Instructor |
Teaching Assistant |
Announcement |
all solutions are up online. hope this helps.
i will be in the office until 4 today. you could email me if you have any question over the weekends. i will try to reply you as soon as i can.
your final grade should be avalible by thursday next week.
good luck!
one more thing for #2 part (d), it's gonna messy in the last step of the gaussian elimination. you do not have to simplify the computations, but here is the final simplified solution
u(0)=(3e^{1/2}+8e+e^{3/2})/(9-6e-3e^2)=-1.05758...
u(1/2)=(3+4e+e^{1/2}-e)/(6-6e)=-0.667004...
u(1)=(12+3e^{1/2}-4e+e^{3/2})/(9-6e-3e^2)=-0.358068...
hope this helps.
again, make sure you know how to do all practise final problems. i will go over some of them in class on friday.
there are a few things i need to clarify for hw8.
1. cancel Exercise set 6.5 #11(a,b).
2. for exercise set 6.5 5(a), 9(a): to do the matrix decomposition, you could simply follow we i did in the class last week and today. you do not have to use the algorithms in the book.
3. for part (e,f,g), you do not hand them in this thursday. they are computational work and count as project 3 for your lab section. i believe they are due on dec 8, but please consult prof. liu for the confirmed due date and any implementation requirements.
4. please do the class final evaluation on eee.uci.edu by this week. this also count for 5% of hw8.
5. solution for hw8 will be posted online this friday.
remember that we will have the final exam next monday.
on wed, i will talk about some interesting properties for decomposing a strictly diagonal matrix and positive definitely matrix using LU decomposition.
on friday, i will have a review section. please prepare any questions you have. i will also go over some proofs in the practise final.
everyone is doing great this quarter. we have been learning lots of materials and i hope you guys enjoy the materials as much as i do.
i have uploaded a checklist you need to know for the final exam to the class webpage. it's under the "reference" section. hope this helps.
the final evaluation will be activated today in eee. please go and do it by dec 3. again, it will be counted 5% of the hw8. thanks a lot.
i have just uploaded the solution keys for hw5 and hw6 to the class webpage. please go and have a look.
since it's holiday on thursday next week, HW7 will due on wednesday next week, 11/22, IN CLASS.
i have uploaded the pratice final on web. you can find the link under the "reference" section. more details of the final will be coming.
thanks for doing the mid-evaluation.
concerning my class:
1. alright, i will slow down a little bit.
2. sure, i will have more examples in class.
concerning the hw and the grading:
1. yes, the homework problems are a little bit difficult. you have to understand the materials well before you know where to start. but this provides a very good way for you to learn. and this is why they weight 35% (more than the midterm). and since you have MUCH MORE time to work on the homework than the midterm, they should be more challenging than the midterm.
2. i have talked to the TA and we will make all problems equally weighted.
3. sorry that i will not change the grading scheme now. i will consider adding things like "dropping the lowest hw score" later in another course, but not this class.
concerning the discussion class:
1. i have this arrangement. on tuesday, the TA will review with you a little bit and then work on some problems similar to those homework problems in details. then you know what we are expecting from the homework. and you will have a day or 2 to work on the problem yourself.
2. then on thursday, the TA will review some materials and also work on some of the practice final problems in details.
i have uploaded a note for piecewise polynomial interpolation online. please check under the reference section in the class webpage.
hw5 and 8 are posted online. please check the class webpage. hw5 will due on nov 9, next thursday. please start working on it now.
there is a special arrangement of hw8. all non-computational parts will due 11/30. question 2(e-g) are computational work and this counts for programming assignment #3 for the lab section. you do not hand it in together with hw8. please consult prof. Liu concerning anything about the due date or other project requirements.
to ENCOURAGE you to do the final evaluation, 5% of hw8 will be the online evaluation. again, please help me to work on the mid-evaluation by wed 9pm. thanks.
someone left something in the classroom today after the midterm. please let me know if you wanna get it back.
i have finished grading the midterm. score will be uploaded to eee by tonight. i will give the paper back to you on monday in class, then you can check for any mistake i made in the grading. here are some statistics of the midterm:
max = 100
min = 0
median = 71.5
mean = 66.087
S.D. = 20.4024
i think the scores are not too bad. it's similar to what i expected. some students work extremely well. some are not doing very good. but anyhow, remember this midterm counts for only 25% of your final grade, while the final worths 45%. you may need to work harder if your score is more than 1 sd from the mean.
again, when you are checking your midterm score, please also spend a few minutes to do the course evaluation. otherwise i wont know how you feel about the class. thanks.
please found the solution of the practice midterm on the class website under the "reference" section.
a note on piecewise linear interpolation is on the way.
i have just turned on the midterm evaluation form on eee.uci.edu. please help me to do it by wed next week and so i know how you feel about both my teaching and also the class. remember, i can only know how many people participate the evaluation and who did the evaluation, but not what you wrote on it and how you rate the class and my teaching. so feel free to write anything.
