Math 260 Honors Calculus II

Semester: Spring 2009

Newton's diagram from Principia
mathematica
Lecture
Prof: Antonella Grassi
grassi AT math.upenn.edu
Time: Tue Thu 12 - 1:30 pm
Loct: DRL 4C8
Office: DRL 3E60
Phone: (215) 898-7887
Office
hours:
Tue 11 am - 12 pm
or by appointment
Prof. Grassi's Math 260 page. Math department's Math 260 page.
Text book: Tom Apostol, Calculus, Volume II, Second Edition,
Wiley, John & Sons: 1969. (find it at Amazon, BN)
Lab
T.A.: Asher Auel
auela AT math.upenn.edu
Time: Lab 201 Wed 6:00-7:30 pm
Lab 202 Wed 7:30-9:00 pm
Loct: DRL 4C8
Office: DRL 3E2
Phone: (215) 898-8175
Office
hours:
Wed 3 - 4 pm
Thu 2 - 3 pm
or by appointment
Note: This course is a continuation of Math 116 from Fall 08. See Prof. Harbater's course page, and Shea Vela-Vick's course page.

Description of course: This is an honors version of Math 240. It will cover the material in greater depth than that course, with more challenging problems and more attention to definitions and to the reasons behind the results. The course assumes familiarity with the material in Math 116, an honors version of Math 114. The precise sequence of topics within each semester will differ somewhat between the Math 114-240 sequence and the Math 116-260 sequence; but over the course of the two semesters, the honors sequence will cover the usual material and more.

Contents of course:
  • More Linear algebra: vector spaces, matrices, systems of linear equations, eigenvalues and eigenvectors.
  • Ordinary differential equations: linear differential equations, systems of differential equations.
  • Calculus of scalar and vector fields: functions of several variables, applications of differential calculus, line integrals, multiple integrals, surface integrals, div/grad/curl.
Two in-class exams (Feb. 24, Apr. 2)   15% each
Quizzes and recitation participation 15% total
Homework and class participation 25% total
Final exam (May 5) 30%
Grades: Your final grades will be based on several components. Notice that Prof. Grassi places more emphasis on exams than on weekly homework assignments in computing your final grade. On the other hand, completing your homework on a weekly basis is the most sure way to success on tests.
Group work, honestly: Working with other people on mathematics is highly encouraged and fun. You may work with anyone (e.g. other students in your section, in the course, not in the course, bums on the street, ...) on your homework problems. If done right, you'll learn the material better and more efficiently working in groups. The golden rule is:
Work with anyone on solving your homework problems,
but write up your final draft by yourself.
Writing up the final draft is as important a process as figuring out the problems on scratch paper with your friends, see the guidelines below. Mathematical writing is very idiosyncratic - I will be able to tell if papers have been copied - just don't do it! You will not learn by copying solutions from others! Also, if you work with people on a particular assignment, please list your collaborators somewhere on the top of the paper. Make the process fun, transparent, and honest.

Selected solutions: If there are problems that seem important enough and sufficiently misunderstood, I'll write up solutions and post them here. These solution sets contain good models and often explicit guidance for writing your own proofs.
  • SS 1 for HW 1, (posted January 28, 2009)
  • Solutions for Midterm 1, (posted April 28, 2009)
  • Solutions for Midterm 2, (updated May 3, 2009)
  • Solutions for practice final exam, (posted (and updated) May 3, 2009)



Policies

(or otherwise the small print)

Homework: Homework will be due in lecture every Thursday (except for the first Thursday of the semester, January 15th, there will be no homework due). Homework will always be posted the Tuesday of the week before it's due (except for the first assignment of the semester).

Late or improperly submitted homework will not be accepted. Period. If you know in advance that you will be unable to submit your homework at the correct time and place, you must make special arrangements with me ahead of time (like emailing it to me if you're trapped on a desert island). For example, if you observe religious holidays, then you already know what their dates are. It is your responsibility to hand in your homework early.

Prof. Grassi will decide each week on a selection of exercises from the text book, together with additional problems, to assign for homework. Once Prof. Grassi collects the homework on Thursday, she will hand it over to me. I will then review it, and select approximately three problems to grade that reflect especially well the concepts and ideas covered that week. I usually grade each problem out of three points, and give one point for general completeness. I consider whether you seem to understand the main idea of the problem and how to convey that understanding. See below.

In general, even if you haven't completed all the homework problems for the week, it is advisable to hand in what you have. This said, and in keeping with the guidelines below, I would advise handing in a selection of problems with complete solutions rather than shaky and poorly written-up solutions to all the problems. Your lowest homework score will be dropped. Of the remaining 12 homework assignments, each is only worth about 2% of your grade.

Your homework must be stapled, with your name and lab number clearly written on the top. Consider the pieces of paper you turn in as a final copy: written neatly and straight across the page, on clean paper, with nice margins and lots of space, and well organized. If I can't read it, I won't grade it.

Exams: Please direct all questions about exam and/or make-up policy to Prof. Grassi.




Homework guidelines: Generally, a homework problem in this course will consist of two parts: the creative part and the write-up.

  • The creative part: This is when you "solve" the problem. You stare at it, poke at it, and work on it until you understand what's being asked, and then try different ideas until you find something that works. This part is fun to do with your friends, and during this part, if you're having trouble, even in understanding what the problem's asking, you should come ask Prof. Grassi or myself for hints, either in person during office hours, or by email. This part should all be done on "scratch paper."

  • The write-up: Now that everything about the problem is clear in your mind, you go off by yourself and write up a coherent, succinct, well-written, and grammatically correct mathematical solution on clean sheets of paper. Consider this your final draft, just as in any other course. This part you should definitely NOT do with your friends.

    This will most likely be one of your first "real" math course, in the sense that some problems will require an argument and not just a long calculation. In order to write an argument, you'll have to use words to convey your ideas and how they connect together. Yes, it may seem strange that in a math course you'll have to use the English language. As in any other course where you use the English language, you'll need to use it correctly, i.e. you must use complete sentences, correct grammar and spelling, etc. It's true that mixing correct English with mathematical symbols is somewhat of an art, but the author of your text, for example, provides a good example of how to do this successfully. My friend Joe Rabinoff wrote a wonderful short note, while he was teaching Math 23 (the Harvard equivalent of this course), with some additional advice for learning how to write mathematics. Also, if your handwriting is illegible, then consider typing up your papers, as you would for an English class. If you are considering this option, you may want to learn LaTeX, especially if you are considering majoring in math, engineering, or physics. Ask me about details.

Please note that a fully correct solution requires both parts: having "figured out" the problem, but not having written it up (or having written up something incoherent that does not express what you know) or conversely, having written up many pages of beautiful prose that still fail to solve the problem, don't count for very much. You will be graded accordingly.