. There will be no session on Monday, January 19, due to the MLK Day US federal holiday.