Math 421: Applied Analysis

Fall 2004, UAF, Bueler

Instructor: Ed Bueler
Office: Chapman 301C.  Hours online.
Contact: 474-7693, ffelb@uaf.edu
Web Site: http://www.cs.uaf.edu/~bueler
 Class Time & Place:  MWF   9:15am-10:15  GRUE 410
                                 T    9:45am--10:45  BROOKS 302
Texts: Schey, Div, Grad, Curl and All That, 3rd ed.
and  Farlow, Partial Differential Equations for Scientists and Engineers.

The course:     Math 421 is really two courses.  First we do a short course in vector calculus, completing the multivariable calculus story which is merely started by Calculus III.  You will then have the tools necessary to do classical electricity and magnitism and the classical parts of other field theories.  Then the last two thirds of the course will be an introduction to partial differential equations---including the heat, wave, and potential equations---and their solution by separation of variables.  Particular problems will be boundary value problems or initial-and-boundary value problems on nice domains (typically rectangles).  We will develop the elementary theory of Fourier series and orthogonal functions as needed.

Lectures and homework together make up the core of the class.  You are expected to ask questions in class about recent lectures or homework assignments.

The grade:  Your grade will be determined by three exams and homework:
20 %
10 %
30 %
40 %
 DivGradCurl Exam
Midterm Exam (on PDEs)
Final Exam (on PDEs)
Homework
 Monday, Oct. 18 (one hour in class)
Monday, Nov. 15 (one hour in class)
Wednesday, Dec. 15  8am-10am (two hours)
    
The course grade will be determined by you total on the above according to the schedule at right. Percent
90 - 100 % 
79 - 89 % 
68 - 78 % 
57 - 67 % 
0 - 56 % 		 Grade
A
B
C
D
F

Prerequisites and related courses:    Math 302 is the prerequisite.  It requires Math 202 Calculus III---which is what you should review immediately! 
    In Math 421 you'll get a clear and detailed presentation of the ideas in vector calculus, which you just touched on in 202. Why do you want vector calculus?  It is the mathematical core of electricity & magnetism (e.g. PHYS 331/332 and EE 311).  It is the mathematical core of the study of fluids (e.g. ME 451, MSL 629, ...).  The majority of the course, covering PDEs and the Fourier series which arise in their solutions, applies in many places.  It occurs in the E & M and fluids context, as above, but also in quantum mechanics, plasma dynamics, glaciers, solid earth dynamics,...
    There is a caviat about the PDEs part of the course, namely, that the methods we use work for linear equations in nice domains.  You will get a feeling for these restrictions.  In future work you are likely to approximate harder problems (nonlinear or nonsymmetric, or both) by simpler problems of the type we solve.

Policies and makeup exams:   The department has specific policies on incompletes, late withdrawals, and early final examinations, etc; see http://www.dms.uaf.edu/dms/Policies.html .  You are covered by the UAF Honor Code.  I will create makeup versions of exams provided I have a convincing reason to do so at least two class days before the exam.  The makeup must occur no later than two class days after the exam date.  I will work with the Office of Disabilities Services (203 WHIT, 474-7043) to provide reasonable accommodation to student with disabilities.