Syllabus for MA 501- 651, Summer 2008

 

A.  Instructor: Dr. H. J. Charlton

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

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 Information

  1. Title: Peter V. O’Neil, Advanced Engineering Mathematics, 6th edition
  2. Copyright year: 2007, ISBN 0-534-55208-0
  3. Cost: 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 would 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 set up the integration.  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. 

 

F. Organization and Scope

Topics and Times

 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

 

G. Projected Schedule of Reading Assignments

 16.  READING AND HOMEWORK ASSIGNMENTS:  Please submit all work to EOL (Fax 919.515.8415)

(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. 

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 passing grade.  No attendance policy as this is a distant education course.

 

L. Academic Integrity Statement

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)

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 Service 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.