Last modified: Fri Jan 27 13:33:17 EST
2006
Neil Martinsen-Burrell
Neil Martinsen-Burrell
| Instructor: |
Neil Martinsen-Burrell Phillips 304B 919-962-9820 nmb@unc.edu |
| Text: | M. D. Greenberg, Advanced Engineering Mathematics, Second Edition. |
| Class Meets: | Phillips 381, TTh, 12:30-1:45 pm |
| Office hours: | Tu 3:00-4:30 W 3:30-5:00 |
| Syllabus |
Prerequisites: MATH 83 & PHYS 24-25 or
equivalent
Note for students new to UNC: MATH 83 comes after the completion
our standard 3 semester calculus sequence (MATH 31, 32, 33). It
is an introduction to linear algebra and differential equations.
It is assumed that students enrolling in MATH 128 know most of
the material in chapters 1-4 of the text.
Objectives: This is the first half of a year-long sequence in applied and computational mathematics for advanced students of engineering and science. The class places equal emphasis on scientific applications which are modeled by differential equations, analytical methods of solution of these equations, and numerical solutions.
Topics:
Programming: Programming is part of the course; each student will be expected to learn Matlab and use it on some of the homework assignments. Online tutorials are listed on the web page.
Homework: Homework and/or programming projects will be given approximately weekly and posted on the course website. Collaboration on homework is allowed and encouraged but copying from another person is prohibited.
Good Problems: Six Good Problems are assigned throughout the semester. These will be ordinary homework problems that will be graded on both content and presentation. The object of this is to practice mathematical writing regularly but in small doses.
Extra Credit: There will be opportunities to complete additional assignments for extra credit.
Exams: There will be two midterm exams and one final exam on the following dates:
Grading
| Homework | 30% |
| Midterm 1 | 20% |
| Midterm 2 | 20% |
| Final | 30% |
| Extra Credit | 10% |
| Total | 110% |
A 90% will guarantee you at least an A-, 80% a B-, 70% a C- and 60% a D.
Honor Code: All work is expected to be completed in accordance with the Honor Code. In particular, copying any other person's work is prohibited.
November 18, 2004
November 23, 2004
Homework 1 (solutions): Due
Th. 9/2
Section 2.3, p. 44: 12(a)
Section 4.5, p. 228: 3(b,c)
Section 5.2, p. 254: 8
Section 5.3, p. 261: 1(e), 11(c)
5.3 1(e) is Good Problem
#1
Homework 2 (solutions): Due
Th. 9/9
Section 5.3, p. 260: 7
Section 5.4, p. 266: 1(e,j,u), 5(a)
Section 5.5, p. 274: 1(e), 2(g), 5(d,j)
5.4 5(a) is Good Problem
#2
Homework 3 (solutions): Due
Th. 9/16
Section 5.6, p. 280: 1(b,e)
Section 5.7, p. 289: 4(a,b)
Section 6.2, p. 298: 1, 2(g)
Get access to Matlab (instructions on using AFS here,
here and here;
instructions on ordering from Software Acquisition here) and print the output
of the following command:
x=0:.1:1;plot(x,x,'-',x,x.^2,'--',x,x.^3,'-.') and
explain what it does.
5.7 4(a,b) is Good Problem
#3
Programming Assignment 1: Due Th. 9/23
Modify the Matlab script euler.m to implement the second and
fourth order Runge-Kutta methods given in class. Use these to
solve the initial value problem
with the exact solution y = (ln x)2 + ln x. For each of the three methods (Euler, RK2, RK4) show that the global error has the expected order by plotting the natural log of the error vs. the natural log of h (ln E vs. ln h) and thus showing that E = O(hp). Turn in the codes that you used and a written explanation of your results including plots.
Homework 4 (solutions): Due
Thu 9/30
Section 17.2, pp. 849-850: 6, 11(b,c), 12(a,d,k), 17
17.2 17 is Good Problem
#4
Note: On number 11, only give the fundamental period.
Homework 5 (solutions): Due
Thu 10/7
Section 17.3, p. 866: 4(c,k,n), 14
Section 17.4, p. 873: 2(b,d,g)
Section 17.5, p. 880: 2(c), 4(a)
17.3 14 is Good Problem
#5
Homework 6 (solutions): Due
Thu 10/21
Section 17.9, p. 919: 2(d,g)
Section 17.10, p. 932: 4(b), 5(b), 6(f,n), 12
17.10 5(b) is Good Problem
#6
(Note on 17.10.12: The minus sign in equation (12.3) should not
be there.)
Optional Homework A (solutions): Not Due
Section 17.11, p. 939: 4, 9(a,b)
Programming Assignment 2: Due Tue 11/2
Using the Matlab file fft_tests.m,
investigate the Discrete Fourier Transforms of the following
functions:
heaviside(x))where N is the number of points included in your sampling of the function. Include printouts of your plots and explanations of the results of the transform for each of the above functions.
Hint: The last two functions have the same DFT due to aliasing, where two functions with different frequencies have the same function values when sampled at equally spaced points.
Homework 7 (solutions): Due
Thu 11/11
Section 18.2, p. 953: 2(a,b), 3(b,g)
Section 18.3, p. 974: 4(a), 6(c,g,k)
There is no Good Problem.
Homework 8 (solutions): Due
Thu 11/18
Section 18.3, p. 974: 6(m), 13, 15, 21(a)
Homework 9 (solutions): Due
Thu 12/2
Section 18.4, p. 989: 10
Section 20.2, p. 1067: 1(d)
Section 20.3, p. 1084: 2(c)
Due Thu 10/28
This class deals with material named after some of the most
famous mathematicians, engineers and physicists of all time. They
include Euler, Laplace, Fourier, Gibbs, Bessel, Legendre,
Heaviside, Dirac, Taylor, Liouville and others. Choose one person
whose name appears in our class and write a 2-3 page paper about
them. Who were they? What were they famous for? What else did
they invent/discover? Explain how their name came to be connected
to the material in this course.
Due Thu 12/16
Problem 6 in Section 20.3 deals with a famous problem in
aerodynamics: finding the lift generated by airflow over a
rotating cylinder. In full Good
Problems style, complete this problem. You may need to look
at Section 16.10 to explain Bernoulli's Equation or consult a
fluid dynamics textbook for more details.
Matlab Tutorials