This course is an introduction to modelling continuums; the mathematics involved in modelling fluids, elastic solids, temperature distributions, mass distributions, electricity and magnetism, et cetera. The course builds on material presented in Calculus III and Differential Equations I. The course covers the basics of vector calculus (div, grad, and curl) and the associated partial differential equations that arise naturally in continuum mechanics.

For instance, consider the vector fields pictured below, one of which represents information about the flow of heat through a solid plate with heat applied to one end and insulated sides and one of which represents information about the flow of an incompressible fluid in a channel. In this course, we will examine the mathematical structures used to analyze such vector fields, and the mathematics involved in the applications giving rise to these vector fields.

This course is designed for students in mechanical engineering, electrical engineering, chemical engineering, engineering physics, physics and mathematics, that will encounter vector calculus and partial differential equations in other courses.

Evaluation will be weekly homework, weekly quizzes, and a few computing projects.