Differential Equations
Haynes Miller and Arthur Mattuck teach MIT's course on ordinary differential equations, the equations that express the laws of nature as functions of a single variable, usually time. The course material includes lecture notes, video lectures, recitations, Mathlets (interactive Java applets built through the d'Arbeloff Interactive Math Project), problem sets with solutions, and exams with solutions, organized by a full syllabus and calendar. One Mathlet shown on the course page models a spring system that oscillates when shaken, with the Laplace transform and its pole diagram used to explain why the amplitude spikes near the system's natural frequency. The course sits in MIT's Mathematics department and is cross-tagged under both Differential Equations and Linear Algebra, reflecting how the two subjects reinforce each other in solving systems of equations. It is typically taken right after single variable calculus and gives you the tools to model and solve real physical systems that change over time.