Numerical Analysis I - Math 4500/6500

Instructor: Caner Kazancı. Best way to reach me is e-mail: caner@uga.edu
Office: 440 Boyd Graduate Studies and 410 Driftmier Engineering Center, (706) 542 0863.
Office Hours: 10:45am-11:30am Tuesdays and Thursdays, and anytime by appointment.
Course Information: You can download the syllabus here.

Announcements

  • Here are the solutions for the last HW assignment.
  • Final exam will be on Thursday, December 14, between 8-11am.
  • Your graded last HWs, and the solutions will be available outside my office (at the engineering) today (Monday, 11/20) after 12pm. Here's a pdf version of the solutions.
  • The second test is scheduled on Tuesday, November 21. There will be a review session on Thursday, November 16. The test will cover the course material since the first test until and including the class on Tuesday, November 14.
  • The second test does not include the whole section 6.1, just a part of it. Here are some exercies that you might wish to look at:
    6.1.4., 6.1.7., 6.1.8.
  • There is a typo in HW set 9 on 17(d):
    h*f(a)-(1/2)*h^2*f'(a) -> h*f(a)+(1/2)*h^2*f'(a)
  • The first test is scheduled on Thursday, October 12. The test will include topics until section 4.2, and part of section 4.3, the Richardson Interpolation. In other words; the test will include topics of Hw1-Hw6. There will be a review class on Tuesday, October 10th, where I will answer your questions.
  • From now on homeworks will be assigned on Fridays, instead of Thursday evenings, as there is no sense in assigning a new HW while the previous one is still due next day. The due dates will not change, HWs are still due Fridays by noon.
  • Octave help: You can find a nice and short tutorial here. A longer tutorial is here. And Octave official documentation can be found here.
  • You need to show all your work on solutions of the HW asignments. Grades will be assigned to correct solutions, not correct answers. For example; just saying that the root is equal to zero in problem 10 (Section 3.1) will be graded as 0/10 unless there is a solution in your paper that leads to this answer. On the other hand, a solution attempt that is correct in nature will definitely get partial credit even though the final answer might be wrong.
  • For computer problems in HW assignments, please attach all your codes to a single e-mail and send it to Jianbao (jwu@math.uga.edu) before the due date. Also do not forget to include printed hard copies of your codes along with the solution of the regular HW problems; please hand them in together.
  • We covered how to use Octave on Tuesday 9/5. Here's the Octave diary file that includes allmost eveything we did. Here are the first two Octave/Matlab codes we have written: first_octave_code.m, max_new.m.
  • Homework Policy: Unless announced in class, or on this website; homework assignments will be posted here Fridays; and they will be due Fridays by noon (obviously not the next day) in the mailbox of Jianbao Wu. His mailbox is located at 4th floor of Boyd Graduate Studies building. No late HW's will be accepted.
  • Some HW assignments are going to contain a starred problem. These problems are optional for students registered in MATH 4500; but a must for those who are registered in MATH 6500. The only reason why this policy exists is because it is a rule of the graduate school, that we (all instructors) must have different (greater) expectations for the graduate students in split-level classes. Please note that all students will be treated equally, whether graduate or undergraduate, whether from mathematics or not, when it comes to tests and assigning grades.
  • There will be class while I am away. Andrew Sornborger will be starting with the third chapter of the book. I will not be repeating what he's going to cover, and you will be responsible form that material. If you have any questions about the first HW assignment, please ask them to me after I arrive, on Tuesday 9/5.
  • You can download Octave for Windows here. Please let me know if you have any trouble installing or running it. This is a relatively recent version, and it seems that they have eliminated some of the annoyances of the previous version.

