Syllabus for MA 501-601, Fall 2009

 

A.  Instructor: Dr. H. J. Charlton

Office Hours:  From 8 to 5 except MW 3:35 to 5:25, and lunch time and, unscheduled meetings
E-mail address:  charlton@ncsu.edu
Office: SAS 2107
Phone Number: 919.513.2291

B. Course Pre-requisites:

Differential Equations or an analysis course beyond calculus

C. GER Designation

This course does not satisfy the Math GER.

D. Learning Outcomes

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 Laplace equations in various coordinates.

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.

E. Textbook And Calculator Information

  1. Title: Peter V. O’Neil, Advanced Engineering Mathematics, 6th edition
  2. Copyright year: 2007, ISBN 0-534-55208-0
  3. Cost: Approximately $100. Call NCSU bookstore at (919)515-2161
  4. Maple, Mathematicia, MathLab, or MathCad can be useful as follows.  Handwork parallel with computer work at this level helps a student learn how to recognize errors in either.  It also helps a student understand the limitations and virtues of both.  There are several problems for which graphs though not necessary are asked for.  There is one problem for which it could take weeks to approximate its integrals by hand.  This is the only problem for which a TI-92 or its equivalent is not sufficient.  For want of a program it would be sufficient to explain why it is needed and how you would set up the integration.  All submitted work is to be hand work except integrals that can not be “evaluated” by elementary methods.  Students are expected to develop the skill to recognize elementary integrals.

F. Organization and Scope

Topics and Times

 A fourteen division of topics corresponding to 42 days of classes 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 OVER THE WEEKEND OF  October 10th                    

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

 

G. Projected Schedule of Reading Assignments

 16.  READING AND HOMEWORK ASSIGNMENTS:  Please submit all work to EOL (Fax 919.515.8415).  All submitted work must be done by hand except as noted above in E.  4. 

(Homework assigned in a week is due the Wednesday of the following week.)

 

Please watch for changes and corrections in the assignments

 

Dates                 section        homework

Week of Aug 19   1.3    pg.  26: 7, 11
                              2.2    pg.
  69: 3, 13

________________________________________________________________________________________________________________________________________________________________________
Week of Aug 23   2.4    pg.  77: 7, 15
                               2.5    pg.
  81: 11, 15
                               2.6    pg.
  93: 5, 13, 29

__________________________________________________________________________________________________________________________________________________________________________

Week of Aug 30   4.1    pg. 160: 7, 13
                              4.2    pg. 165: 5, 11                          

__________________________________________________________________________________________________________________________________________________________________________
Week of Sep 06
   4.3    pg. 173: 1, 3, 5, 7                                                                                                           

4.4    pg. 180: 1, 3, 11                                                                                                           

14.2  pg. 592: 1, 5, 7 
                            

Week of Sep 13 14.3 pg. 609: 5, 9

..........................14.4 pg. 614:5, 7, 11

` ` ` ` ` ` ` ` ` ` ` 14.5 pg. 623: 3, 5

 

_____________________________________________________________________________________________________________________________________________________________________________

             Week of Sep 20 15.1    pg. 640: 1,9
                                        15.2    pg. 642: 1, 7

                                        15.3    pg. 652: 1, 13, 21

 

_____________________________________________________________________________________________________________________________________________________________________________________

Week of Sep 27   15.4    pg. 669: 5, 9, 13
                             15.5    pg. 672: 5
                             15.6    pg. 674: 7, 11

____________________________________________________________________________________________________________________________________________________________________________________

Week of Oct 04   16.1    pg. 718: 3, 7, 13

                                         16.2   pg. 744: 3, 11, 25

____________________________________________________________________________________________________________________________________________________________________________________

TAKE HOME MIDTERM TEST OVER THE WEEKEND OF October 9TH THROUGH 15.6.   MA 501-601 STUDENTS SHOULD ARRANGE WITH ENGINEERING ONLINE TO TAKE THE TEST AS CLOSE TO THS DATE AS POSSIBLE.  PLEASE SUBMITT BY October 13TH.    

______________________________________________________________________________________________________________________________________________________________________________________

Week of Oct 11 16.3   pg. 765: 3, 8

                                17.1  pg.785: 3

_ ______________ 17.2  pg. 806: 1, 5, 11

_______________________________________________________________________________________________________________________________________________________________________________________________________________________                                                                 

Week of Oct 18  17.3    pg. 821: 1, 3, 7, 9, 11, 13
                          17.4 pg. 830: 5,

17.5 pg. 834: 1 (light), a(1), a(2), a(3) graph if you have the capability

_______________________________________________________________________________________________________________________________________________________________________________________________________

Week of Oct 25  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.                                   

_______________________________________________________________________________________________________________________________________________________________________________

Week of Nov 01  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.
                            18.3    pg. 873: 1, 7, 9

`` ````````````````` 18.4    pg. 877: 1

______________________________________________________________________________________________________________________________________________________________________________

          Week of Nov 08     18.5    pg. 878: 1

                             19.2    pg. 883: 3

19.3    pg. 886: 5, 11


______________________________________________________________________________________________________________________________________________________________________________

Week of Nov 15  19.4    pg. 888: 1                                                                                                                

19.5    pg. 895: 3                                                                                                     

19.6    pg. 898: 1                                                           

________________________________________________________________________________________________________________________________________________________________________________

Week of Nov 22   19.7    pg. 902: 7                                                                                                   

19.8    pg. 908: 1, 7, 9                                                                 

________________________________________________________________________________________________________________________________________________________________________________

EOL MA 501-601 EXAM BETWEEN December 9 th AND December 14th  INCLUSIVELY: OPEN TEXT BOOK AND LECTURE NOTES.  BEGINNING WITH RESULTS IN THE TEXT PLEASE SHOW ALL 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.  WORK IS TO BE SUBMITTED BY 5 PM December 15th.  The exam is comprehensive except there sill be no method

of Frobenius problem.


  H. Projected Schedule of Homework, Quizzes, and Exams

See G. 

I. How Grades are Determined

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 

 

J. Policy on Incomplete Grades and Late Assignments

 As this is a graduate EOL course late assignments are accepted within reason upon discussing the reasons with the instructor (email is sufficient).

K. Policy on Attendance, Excused Absences, Missed Work

All work must be completed for a grade.  No attendance policy.

 

L. Academic Integrity Statement

Students are required to follow NCSU policy   "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)

The Student Affairs web site has more information (http://www.ncsu.edu/student_affairs/osc/AIpage/acaintegrity.html).

Utilization implication of the Honor Pledge

"I have neither given nor received unauthorized aid on this test or assignment."

Expectations concerning honesty in the completion of test and assignments.

This has been outlined above

M. Students with Disabilities.

Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation.

N. Laboratory Safety

NA

O. Pass-through charges

There are no charges or fees beyond the purchase of your textbook.  Maple, Mathematicae, MatLab, or MathCAD are very useful though not necessary.

P. Transportation

There are no field trips for this course.

Further Information:

NCSU Academic Regulations can be found at http://www.ncsu.edu/policies/index.phb