The course AMATH 361 is a rather rare thing among undergraduate math courses. The chief difficulty for students lies in its reliance on previous courses (especially vector calculus, AMATH 231). However, a true appreciation of the subject matter also depends on some level of interest in and enthusiasm for classical physics. Of course, there are no formal requirements for this sort of thing when students enroll in AMATH 361, and one of the goals of this web page is to provide extra material that piques your curiosity. In particular many parts of the "pre-continuum mechanics" web page may prove of interest. This is especially true since the visual aspect of computation allows for the construction of tutorials for a variety of topics that were formerly rather dry.
The actual course AMATH 361 is divided into three parts, each of which has a relevant tutorial:
- Memory in physical laws and one dimensional linear viscoelasticity
- Deformation, stress and strain
- Modeling flow by Conservation Laws
For the mathematics student, the three parts consider the following mathematical topics:
- Laplace transforms for ordinary differential equations and the convolution integral in physical laws
- Forces in a continuum and the concept of traction, Cartesian tensors as a notational tool and as an expression of fundamental physical principles
- Material Volumes, the Transport Theorem, reductions of non linear systems of partial differential equations to simpler (usually linear) equations
The three parts have connections with various mathematical theories and different courses, namely:
1) AMATH 351 ordinary differential equations
2) AMATH 231 vector calculus, classical differential geometry
3) AMATH 231 vector calculus, AMATH 353 partial differential equations
Parts 2 and 3 also have significant conceptual overlap with the electricity and magnetism courses (PHYS 222/252, PHYS 223/253) offered by physics. The physics course on thermodynamics (PHYS 358) is a complement to the entire subject matter and a requirement for further study.
Of course the actual range of material behaviour is so much more extensive than a one term course can cover. Three examples are material failure, non-newtonian fluids, and postglacial rebound near Hudson Bay (the land that was squished by the massive Laurentide ice sheet during the last ice age, 20 000 year ago, is rising and making former beaches into cliffs).