Office Hours: From 8 to 5 except
lunch time and unscheduled meetings
E-mail address: charlton@ncsu.edu
Office: HA 203
Phone Number: 919.513.2291
This course does not satisfy the Math GER.
Goal: Starting with the series solutions of DEs to develop and apply
classical mathematical methods to the solution of PDEs such as the Wave, Heat,
and
Learning outcomes: The students will demonstrate through daily homework and test work that they know the theory and can apply it to the solution of the problems as outlined in the topics listed in section F below.
A fourteen division of topics corresponding to 42 lectures allowing for a 46 day semester are as follows (for a detailed schedule see section G).
SECTIONS TOPICS
1 1.3, 2.2, 2.4-2.6 Review of DEs
2 2.6, 4.1-4.3 review of power series
solution of DEs, method of Frobenius
3 4.3-4.4, 14.1-14.2 method of Frobenius, Fourier series of a
function
4 14.2, 14.3 Convergence of the Fourier
series
5 14.4-14.5, 15.1-15.2 Fourier sine and cosine series
6 15.3, 15.4 Fourier integral and Fourier
transform
7 15.5-15.6, 16.1 Fourier cosine and sine transforms
and Fourier finite transform
8 16.1, 16.2 Legendre polynomials and
Bessel functions
TAKE HOME MIDTERM TEST TO BE TAKEN BETWEEN June 28 AND Jyly 7 INCLUSIVELY
9 16.2, 16.3 Strum-Louiville theory and
eigenfunction expansions
10 16.3, 17.1-17.2 Fourier series solution of the Wave
equation
11 17.2-17.4 wave motion along an
unbounded string and d’Alembert’s solution
12 17.4-17.7, 18.1-18.2 vibration of membranes and heat equation
13 18.2-18.3 Heat equation and
conduction in infinite medium
14 18.3-18.5, 19.1-19.8 heat conduction in cylinders, Dirichlet and Neuman problems
16.
(Homework assigned in a week is due the Wednesday of the following week.)
All submitted work on the mid-term and exam must be done with hand computations supplemented only with tables when supplied. You can check your work with a computer or calculator. You can type your work but each step or calculation must be done by hand. Homework is to follow the same general rule with the following exceptions: Easy integrals are to be computed by hand. You are expected to develop the ability to recognize the complexity of evaluating an integral. An integral involving say more than two integrations by parts can be regarded as needing a computer, calculator, or table. You must be able to identify the exceptional cases when using such general solutions. When an integrand involves a Bessel function you will have to use a computer program if available. For transforms you are to use the tables supplied in the notes.
Please watch for changes and corrections in the
assignments
Dates
section homework
Week of May18 1.3
pg. 26: 7, 11
2.2 pg. 69: 3, 13
2.4 pg.
77: 7, 15
2.5 pg. 81: 11, 15
2.6
pg. 93: 5, 13, 29
4.1 pg.
160: 7, 13
___________________________________________________________________
Week of May 25 4.2 pg.
165: 5, 11
4.3
pg. 173: 1, 3, 5, 7
4.4 pg. 180: 1, 3, 11
Week of June 1 14.2 pg. 592: 1, 5, 7
14.3 pg. 609: 5, 9
14.4
pg. 614: 5, 7, 11
14.5 pg. 623: 3, 5
15.1 pg. 640: 1,9
15.2 pg. 642: 1,
7
_________________________________________________________________________
Week of June 8 15.3 pg. 652: 1, 13, 21
15.4 pg. 669: 5, 9, 13
15.5 pg. 672: 5
15.6 pg. 674: 7, 11
___________________________________________________________________
Week
of June 15 16.1 pg. 718: 3,
7, 13
16.2 pg.
744: 3, 11, 25
___________________________________________________________________
TAKE HOME MIDTERM TEST TO BE TAKEN BETWEEN JUNE 28 AND JULY 6 INCLUSIVELY COVERING THROUGH 15.6. STUDENTS SHOULD ARRANGE WITH ENGINEERING ONLINE TO TAKE THE TEST IN THIS PERIOD.
