**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

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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 234) 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).

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land promised to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.