Multivariate Calculus with Matrices
Math 2720, Section 105
Fall Semester 2009
General Information and Syllabus
Homework Assignments and Announcements
Contact information for your instructor
Course Description. (Copied from University website.) Vectors and geometry in two and three dimensions, matrix algebra, determinants, vector differentiation, functions of several variables, partial differentiation, linear transformations, multiple integration, and change of variables. The computer algebra system Maple will be used to explore some of these topics. Prerequisites & Corequisites: Prerequisite: MATH 1710 or MATH 1230. Credits: 4 hours.
Coordinates of Class Meetings. Mondays, Tuesdays, Thursdays, Fridays, 8:00-8:50, room 3395 of Rood Hall.
Basis of Evaluation.
Homework: 10%
Quizzes (about 10): 25%
Maple Lab Project: 10%
50-Minute Exams (3): 30%
Final Exam: 25%
Homework. There is at least one homework assignment for each section we cover during the semester. Generally, you are given a week to work each assignment from whence it is assigned.
Quizzes. Quizzes count for a significant part of your grade. Quizzes are usually given 10-15 minutes before the end of class. Expect a quiz nearly every week.
Maple Lab Project. At some time near the middle of the semester, you are assigned a project whose completion requires use of the computational software Maple. Your work on this project is due near the end of the semester. Maple is installed on all of the computers in the Rood Hall computer lab. You must work on this project in teams of 2 or 3 students per team.
50-Minute Exams. There are 3 exams given throughout the semester, each lasting a duration of 50 minutes. The dates of the exams are September 25, October 23, and November 24. The topics covered on each exam are announced at least a week in advance of the exam.
Final Exam. The final exam is comprehensive over all material covered throughout the semester. Unless otherwise announced or arranged, the final exam lasts from 10:15 a.m. until 12:45 p.m. on Tuesday, December 15.
Required Text. Thomas H. Barr. Vector Calculus. 2nd ed. Prentice Hall, 2001. ISBN 0-13-088005-1. Bring your copy of the text to every class meeting.
Calculator. You must have a graphing calculator, know how to use it, and bring it to every class meeting. Calculators are allowed on most quizzes and exams, although exceptions are bound to arise. You are not allowed to use a device having a qwerty keypad on any exam or quiz.
Other Technologies. Neatness is a requirement for all homework you submit. If you normally use pencil, eraser, straightedge or ruler, and standard notebook paper, then this is probably not a major concern. Thus, you are advised to refrain from using ink pens, remove the rough edges if you use a spiral-bound notebook, and bind your pages with a staple or a paper clip if necessary. More suggestions are offered here.
Student Conduct. Your instructor assumes that you are enrolled in this class because, at the very least, you want to participate in the University Community. In case there is any doubt, there is a code of conduct which you must follow and which your instructor enforces. In particular, the use of any radio communication device during class violates this code (unless there is a life-or-death emergency). These policies and procedures are described at the website for the Office of Student Conduct.
Expectations. Attend and participate in every class meeting. Spend at least 10 hours per week outside of class on this subject. Improve your writing skills. Improve your sketching/drawing skills. Take pride in your work. Be enthused and curious about calculus and geometry. Appreciate three dimensions and try to imagine more. Maintain a positive attitude. Have an open mind, and never assume anything.
Course Outline. This course covers topics in multivariable calculus, especially vectors, linear transformations, matrices, dot and cross products, quadratic forms, conic sections, quadric surfaces, functions of several variables, continuity, partial differentiation, directional derivatives, Taylor series, parametrizations of curves and surfaces, divergence, gradient, curl, the Hessian, path integrals, multiple integrals, surface integrals, changes of variables for multiple integrals, the Jacobian, rectangular coordinates, polar coordinates, cylindrical coordinates, spherical coordinates, and Stokes's theorem.