Homework Assignments

  • Homework Set 1 (due Wednesday, 9/6/06)
    Section 1.2 : 1., 9., 20., 52.
    Section 2.1 : 2.
    Section 2.2 : 20., 21., 38.
    Section 2.3 : 1., 4., 27., 29.
  • Homework Set 2 (due Friday, 9/15/06)
    Please read the announcements before starting this HW set.
    Section 3.1 : 8., 10., 12., 14(c).
    Section 3.1 (Computer) : 1., 3. (Modify bisection.m which was written in class)
    Section 3.2 : 9., 12(b)., 15., 19.
    Section 3.2 (Computer): 14., 19.
  • Homework Set 3 (due Friday, 9/22/06)
    Section 3.2 : 33., 38., 39.
    Section 3.2 (Computer) : 23(d)., 23(f).
    Section 3.3 : 1., 3., 13.
    Section 3.3 (Computer): 1.(first part only, do not do the Newton's method)
  • Homework Set 4 (due Friday, 9/29/06)
    Section 3.3 (Computer): 7.
    Section 4.1 : 1., 2., 4., 10., 12., 27., 34.*, 35.*
  • Homework Set 5 (due Friday, 10/6/06)
    Section 4.1 : 46.
    Section 4.2 : 2. 4. 5. 10.
    Section 4.2 (Computer): 1. 2. 5. 7. 10.
    On 4.2.5: Here, a linear interpolation is a polynomial interpolation with only two nodes.
    On 4.2.1-2(computer): Use the code given in class; and instead of printing error values at 41 nodes; print the computer plot and hand in with your solutions.
    On 4.2.5(computer): Again, use the same code and include a plot.
    On 4.2.7(computer): Do only for 16; and include plots (for uniform and Chebyshev nodes) instead of printing errors.
    On 4.2.10(computer): As an experiment, plot the product(the term in absolute values) on [-1,1] and observe that the plot lies below 2^n. Include the three plots (n=3,7,15) with your solutions.
  • Homework Set 6 (due Tuesday, 10/17/06) Please see the announcements
    Section 4.2 : 17.
    Section 4.3 : 2. 3. 6. 9. 12. 16. 18.
    HW Problem : To find the derivative of cos(x) at x=1; compute (cos(1+h)-cos(1-h))/(2h) for h=2, h=1, h=0.5 and h=0.25. Using a calculator, carry out Richardson Extrapolation to achieve the highest order approximation possible using this data. Provide at least 4 digits of precision, and include all steps in your solution.
    There is a typo on problem 4.3.9b. The first and the last terms in the brackets are the same. The last one should be f(x-2h) instead of f(x+2h). Thanks Larry for pointing this out. Also on problem 4.3.3, please only show that the error is of second order. Thanks Tim for pointing this out.
  • Homework Set 7 (due Friday, 11/03/06)
    Section 4.3 : 21. (Hint: Start by t*f(x+t) = t*f(x) + t^2*f'(x) + ... )
    Section 5.1 : 1. 2. 4. 6.
  • Homework Set 8 (due Friday, 11/10/06)
    Section 5.1 : 11. 12.
    Section 5.1 (Computer) : 3.
    Section 5.2 : 1. 4. 7. 8. 13. 16. 17(c). 18(a). 29.
  • Homework Set 9 (due Friday, 11/17/06) Please see Announcements for the next test date!
    Section 5.2 : 6. 9. 17(a). 17(d). Please see announcements for a typo in 17(d).
    Section 5.2 (Computer) : 2(a). Write the code so that the only input it takes is the number of sub-intervals. Run your code using 10, 100, 1000 subintervals and print the error (Error=|2-approximation|) for each case. Does the change in the error represent the quadratic convergence of this method?
    Section 5.3 : 2. 4. 8. 21. 22.
    Section 5.3 (Computer) : Use your code in 5.2.2(a) and a calculator to compute R(4,4) for the same integral.
  • Homework Set 10 (due Monday, 12/11/06)
    Section 6.1 : 4. 7. 8.
    Section 6.2 : 1. 2(a). 2(b). 3. 5. 7. 12. 13. 16.
    Section 6.2 (Computer) : 10. (Try for n=1,2,3 for each integral)