Elizabeth Denne Office: 310 Burton Hall Telephone: (413) 585 3757 Email: edenne[at]smith [dot] edu

Teaching Research Home

Quick links: Handouts ..... Homework Assignments ..... Essential Information ..... Syllabus ..... Calculating Grades ..... Homework and class participation policy

Course Announcements

Date Time Announcement Feb 22 3:00pm Office hours this week almost back to normal. Wed 2/25 11-2pm (may go longer), Thurs 3-5pm. Feb 16 9.20am Office hours this week: Thur 2/19 3-5pm, Fri 2/20 2-4pm. (Note: no office hours Wed 2/18 due to Rally Day.) Feb 10 9.30am Office hours this week: 12-2pm Wed 2/11, 2-4pm Fri 2/13. Feb 3 4.10pm HW 2 has been updated. Jan 26 3.00pm Office hours cancelled Wed 1/26. Extra hours 2-4pm Fri 1/30.

Essential Information:

Classes: TuTh 10.30 - 11.50am in Burton Room 209 Course webpage: http://www.math.smith.edu/~edenne/teach/math225.html Office hours: Wednesdays 12-1pm, 3-4pm, Thursdays 3-5pm, and by appointment. Office: 310 Burton Hall Phone: 413 585 3757 E-mail: edenne[at]email [dot] smith [dot] edu Required Textbook: Calculus on manifolds: a modern approach to classical theores of advanced calculus by Michael Spivak. Benjamin/Cummings Pub. Co., California, [1968], c 1965. Drop date: The drop date for the course is Friday February 6. Help: There are three main sources of help for the course. Firstly, each other! Talk to each other about the material, it will make the material even more enjoyable to learn. Secondly, the library. Use other texts and references. Finally, come talk to me. I have regular office hours each week when I am available to answer any questions you might have.

Cool Stuff for Advanced Calculus folks to do:

Reading Flatland: A romance of many dimensions by A. Square (Edwin A. Abbott). A classic for its satire of Victorian society as well as the neat way it develops an understanding of higher dimensions. Science and Technology Fair Monday February 2, 3:30pm - 6:0pm Campus Center Carroll Room. Click here for more details. Hudson River Undergraduate Mathematics Conference Saturday April 18. Click here for more details. If you are interested in attending, please let Professor Bush know by 2/19. Jhalak 7-9pm Friday March 27 Sage Hall. There is also a dinner before and a party afterwards. Mahler's Symphony No. 3 "Preston" Sunday, April 19 3:00 p.m. John M. Greene Hall. Tickets: $5 General; $1 Students (at the door only). Krista River, mezzo-soprano, joins the Smith College Orchestra, Jonathan Hirsh, conductor; also featuring the Smith College Glee Club and Chorus, Ryan James Brandau, director; the Mount Holyoke College Glee Club, Kimberly Dunn, director; the Amherst College Women's Chorus, Mallorie Chernin, director; the South Hadley Children's Chorus, Catharine Melhorn, director, and the Hampshire Young People's Chorus, K.C. Conlan, director. Community Service annual Fund Drive Friday April 24 at 4pm with a tea in Bodman Lounge (lower level of Helen Hills Hills Chapel) to raise awareness surrounding local hunger, sustainability, and fair food. The "Coming to the Table" Event is FREE, will feature speakers from the Northampton Survival Center and the Hilltown Food Pantry, and will provide an opportunity for students to discuss the issues in a round table format. One of the main questions the event focuses on is "How can we make local, good quality food available to low income families and individuals?" There will also be cider (and tea), assorted cakes and pastries, and a raffle to raise funds for local pantries.

Course Summary and Syllabus:

Summary: Functions of several variables, vector fields, divergence and curl, critical point theory, implicit functions, transformations and their Jacobians, theory and applications of multiple integration, and the theorems of Green, Gauss, and Stokes. Syllabus: Chapter 1 Review of linear algebra Open sets Multivariable functions and continuity Chapter 2 Differentiation Definition Basic results Partial derivatives and Jacobian matrix Chain rule Inverse function theorem Implicit function theorem Midterm 1 held March 10-13 Chapter 3 Integration Measure and content zero Integrable functions Fubini's Theorem Change of Variables Chapter 4 Integration on Chains Dual vector spaces Tensors Fields and forms Chains Integration and Fundamental Theorem of Calculus Closed and exact forms Midterm 2 held April 15-18 Coda: Fundamental Theorem of Line integrals, Green's Theorem and Stokes's Theorem.