Please submit the midterm on Monday 07/07/08.
_________________________________________________________________________________________
Week of June 22 16.3 pg. 765: 3, 8
17.1 pg. 785: 3
17.2 pg. 806: 1, 5,
11
17.3
pg. 821: 1, 3, 7, 9, 11, 13
___________________________________________________________________
Week of July 6 17.4 pg. 830: 5, 8
17.5 pg. 834: 1
(light), a(1), a(2), a(3) and
graph if you have the capability
17.6
pg. 837: 1 (light), (a) Solve the
g(r,theta) zero case and (b)
setup the coefficients in the f(r,theta)
zero case with g(r,theta)=theta.
17.7
pg. 840: 3, this is the non-zero velocity
non-zero case.
18.2
pg. 863: 1, 5, 15, 17, 19. For 17 use
the substitution
u(x,t)=w(x,t)*exp(-at) and choose
the a so as to eliminate the
w(x,t) term from the
resulting heat equation.
________________________________________________________________________
Week of
July
13 18.3
pg. 873: 1, 7, 9
18.4 pg.
877: 1
18.5
pg. 878: 1
19.2
pg. 883: 3
19.3
pg. 886: 5, 11
19.4 pg. 888: 1
_______________________________________________________________________
Week of July 20 19.5 pg. 895: 3
19.6 pg.
898: 1
19.7 pg.
902: 7
_________________________________________________________________________
Week
of July 27 19.8
pg. 908: 1, 7, 9
___________________________________________________________________
EOL MA 501-651 EXAM BETWEEN JULY 31 st AND August 4 th : OPEN TEXT BOOK AND LECTURE NOTES. SHOW ALL STEPS IN A SOLUTION. If YOU BEGIN
WITH RESULTS IN THE TEXT PLEASE SHOW ALL SUBSEQUENT STEPS IN THE
SOLUTIONS.
The EOL exam is to be a three-hour proctored exam. Please arrange with the Engineering Online Office for a time and proctor. Please submitt by 08/05.
H. Projected
Schedule of Homework, Quizzes, and Exams
See G.
|
Weight |
Category of
Assignment |
|
1/3 |
Midterm |
|
1/3 |
Homework |
|
1/3 |
Final Examination |
|
Range |
Grade |
|
97.6 <= X <= 100 |
A+ |
|
92.3 <= X < 97.6 |
A |
|
90.0 <= X < 92.3 |
A- |
|
87.6 <= X < 90.0 |
B+ |
|
82.3 <= X < 87.6 |
B |
|
80.0 <= X < 82.3 |
B- |
|
77.6 <= X < 80.0 |
C+ |
|
72.3 <= X < 77.6 |
C |
|
70.0 <= X < 72.3 |
C- |
|
67.6 <= X < 70.0 |
D+ |
|
62.3 <= X < 67.6 |
D |
|
60.0 <= X < 62.3 |
D- |
|
X < 60 |
F |
As this is a graduate EOL course late assignments are accepted within reason upon discussing the reasons with the instructor (email is sufficient).
All work must be completed for a passing grade. No attendance policy as this is a distant education course.
Students are required to follow NCSU policy available at www.ncsu.edu/provost/academis_regulations/integity/reg.htm . "Academic dishonesty is the giving, taking, or presenting of information or material by a student that unethically
or fraudulently aids oneself or another on any work which is to be considered in the determination of a grade or the completion of academic requirements or the enhancement of that student's record or academic career." (NCSU Code of Student Conduct
http://www.ncsu.edu/student_affairs/osc/AIpage//acaintegrity.html)
"I have neither given nor received unauthorized aid on this test (or assignment)."
This has been outlined above
Reasonable accommodations will be made for students with
verifiable disabilities. In order to take advantage of available accommodations,
students must register with Disability Service for Students at 1900
For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation.
NA
There are no charges or fees beyond the purchase of your textbook. Maple, Mathematicae, MatLab, or MathCAD are very useful though not necessary.
There are no field trips for this course.