Syllabus for MA 501-601, Fall 2005

 

A.  Instructor: Dr. H. J. Charlton

Office Hours: 8:30 – 12:00 and 1:30 – 5:00 except T and H 1:30 to 2:45.
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 mathematical methods for the solution of PDEs such as the Wave, Heat, and Laplace equations in various coordinates.

Learning outcomes: The students will demonstrate through 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, 5th edition
  2. Copyright year: 2003, ISBN 0-534-40077-9
  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 to 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.

F. Organization and Scope

Topics and Times

 A fifteen division of topics corresponding to 73 days of classes are as follows (for a detailed schedule see section G).

            SECTIONS                 TOPICS

1          1.3,2.2-2.6                   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, 13.1-13.2       method of Frobenius, Fourier series of a function

4          13.2, 13.3                    Convergence of the Fourier series

5          13.4-13.5, 14.1-14.2   Fourier sine and cosine series

6          14.3, 14.4                    Fourier integral and Fourier transform

7          14.5-14.6, 15.1            Fourier cosine and sine transforms and Fourier finite transform

8          15.1, 15.2                    Legendre polynomials and Bessel functions

TAKE HOME MIDTERM TEST OVER THE WEEKEND OF OF OCTOBER 15TH

9          15.2, 15.3                    Strum-Louiville theory and eigenfunction expansions

10        15.3, 16.1-16.2            Fourier series solution of the Wave equation

11        16.2-16.4                     wave motion along an unbounded string and d’Alembert’s solution

12        16.4-16.7, 17.1-17.2   vibration of membranes and heat equation

13        17.2-17.3                     Heat equation and conduction in infinite medium

14        17.3-17.5, 18.1-18.5   heat conduction in cylinders and plates and the Dirichlet problem

15        18.5-18.8                     Dirichlet problem for different geometries and the Neuman problem

 

 

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.)

Dates                 section        homework

Week of Aug 14   1.3    pg.  27: 11, 13
                             2.2    pg.  73: 3, 13

_____________________________________________________________________________________________________________
 Week of Aug 21   2.4    pg.  81: 7, 19
                             2.5    pg.  85: 11, 19
                             2.6    pg.  97: 5, 13, 47

_____________________________________________________________________________________________________________

Week of Aug 28    4.1    pg. 168: 7, 17
                             4.2    pg. 174: 5,11

                             4.3    pg. 181: 1, 3, 5, 7, 19

 

 
Week of Sep 4      4.4    pg. 189: 1, 3, 11                                                                                           
                             13.2  pg. 635: 1, 5, 7

_______________________________________________________________________________________________________________       

Week of Sep 11   13.3    pg. 650: 5, 11
                            13.4    pg. 657: 5, 7, 13
                            13.5    pg. 666: 3, 5

Week of Sep 18   14.1    pg. 684: 1,9
                            14.2    pg. 687: 1, 7                                                                                                                                                                                        14.3    pg. 697: 1, 13, 27

_____________________________________________________________________________________________________________
Week of Sep 25 14.4    pg. 715: 5, 9, 13
                          14.5    pg. 719: 5
                          14.6    pg. 726: 7, 11

___________________________________________________________________________________________________________

Week of Oct 2   15.1    pg. 781: 3, 13, 17

                                      15.2   pg. 831: 3, 13, 33, 35

__________________________________________________________________________________________________________

           Week of Oct 9  15.3   pg. 835: 3, 9

                                     16.1    pg. 861: 3
 

TAKE HOME MIDTERM TEST OVER THE WEEKEND OF OCTOBER 15TH THROUGH 14.6.   STUDENTS SHOULD ARRANGE WITH ENGINEERING ONLINE TO TAKE THE TEST AS CLOSE TO THIS DATE AS POSSIBLE

EXAM NOTES 
Problem 5. Your answer should contain no integrals

___________________________________________________________________________________________________________

 Week of Oct 16   16.2    pg. 878: 1, 5, 13
                             16.3    pg. 893: 1, 3, 11, 13, 17, 19
                             16.4    pg. 903: 5, 17

___________________________________________________________________________________________________________
Week of Oct 23   16.5    pg. 907: 1 (light), a(1), a(2), a(3) and
                                       graph if you have the capability

                             16.6    pg. 910: 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.
                             16.7    pg. 913: 3, this is the non-zero velocity non-zero case.

____________________________________________________________________________________________________________

Week of Oct 30   17.2    pg. 938: 1, 5, 17, 21, 25.  For 21 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.
                             17.3    pg. 949: 1, 9, 13
                             17.4    pg. 952: 1

___________________________________________________________________________________________________________
Week of Nov 6   17.5    pg. 954: 1

                             18.2    pg. 959: 3
                             18.3    pg. 962: 5, 11

__________________________________________________________________________________________________________
Week of Nov 13   18.4    pg. 964: 1
                             18.5    pg. 971: 3
                             18.6    pg. 974: 3

__________________________________________________________________________________________________________
Week of Nov 20   18.7    pg. 978: 7

__________________________________________________________________________________________________________

Week of Nov 27   18.8    pg. 985: 1, 7, 13.


EXAM BETWEEN DECEMBER 5th AND DECEMBER 13TH : OPEN TEXT BOOK AND LECTURE NOTES.  BEGINNING WITH RESULTS IN THE TEXT PLEASE SHOW ALL STEPS IN THE SOLUTIONS.

The exam is to be a three-hour proctored exam.  Please arrange with the Engineering Online Office for a time and proctor.


  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 available at www.ncsu.edu/provost/academic_regulations/integrity/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)

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://www2.ncsu.edu/unity/project/www/ncsu/provost/info/academic_policies/ (link)