Grades, attendance and other matters:

Prerequisites: Math 212 Multivariable Calculus, Math 211 Linear Algebra, or consent of the instructor. Exams: 2 self-scheduled midterm exams, and 1 take-home final exam. Grading Policy: Homework 20%; midterms 20% each; class participation 10%; final exam 30%. The class will not be graded "on a curve": if everyone deserves an A, everyone will get an A. Attendance: Attendance will not be taken at each class. However, it is much harder to learn the material on your own, so you are strongly encouraged to attend each class. You must complete the midterm exams and final exam. Make-up exams will only be given in special circumstances.

Final Exam Information:

What/when: A take home final exam from Thursday 30th April through 4.45pm Friday May 8. Click here for a .pdf file. Office hours: 1.30-3.30pm Sun May 3, 1-3pm Wed May 6, 3-4pm Thurs May 7 and by appointment. What you can use on the final: It is an open book exam. You may use your notes and homework from class, your textbook or any other reference. You must give references for material take from any source other than class work. Students are reminded that they are expected to follow the Smith honor code when doing this exam. Review questions: Practice questions from Midterm 2. Partial derivatives + chain rule review (119 Kb). Solutions: question 2 and question 3 (1.1Mb). Inverse function theorem review. Solutions found here. Implicit function theorem review. Solutions found here. Integration: definitions, measure 0, etc review. Solutions found here. Comments and corrections to solutions found here. Practice questions from Midterm 1. Norm and inner product review. Solutions found here. Open sets review Solutions found here. Continuity review Solutions found here. Differentiation review Solutions found here (1.1 Mb). Jacobian and chain rule review Solutions found here (1.4 Mb). Extra problems Solutions found here.

Handouts:

Date What it's about Where to find it Jan 29 QLC Review sessions Click here Feb 10 Tips for QLC tutoring sessions Click here Feb 26 Summary of derivatives Click here Mar 12 Derivatives, inverse and implicity function theorem notes Click here April 5 Notes on the proof of the inverse function theorem Click here April 22 Notes on Fubini's Theorem Click here April 22 Midterm 2 solutions Click here

Homework Assignments:

ComingComing Assignment Date due Feedback HW 1 (pdf file) Fri Jan 31 Solutions 1 (pdf file) HW 2 (pdf file) Fri Feb 6 Solutions 2 (pdf file) HW 3 (pdf file) Fri Feb 13 or Mon Feb 16 Solutions 3 (pdf file) HW 4 (pdf file) Fri Feb 20 Solutions 4 (pdf file) HW 5 (pdf file) Fri Feb 28 Solutions 5 (pdf file) HW 6 (pdf file) Fri March 6 Solutions 6 (pdf file) HW 7 (pdf file) Fri March 13 Solutions 7 (pdf file) HW 8 (pdf file) Fri April 3 Solutions 8 (pdf file) HW 9 (pdf file) 3pm Tues April 14 HW 10 (pdf file) 4pm Fri May 1 No extensions granted

Homework and class participation policy:

Class participation: Everyone is expected to particiapte - this includes asking and answering questions in class. The text book is very terse. The idea behind this part of the grade is to show you that you can read any mathematics text. Two students will be assigned to each class to create supplementary notes for the text. By the end of semester everyone will have a set of notes for the course and will have developed the skills and confidence to tackle even more advanced mathematics texts. How it works: The notes for each class help fill in any missing details. For example providing extra examples of concepts or theorems, looking at other texts for missing background material, thinking of good review questions. (I will provide guidance for this.) Two students will be assigned a class, say it is Tuesday. They will meet with me to discuss any questions or go over a draft. The final version of the notes will be due the following Tuesday. The notes produced will varying in length depending on the class, roughly 1-4 pages. Homework: Assignments are handed out each week. They will form an essential part of the course. The questions will consists of basic examples, simple proofs and problems which develop material beyond what is seen in class. They are due at 3pm each Friday. Submitting HW: Homework should be turned in to me (or left in my office door mailbox) by 3pm on the day that the assignment is due. Late HW: Late homework will be accepted only in exceptional circumstances and only with prior approval. HW grade: Your lowest homework score will be dropped at the end of the semester. Working together: You are strongly encouraged to discuss the homework problems with your fellow students and with me. However, you must write up your solutions by yourself. (Copying someone else's homework is unacceptable.) Please list your collaborators on your assignment. Collaborating on exams is not permitted. Students are expected to follow the Smith honor code. Keep your grader happy: To make the job of grading easier, please follow the following guidelines: Write your name on your HW. Neat, legible handwriting. I will not grade anything I cannot read! The problems should be in the order assigned. Staple (or paper-clip) all pages together.