MATH 471: Advanced Engineering Mathematics

MATH 471: Advanced Engineering Mathematics - Fall 2006

Time: Mon & Wed 12:30pm-1:45pm, Sears 480
Instructor: Christophe Geuzaine (Office: Yost 213; Phone: 368 29 09; Email: cag32(at)case(dot)edu)
Office hours: Mon & Wed 2:30pm-3:30pm, Yost 213. If you want to see me, don't feel that you have to wait for an office hour. For shorter questions, just drop by at any time. For longer consultations, please make an appointment.
Textbook: Applied Partial Differential Equations (with Fourier Series and Boundary Value Problems) by Richard Haberman (Prentice Hall, 4th edition, 2003).
Course description (from the catalog): Vector analysis, Fourier series and integrals. Laplace transforms, separable partial differential equations, and boundary value problems. Bessel and Legendre functions. Emphasis on techniques and applications. Students may not take both MATH 345 and MATH 471 for credit. Prereq: MATH 224.
Grading: There will be an in-class midterm exam and an in-class final exam. The midterm will determine 30% of your grade, and the final will determine 40%. The remaining 30% will be based on homework assignments.
Homework: Homework will be assigned and collected every week. It is important that you keep up with the work: do the homework as it is assigned, and ask questions right away if you find there is something you don't understand. The easiest way to do poorly in this class is to get behind on the homework assignments.
Midterm exam: Wed 10/18
Final exam: Tue 12/19, 8:30-11:30am, Sears 480

Schedule and Assignments

	Chapter	Homework
Mon 08/28	administrative	.
Wed 08/30	1.1-1.3, 2.1, 2.3: heat equation: physical derivation, boundary conditions, dimensionless form; separation of variables	.
Mon 09/04	no class (labor day)	.
Wed 09/06	2.2, 2.3: separation of variables; linearity, homogeneity, principle of superposition; full solution of the heat equation	Assignment 1
Mon 09/11	2.3, 2.4: example problem, finite-sum approximation	.
Wed 09/13	2.5, 3.1-3.3: uniqueness of solution for heat equation; review of Fourier series	Assignment 2
Mon 09/18	3.2-3.5: more on Fourier series; uniform convergence, differentiation and integration of infinite series	.
Wed 09/20	x.x, 1.4: more on uniform convergence: M-test, ratio test, application to heat equation, steady state	Assignment 3
Mon 09/25	no class	.
Wed 09/27	1.2, 2.4, 5.1, 5.2, 8.1, 8.2: variations on the basic heat problem: Dirichlet and Neumann boundary conditions, volume sources	.
Mon 10/02	2.4, 8.3: variations on the basic heat problem: time-periodic boundary conditions	.
Wed 10/04	4.1-4.4: wave equation: physical derivation, boundary conditions, separation of variables	Assignment 4
Mon 10/09	4.4, 12.1-12.3: D'Alembert's solution for the wave equation	.
Wed 10/11	12.3-12.5: characteristics for linear wave equation: infinite and finite string	.
Mon 10/16	x.x: homework review, intro to nonlinear PDEs	.
Wed 10/18	midterm exam	Midterm (w/ sol)
Mon 10/23	no class (fall break)	.
Wed 10/25	no class (fall break)	.
Mon 10/30	midterm exam correction	.
Wed 11/01	12.6: method of characteristics for quasilinear PDEs	Assignment 5
Mon 11/06	12.6: method of characteristics for quasilinear PDEs: traffic flow example	.
Wed 11/08	1.5, 4.5, 4.6, 7.1: 2D and 3D heat and wave equations	Assignment 6
Mon 11/13	7.2, 7.5, 7.6, 5.3, 5.5: separation of variables in 2D and 3D, uniqueness of solution of 3D heat problem, Rayleigh quotient, orthogonality of eigenfunctions	.
Wed 11/15	7.3, 7.4: 2D heat and wave equations on a rectangle with homogeneous BCs	Assignment 7
Mon 11/20	2.5.1, 8.1, 8.2: Heat equation on a rectangle with inhomogeneous BCs	.
Wed 11/22	2.5.4, 8.1, 8.2: Heat equation on a disk, Bessel functions	.
Mon 11/27	no class	.
Wed 11/29	10.1, 10.2: infinite spatial domains	.
Mon 12/04	10.4: infinite spatial domains and Fourier Transform	.
Wed 12/06	(9, 11, 12): introduction to Green function theory (last class)	.

Useful links

Matlab is available via the software center. (Here are some Matlab tutorials.)