Math 444/544 Fundamentals of Applied Mathematics II Spring 2009 revised Jan 12

Instructor: B. Hassard, 645-6284 ext. 103, room Math 226, hassard@buffalo.edu

Lectures: M/W/F 1-1:50, room Math 150

Office hours: M/W 2-3 and by appt.

Course Description: The mathematical description of material behavior for solids, liquids and gases using the unified framework of continuum mechanics. The main themes are: derivation of the equations governing material behavior and the application of the equations to describe material phenomena.

Course web page: http://www.math.buffalo.edu/~hassard/444-544/

Texts: Required portions of [LS] and of [S] will be available from Great Lakes Graphics in the UB Commons:

[LS] Mathematics Applied to Deterministic Problems in the Natural Sciences (C.C.Lin and L.A.Segel, SIAM, Philadelphia, 1995)

[S] Mathematics Applied to Continuum Mechanics (L.A. Segal, Dover, New York, 1987)

Prerequisites: MTH 141, 142, 241, 306 all with C or better. While not required, some exposure to partial differential equations (e.g. MTH 418 or other courses) and the physically-oriented view of science/engineering would be beneficial. Being unafraid of "gradient, divergence and curl" is necessary. It is not necessary to have taken Part I (MTH 443/543).

Coursework and Grading:

Homework: Assigned homework is due about once a week. Homework points are based upon difficulty/effort required (5 pts = easy, 10 pts = moderate, 15pts = more difficult)

Exams: 2 exams on dates listed in Lecture Plan

Late Homework policy: Assignments are due in lecture on the due date. Late assignments are accepted up to one day late with the following penalties:
-10% if turned in by 5pm same day,
-20% if turned in by 5pm next day.

Course grades: Plus and minus letter grades will be assigned. Grades will be determined by averaging homework and exam grades with the weightings:

Homework	50%
exam #1	25%
exam #2	25%

MTH 544 students: Graduate students will have additional coursework consisting of additional homework and/or exam questions, and MTH444 and MTH544 will have separate grading scales.

Important Dates
Jan 19	Martin Luther King Day Observed
Jan 23	Last day to drop/add Spring 2009 courses without a grade of "R"
Mar 9-14	Spring break
Mar 27	Last day (by 11 p.m.) to "resign" a Spring 2009 course with a grade of "R"
Apr 27	Last day of class
May 8-10	Commencement weekend

Lecture Plan (approximate lecture dates)
The Continuous Medium		[LS]
1-12	Intro to course, the continuum model	13.1
1-14	kinematics of deformable media	13.2
1-16	material derivative, Jacobian of deformation	13.3-13.4
Field Equations of Continuum Mechanics		[LS]
1-21	conservation of mass	14.1
1-23	conservation of linear momentum	14.2
1-26	conservation of angular momentum	14.3
1-28	conservation of energy	14.4
1-30	constituitive equations	14.5
Inviscid Fluid Flow		[LS]
2-11	inviscid fluids	15.1
2-13	compression waves in gasses	15.3
2-18	flow past a cylinder	15.4
2-23	Review for Exam #1
2-25	Exam 1 on [LS] Ch 13-15
Viscous Fluid Flow		[S]
2-27	tensors and tensor notation	Ch 1-2
3-2	Navier-Stokes equations	3.1
3-4	exact solutions to Navier-Stokes equations part 1	3.2
3-9	SPRING BREAK
3-11	SPRING BREAK
3-13	SPRING BREAK
3-16	exact solutions to Navier-Stokes equations part 2	3.2
3-18	boundary layers- introduction	3.3
3-20	boundary layers- examples	3.4
3-25	slow viscous flow past a small sphere	3.6
Foundations of Elasticity		[S]
3-30	analysis of strain	4.1
4-3	Hooke's law and elasticity solutions	4.2
4-6	linear elasticity formulation	4.3
Static Problems in Elasticity		[S]
4-8	plane elasticity problems	5.3
4-10	Dynamic Problems in Elasticity	[S]
4-15	elastic waves	6.1
4-22	elastic surface waves	6.2
Review for exam 2
4-24	Exam 2 on [S] Ch 3-6 + tensor notation
4-27	Meet and discuss exam, HW