Math 132: Advanced Calculus
Fall 2009

Contents of this page

News
Lecture time and location
Prerequisite
Office hours
Textbook
Syllabus
Exams
How to...
Grading policy
Handouts
Homework
Policy on calculators
Academic integrity
Anonymous feedback
Furloughs

News

(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.


Lecture time and location

TuTh 2:30-3:45 in MH 424

Prerequisite

Math 32 and Math 129A (with a grade of "C-" or better in each) or instructor consent.


Office hours

ThTh 10:00-10:30, 11:45-1:00, 1:45-2:30, and by appointment


Textbook

Wendell Fleming: Functions of several variables, Springer UTM, 1987, second edition


Syllabus

Green sheet

We will study the differential and integral calculus of functions of several variables, both vector- and real-valued. The core of the corse is the first five chapters of Fleming. The culmination of the course will be the Inverse and Implicit Function Theorems, the development of Lebesgue integral and the Change of Variables Theorem.

If time permits, we will also discuss the calculus of differential forms with applications to physics.


Exams

There two midterms and a final exam. The exam schedule:
Midterm 1: October 1
Midterm 2: November 5
Final exam: take home, TBD
There will be no make-up exams.


How to...

How to study for this and other math classes

How to take the exam


Grading policy

Homework 20%, Midterms 40%, Final 40% + extra credit (= XC problems + participation)


Handouts

Banach's fixed point theorem


Homework

There will be weekly homework assignments.

Late homework policy:

1 class late: 50% penalty; 2 classes late: 75% penalty; 3 classes late: no credit.

# Due date Assignment Solutions
1 9/1 Sec. 1.2, ex. 5, 6, 10. Sec. 1.3, ex. 7, 8, 10 HW 1
2 9/10 Sec. 1.4, ex. 2, 4, 5. Sec. 2.2, ex. 1(a), 3, 6 HW 2
3 9/17 Sec. 2.2, ex. 7(a), 10. Sec. 2.3, ex. 3, 5. Sec. 2.4, ex. 4, 6. HW 3
4 9/24 Sec. 2.5, ex. 6, 8. Sec. 2.6, ex. 5, 10. Sec. 2.7, ex. 7. Sec. 2.8, ex. 4(a, b) HW 4
5 10/1 Sec. 3.1, ex. 1, 3, 4. Sec. 3.3., ex. 1, 3, 5. HW 5
6 10/15 Sec. 3.3, ex. 8, 10. Sec. 3.4, ex. 1, 2, 4, 6. HW 6
7 10/22 Sec. 3.4, ex. 7. Sec. 3.5, ex. 2ab, 3, 4, 5, 7. HW 7
8 10/29 Sec. 3.3, ex. 4, 6. Sec. 3.5, ex. 1, 9. HW 8
9 11/3 Sec. 4.1, ex 1. Sec. 4.2, ex. 1, 2. Sec. 4.3, ex. 5, 6.
10 11/19 Sec. 4.4, ex. 2, 5, 7. Sec. 4.5, ex. 1, 6.
11 11/24 Sec. 4.6, ex. 1, 2, 5. Sec. 4.8, ex. 1, 2.


Policy on calculators

Calculators will not be permitted on exams.


Academic integrity

By default, I regard my students as honest individuals and expect them to abide by the University policy on academic integrity.


Anonymous feedback

If you have any comments or suggestions, please fill out this anonymous feedback form.


Furloughs

This year across this campus and around the CSU system some class days will be cancelled because of furloughs. A furlough is mandatory un-paid time off; faculty and staff on each CSU campus are being "furloughed" two days per month.

It is important to recognize that these days off are not holidays. Instead, they are concrete examples of how massive state budget cuts have consequences for you as students and for me as a faculty member.

The CSU has suffered chronic underfunding for at least 10 years. This year the budget cuts are the worst in the history of our university system - 584 million dollars or 20% of our budget.

The CSU administration is attempting to deal with these cuts with huge increases in your student fees (32%), eliminations of your classes, and lay-offs of faculty and other university employees.

In addition to paying higher fees, you will be affected by reduced services and classes. The library will have shorter hours. Many campus support services will be decreased or eliminated. It will be more difficult to get signatures to meet deadlines. Classes you need may have been cut from the class schedule or are full.

If you would like to take action, or simply learn more, I strongly recommend you contact the California Faculty Association on campus.


Slobodan N. Simić

Last modified: Mon Nov 16 13:53:17 PST 2009