# MATH 710D, Spring 2007 Continuum Mechanics

## Course information

 Course: MATH 710D [catalog #3862] Continuum Mechanics Time/Place: MW 1:00pm–2:15pm, ACIV 010 Instructor: Dr. Rouben Rostamian Office: MP 402 Phone: 410–455–2458 Email: rostamian@umbc.edu Office hours: MW 3:00–4:00 and by appointment

This paper gives wrong solutions to trivial problems. The basic error, however, is not new.

Clifford A. Truesdell in Mathematical Reviews, 12,561a

[Halmos and I] share a philosophy about linear algebra: we think basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury.

Irving Kaplansky in Paul Halmos: Celebrating 50 Years of Mathematics

## Course Description

Continuum mechanics is the study of the relationship between forces and deformations in continuous media. The subject encompasses fluid mechanics, gas dynamics, linear and nonlinear elasticity, viscoelasticity and many other types of material behavior.

This course in continuum mechanics intended for graduate students of mathematics.

## Textbook

An Introduction to Continuum Mechanics by Morton Gurtin.

## Course contents

• Review of the prerequisite mathematics: linear algebra and operator theory
• Kinematics, deformations, the transport theorem
• Balance of mass, momentum and angular momentum
• Stress and strain
• Constitutive equations
• Frame-invariance (objectivity)
• Symmetry, isotropy
• Representation theorems for isotropic tensor functions
• The Navier-Stokes equations: derivation and examples
• Nonlinear elasticity: derivation and examples
• Linear elasticity: derivation and examples

Topics in viscometric flows, elastic waves and gas dynamics will be added as time permits.

The subject will be developed starting from first principles. Prerequisites are:

• a working knowledge of basic concepts of physics, such as pressure, force, mass, acceleration, and Newton's laws.
• a solid knowledge of undergraduate-level linear algebra including eigenvalues and eigenvectors
• facility with multi-variable calculus

## Homework and course evaluation

There are are no exams in this course. Your work will be evaluated solely based on your performance on homework assignments. I will assign homework problems as we go along. You may work together on studying and solving problems, however I expect that you will write your solutions on your own. See The Official UMBC Honors Code below.

## The Official UMBC Honors Code

By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal.

For detailed policies on academic integrity consult: