Elizabeth Denne Office: 312 Burton Hall Telephone: (413) 585 3757 Email: edenne[at]smith [dot] edu

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Quick links: Syllabus ..... Calculating Grades ..... Homework policy Website last updated 1/25/2012.

Essential Information:

Classes: MWF 10:00 - 10:50am in McConnell 404. There will be an extra class, a problem session, held each week at a time to be determined. Course webpage: http://www.math.smith.edu/~edenne/teach/math225sp12.html Office hours: TBA and by appointment. Office: 312 Burton Hall Phone: 413 585 3757 E-mail: edenne[at]email [dot] smith [dot] edu Required Textbook: Vector Calculus, Linear Algebra, and Differential Forms: A unified approach 4th Edition by John H. Hubbard, Barbara Burke Hubard. Matrix Editions 2009. Errata for the text can be found here. Drop date: The online drop date for the course is Wednesday February 8. Homework: The weekly homework assignments will be posted on Moodle. Help: There are many 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. Origami movie A fascinating 1 hour documentary about origami, from its origins to its place in modern art and engineering. Between the Folds was recently televised by Independent Lens on PBS. Something Fun The Declaration of Linear Independence. Click here.

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: Week 1 Section 3.1 (sort of) Multivariable functions. Section 3.1 and 1.3 Linear transformations Section 1.5 Open sets Week 2 Section 1.5 Limit of a function Section 1.5 Limit of a function Section 1.5 Continuity Review: quantifiers, logical negation, function definition. Length of a vector, dot product angles, cross product. Week 3 Section 1.5 Continuity Section 1.6 Theorems on continuity Section 1.7 Derivatives as a linear approximation Week 4 Section 1.7 Partial derivatives, the Jacobian matrix, Section 1.7 Jacobian and directional derivatives. Catch up day Midterm 1 here Week 5 Section 1.8 Rules for computing derivatives Section 1.8 The chain rule Section 1.9 Criterion for Differentiability (overview only) Week 6 Section 2.5 Review of Linear Algebra, including invertibility and rank-nullity theorem Section 2.10 Inverse function theorem Section 2.10 Implicit function theorem Week 7 Section 3.1 Manifolds three ways Section 3.2 Tangent Spaces Spring Break March 17 - 25 Week 8 Section 3.2 Tangent Spaces Section 4.1 Defining the Integral Section 4.1 Rules for Integrals, Examples Week 9 Section 4.1 Volume and pavability Section 4.3 What functions can be integrated? Section 4.5 Fubini's Theorem and interated integrals Midterm 2 here Week 10 Section 4.8 Determinants (review Section 1.4) Section 4.9 Volume and determinants Change of Variables in one dimension Week 11 Section 4.10 Change of variables Section 5.1 Parallelograms and their volumes Section 5.2 Parametrizations Week 12 Section 5.3 Computing volumes of manifolds Line Integrals and Fundamental Theorem Green's Theorem Week 13 Div, Grad, Curl Stokes' Theorem Review Day

Grades, attendance and other matters:

Prerequisites: Math 212 Multivariable Calculus and Math 211 Linear Algebra, or consent of the instructor. Exams: 2 self-scheduled midterm exams, and 1 self-scheduled final exam. Grading Policy: Homework 25%; midterms 20% each; final exam 35%. 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.

Homework policy:

Homework: Assignments are handed out each week and will be due the following 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. Submitting HW: Homework should be turned in to me (or left in my office door mailbox) on the day that the assignment is due. Usually HW will be due on Fridays at 4pm. 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.