Advanced Calculus Buck Homework Solutions

(12/17) I just finalized the grades, so if you'd like to find out what you got, just email me.

I also posted Homework 12 solutions. At this point, I don't know if I'll be posting HW 11 solutions.

And finally: HAPPY HOLIDAYS AND HAVE A WONDERFUL WINTER BREAK!

(12/15) Here are some hints for the final exam.

(12/8)Homework 12 hints have been posted.

(12/2, part 2) The final exam has been posted. It's due on December 16 by 2 PM.

(12/2) I will have regular office hours tomorrow (12/8). After that my office hours will be: Wednesday (12/9) 2:30-4, Monday (12/14) 1-2:30, and Wednesday (12/16) 10-12.

(12/2)Homework 10 solutions have been posted.

(12/1)Homework 11 hints have been posted.

(11/25) A typo in problem 5b in homework 12 has been corrected. The problem, stated correctly, says: if f is a non-negative integrable function whose integral over a rectangle Q equals zero, then f equals zero, except possibly on a set of measure zero. Thanks to Khan for pointing out the typo.

(11/24)Homework 10 hints have been posted.

(11/23)Homework 9 solutions have been posted. The last homework (number 12) for the semester is also online and is due on December 3.

(11/16, part 2) A few words about the notation (in response to anonymous feedback just received). If f is a function, then f_{ij} (f with the subscript ij) in Fleming's book always means the second order partial derivative with respect to x_i and x_j (in that order). For the same object, I prefer to use (and have been using) the "del-notation": \del_{ij} f, or the notation f_{x_i x_j} (both forumulas appear as they are written in LaTeX). Hope that clarifies things.

(11/16)Midterm 2 solutions have been posted. Also, HW 8 solutions and homework 11 (due on November 24) have been (re)posted.

(11/12)Homework 9 hint has been posted.

(11/11, part 3)Homework 10 has been posted and is due on November 19. By the way, I temporarily took down homework 8 solutions. I'll repost them on Thursday (the due date for the rewrites).

(11/11, part 2) As requested, hint for problem 3 on the midterm: apply the Chain Rule. It may also help to write \gamma(t) as (x(t),y(t)).

(11/11)Homework 8 solutions have been posted.

(11/5)Homework 8 hint has been posted. Sorry for the delay.

(11/4, part 2) The second midterm has been posted and is due on Thursday, November 12 in or before class. Please email me if you have any questions or come by my office next Tuesday. (Remember that tomorrow, 11/5, is our furlough day.)

(11/4)Homework 7 solutions have been posted.

A few words about the final exam. It will be take-home and there will be six problems on it. I am planning to assign it on the last day of class, December 8 and give you about a week to do it. If this date doesn't work for you, please let me know ASAP.

(10/29) Well, I made another mistake (sleep deprivation can make even simple addition hard) in the "last problem" on homework 8, so you should jusk skip it. Sorry if you wasted a lot of time on it! If you are curious what the correct problem would ask, try this one: For which value of a is the function |x|^a harmonic on E^n minus the origin?

(10/28) The last problem on homework 8 is wrong. Thanks to Khanh for pointing that out. Here is the correct problem. Sorry about that! You can turn in the last problem next Tuesday instead of tomorrow.

(10/27, part 2) Homework 7 hints are here.

(10/27)My extra office hours tomorrow will be from 1:30 to 3 PM.

(10/26, part 2) I just posted homework 9, which is due on Tuesday, November 3.

(10/26) My office hours tomorrow will be: 10-10:30 and 1:45-2:30 (i.e., no noon office hour - sorry about that). I will have extra office hours on Wednesday (10/28), either 12-1 or 1:30-3 (TBD).

(10/23) I just uploaded homework 6 solutions. By the way, for problem 6(d) in section 3.3, you are allowed to use a computer to plot (or gain some intuition about) the sets f(x,y) = c.

(10/21) I just posted Homework 8, due on October 29.

Contrary to what I may have said, we will have one more furlough day this semester: November 5 (Thursday). There will be no class that day. This is the day I will assign (take-home) Midterm 2, so you will at least get some extra time to do it.

And lastly, I will have extra office hours next Wednesday, October 28, from 12 to 1 PM.

(10/20) Here are some hints for Homework 6 revision. Also, my office hours on Thursday, October 22, will be a little shorter (due to an "advising social" in MH 320): 10-10:30 and 1:45-2:30.

(10/14)Homework 5 solutions have been posted. Also homework 7 has been assigned and is due on October 22.

(10/9)Midterm 1 solutions have been posted.