i have received some requests asking to postpone the due date for hw4. since i have just finished bi-linear interpolation today, let's postpone the due date to next tuesday (10/31) in the discussion class.
solution for hw3 is up online. please check it out.
i will go over Q4-11 of the practise midterm on wed in class. please try to work on them before class.
good luck for the midterm.
you are given
g(x)=x-2f*f'/(2[f']^2-f*f'').
you NEED to prove both g'(p)=g''(p)=0. for g'(p), you should get
g'(x)=f^2 (3[f'']^2-2f'f'')/(2[f']^2-ff'')^2
now, since f(p)=0, you have g'(p)=0.
to compute g''(x), you first write g(x)=f^2*h(x) where
h(x) = (3[f'']^2-2f'f'')/(2[f']^2-ff'')^2
so, g''(x)=2ff'*h(x)+f^2 h'(x)=f*( 2f'h+fh' )
and so you get g''(p)=0.
hope this helps.
i have uploaded the homework solutions 1 and 2 on the class website. they are just my solution and do not reflect the marking scheme the TA is using. these solutions are just some suggested solution. let me know if you think there is anything suspicious.
hw3 solution will be out by monday next week.
i have also posted a note "maximizing a function" under the "reference" section. if you are not very sure how to maximizing a function, which will be used several times in this class, you may wanna refresh your memory a little bit.
hope these helps.
hw4 is up online. please go the class webpage to have a look. this hw will due on october 26. this means you will have around 2 weeks to work on it.
yes, i will post the homework solutions online. but i have to find a scannar to scan them first. i will work on it and hopefully i can get it done by next friday.
i have decided to have the midterm exam on friday october 27 in class. there is a practice midterm posted online. please go and look at those questions. you can find the link under the "reference" section in the class webpage. i will discuss those problems in class on wednesday october 25. please try it out before the class. we will also have a question section that day. please prepare anything you wanna ask.
in Q2 the algorithm for trisection method, there is a typo in Step 3. the expression
q=a+2(b-1)/3
should be
q=a+2(b-a)/3.
and if you missed the class today, we have postponed the due date to tuesday in the discussion class.
hw3 is up. please check my class homepage.
note that the due is now moved to thursday in the disssion class. then you guys can come to my office hour or TA's office hour to ask about it before the due.
concerning the midterm, i am planning to have the midterm after we have finished Chapter 3 (Interpolation). and that would be near the end of this month or early next month. if you have any specific date (with a strong reason) you dont want to have the midterm, please let me know by wednesday (10-11) next week.
another question i got so far concerns the portion of proof in this class. as i mentioned in the first class, we will explain how one can solve a problem numerically, by "teaching" a computer to do it for us. this is the "NUMERICAL" part of the course. and then, we will ask questions like "how it works?", "why it works?", "when it works?"... this is the "ANALYSIS" part.
since there is this "ANALYSIS", please expect to prove something in the midterm and the final. i would say, PROBABLY at most half of the questions in midterm and final are proofs.
there are some questions concerning this problem. here are some hints to this problem.
here is what my suggestion:
case 1: if x_0=sqrt(A). x_n=sqrt(A). and so lim_{n->inf} x_n = sqrt(A).
case 2: if x_0>A, prove sqrt(A)< x_1< x_0 and this implies sqrt(A)< x_{n+1}< x_n< ...< x_0. since {x_n} is decreasing and is bounded below by sqrt(A), the sequence will converge. now, let p be the limit and you can prove that p=sqrt(A).
case 3: if 0< x_0< sqrt(A), then you can prove sqrt(A)< x_1. now, use the result from case 2, you can conclude lim_{n->inf} x_n=sqrt(A).
of course, other solutions are welcome.
this problem is interesting because it comes from solving f(x)=x^2-A using Newton's method. (of course we know the roots are sqrt(A) and -sqrt(A).) this exercise shows that if you pick an initial guess x_0>0, newton's method will converge to sqrt(A); if you pick an initial guess x_0<0, newton's method will converge to -sqrt(A).
i have been receiving some requests concerning my office hours, i will now add an extra hour each week. here are my new office hours:
Mon, Wed 200pm-400pm
but since there are department meetings at 4pm on monday and wed, i may sometimes need to leave my office at around 350pm.
in case you didnt notice, HW1 was posted online and it will due NEXT MONDAY 10-2. you can find the questions here, with solutions later:
http://math.uci.edu/~syleung/105a.06f/
i have just posted the questions for HW2 online. it will due 10-9. you should have plenty of time to do it.
if you have any suggestions for the class, feel free to let me know. hope you enjoy the materials as much as i do.
Homework |
There will be 8 homework assignments. They will be collected in class. You will find the problems, with their corresponding deadlines, in the course homepage. No late homework will be collected.
Homework Solution |
Reference |
Exams |
There will be one midterm exam and one final exam. No makeup exam will be given.
Grading System |
Your grade will be determined according to 30% homework, 25% midterm and 45% final.
Schedule of Lectures (Tentative) |
Actual Schedule |