Math 205b: Multivariable Calculus and Linear Algebra

 

Spring 2007
Monday, Wednesday, Friday at 10:10 - 11:00 a.m. in SC 1210
Thursday at 10:00 - 10:50 a.m. in SC 1214                       

Instructor: Prof. Bruce Hughes
Office: SC 1528
Phone: 2-6660
Electronic mail: bruce. DOT hughes @AT vanderbilt. DOT edu
Web page: http://math.vanderbilt.edu/~hughescb/Math205b_2007.html

Office Hours: MWR 3:10-4:00, or by appointment.

Teaching Assistant: Piotr Nowak   
 Office hours: MW 11 -1 and by appointment
 Office: SC 1229-C
 Electronic mail: piotrDOT.nowakAT@vanderbilt.DOTedu

Prerequisite: Math 205a

Textbook: Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds by Theodore Shifrin (published by John Wiley & Sons, Inc. 2005).

Syllabus: We will cover chapters 6 through 9 of the textbook, a few topics from the first five chapters that we didn't discuss completely in Math 205a, and a few additional topics such as: Complex vector spaces and eigenvalues, Jordan canonical form, Caley-Hamilton theorem, Hermitian matrices and unitary transformations, and Multivariable Taylor polynomials.

 

      Mid-Term Exams: Three tests will be given during the semester on the following days:

Final Exam: A comprehensive final examination will be given 3:00 p.m. to 5:00 p.m. on Tuesday, May 1.

Homework: Homework is an important component of this course and will be assigned daily. Some assignments will be collected and graded, others will be discussed in class by students and the instructor. On some assignments students will not be allowed to work together. On others, students are encouraged to work together. However, a student should not present as their own work solutions to which they did not make a substantial contribution. Collaborators in a solution should be acknowledged. Avoid looking up solutions in books. If you do use a book, be sure to site the source (including page number).

Grades: Your final grade will be determined from a total of 1000 possible points as follows:

  1. Three tests...............................................................................100 points each
  2. Final exam................................................................................150 points
  3. Homework (including in-class presentations and participation)...550 points
Attendance: Attendance is expected for each class meeting. More than two absences will be considered "excessive" on the mid semester progress reports. See the College of Arts and Science policy on class attendance in the University Bulletin.

Honor System: Vanderbilt's Honor Code governs all work in this course.

Web Resources for Undergraduate Mathematics Majors: The American Mathematical Society maintains a very useful page for undergraduate mathematics majors at http://www.ams.org/outreach/undergrad.html  It includes information on summer programs (Research Experiences for Undergraduates), semester programs, graduate studies in mathematics, clubs, undergraduate journals, competitions, careers, jobs and much more.

Notes on Proofs by Greg Friedman: Click here for pointers for beginners on how to do proofs.

Shifrin's list of errata for his book: Click here.

TeX and LaTeX:
A guide to using TeX in the micro computer labs at Vanderbilt: Click here.
For all other links for TeX information and downloads: Click here.

Digital Resources related to Multivariable Mathematics:
Mathematical Association of America's Digital Classroom Resources: Click here.
For a Collection of Tools for Multivariable Calculus: Click here.
 

Updated 28 December 2006