(10/8)Homework 5 hints have been posted.

(10/7)Homework 6 has been posted and is due on Thursday, October 15.

(10/5, part 2)Homework 4 solutions have been posted. Please let me know if you have any suggestions how I can make these solutions more helpful.

(10/5) I was asked to give a hint for problem 3 on the midterm. Here's one: look at f on the unit sphere S and relate f(x), for general x, to f(p) for some p in S using the given assumption about f, namely, f(ax) = a f(x), for all positive a and all x.

(10/2) I just posted a handout on the Banach fixed point theorem. Read it to get an idea why Lipschitz functions are important.

(9/30, part 2)Midterm 1 has been posted. It is due on Thurday, October 8 in or before class.

(9/30)Homework 3 solutions have been posted. I will post the midterm this evening and also bring copies of it tomorrow to distribute in class.

(9/29)Homework 4 hints have been posted.

(9/25)Homework 3 hints have been posted.

(9/22)Homework 5 has been assigned and is due on October 1. Recall that Midterm 1 will be on October 1. More details to follow.

(9/21)Homework 2 solutions have been posted.

(9/16, part 2) Next Tuesday, September 22 is a campus furlough day. This, among other things, means that there will be no class that day. Recall that the reason for furloughs is the 584 million dollar cut from the CSU budget for this year. To put this in perspective: this cut is happening at the same time when this society instantly finds 700+ billion dollars to help the "financial industry" and the likes of Goldman Sachs, JP Morgan, Citigroup, etc. (Not to mention billions spent on war.) For more information on furloughs, click here.

(9/16)Homework 1 solutions have been posted.

(9/14)Homework 4 has been posted and is due on September 24. All the problems are for subsets of Euclidean space (i.e., ignore terms like "topological space"). I will post solutions to homework 1 tomorrow.

My plan is to summarize and finish the topology part of the course (i.e., the notions of connectedness and compactness of subsets of Euclidean space) this week. I will not talk about general topological and metric spaces, although I encourage you to read about them in Fleming.

In case you thought topology is just an abstract branch of mathematics with no applications, check out this aricle. In fact, topology has many applications to diverse fields as physics, robotics, chemistry, and many others. (Though as it always goes, topology was originally invented/discovered to solve "internal", or "pure", mathematical problems.)

(9/10) If you're thinking of getting a math Ph.D., come to the Graduate School Workshop next Wednesday, Sept. 16 at 2 PM (room MH 426). We will discuss questions like, how to prepare for and get into grad school, what your life will be like in grad school, and what kind of job you can get afterwards. If you're planning to attend, please send me an email. Note that snacks will be served!

(9/7)Homework 3 has been posted and is due on Thursday, September 17.

Tomorrow, September 8 (due to a specialist exam I'm giving), my office hours will be from 1:30 to 2:30. Sorry for the inconvenience.

(8/31, part 2)Homework 2 has been posted and is due on Thursday, September 10.

(8/31) My office hourse tomorrow will be: 10:00-10:30 (as usual) and 1:30-2:30. On Thursday I'll have my regular office hours.

For grading the homework I will use the rewrite system. This means that after I grade your homework, you will be allowed to revise and rewrite it based on my comments and suggestions. The revised homework is always due the first class session after you receive your homework back. The revised assignment will then be regraded and the score you receive will be the score I will use for your final grade. However, there is one basic rule: you have to try to solve every assigned problem the first time around (which means you have to write down your attempt at a solution), otherwise you will not be allowed to do a rewrite of that problem.

(8/24) Welcome to Math 132! Please check this page often for latest updates. All homework assignments, take-home exams, solutions, handouts, etc. will be posted here. I usually will not give out hard copies of these course materials.

And last but not least, Homework 1 has been posted and is due on Tuesday, September 1. In the future, homework will usually be due on Thursdays.

This material is rather challenging. I am happy to report that in spite of the challenging nature of the material many of our undergraduates have been equal to the task of dealing well with it. You should not take this course unless you have had prior experience with proving things and with mathematical abstraction. We don't have higher level honors courses but if we did these courses would be among them. It is also absolutely necessary for more advanced work in mathematics and can come in handy in other branches of science and engineering.

In previous calculus courses you learned to differentiate and integrate functions of one or more real variable and to apply these techniques to solve problems of various sorts. You probably didn't pay may attention to mathematical rigor. In fact, when you studied things like integration formulae in several variables you probably didn't pay much attention to intellectual rigor either. I assume that part of the reason you are taking this course is to get all that stuff straight.

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