Northeastern University
Mathematics Department


MATH 1223: Multivariable Calculus

Fall 2001

Hours: Tues,Fri 9:15-10:20; Wed 2:50-3:55
Location: 233 Ryder; Key# 14284

Instructor: Stephen Lovett
Office: 535 Nightingale Hall (NI)
Office Hours: TBA
Phone: 373-2080
Email: slovett@lynx.neu.edu

Your computer's date must be accurate.
   

Required Text: Thomas's Calculus
by Finney, Weir and Giordano


Course Description

This course first introduces vectors, vector operations and vector-valued functions in the plane and in space and then covers multivariable functions. We study partial differentiation and multiple integration of multivariable functions with applications primarily taken from physics.

Chap.TopicHomeworkComments
9.1Vectors in the Plane5-12,19,26,30,36,40,49,50 p. 726 
9.2Dot Product2,5,8,15,20,23,38,39 p. 735 
9.3Vector-valued Functions4,6,9,16,19,20,25,28,34,36 p.746 
9.4Modeling Projectile Motion1-4,9,26,29 p.757P1, P2, P3
9.5Polar Coordinate and Graphs4,6,10,12,19,22,26,42,49,78 p.768 
10.1Cartesian Coordinates and Vectors in Space5,10,12,17,22,30,34,44,54,63 p.794 
10.2Dot and Cross Product3,4,8,17,18,26,30,35,40,41 p.805 
10.3Lines and Planes in Space1,2,8,16,17,20,31,34,40,42,45,49 p.813 
10.4Quadratic Surfaces1-12,13,17,18 p.824 
10.5Vector-valued Functions and Space Curves2-3,7-8,14,20,25-26,32,34 p.835 
11.1Functions of Several Variables8-10,13-18,24,39,40,45,49,50 p.880 
11.2Limits and Continuity12,14,35,36 (55,57) p.887 
11.3Partial Derivatives1-3,8-14(even),19,24,26,31,41,44,51, 57,65,67 p.899 
11.4The Chain Rule1,4,7,9,25,33,34,39,43 p.908 
11.5Directional Deriv. Gradient Vectors, Tangent Planes2,3,12,13,17,22,28,37,38,52,54,60 p.923 
11.6Linearization and Differentials5-7,19,20,27,34 p.934 
11.7Extreme Values and Saddle Points2-4,15,22,29,31,37,41 p.944 
12.1Double Integrals1,8,9,11,19,20-22,32,41,46,54 p.984 P1, P2
12.2Areas, Moments, and Center of Mass1,4,13,16,22,24,34,38,44 p.997 P1, P2
12.3Doubles Integrals in Polar Coordinates2,6,12,13,18,22,24,30,37 p.1005P1
12.4Triple Integrals in Cartesian Coordinates7,8,14,21,22,26,35,38 p.1014 
12.5Masses and Moments in Three Dimensions3,4,6,14,18,23,28 p.1021 
12.6Triple Integrals in Cylindrical and Spherical Coords.  
FINAL Practice Questions: P1, P2, Answers


Course Policies

  1. Help and Tutoring: There are many resources for improving your Calculus skills. The best way is to come see me. Other resources: walk-in tutoring in Cahners Hall and from Engineering tutors in 222 Snell Engineering, tutoring by appointment (sign up in the Media Center in the library), and study aids in the library (Schaum's Outlines are great).
  2. Attendance: I do not keep attendance but the student is responsible for keeping up with any changes announced in class, whether or not he or she is present.
  3. Excused Absences: In order to take a make-up a late quiz or exam you must have talked to me first. For any other emergency situations, you will need to bring me valid documentation (from court, doctor,…) of your absence. Notes from family members are not acceptable.
  4. Tools 1: At times, I may assign homeworks that require the use of a computer algebra system. I will use Maple and I've provided a tutorial as well as examples for our course at Maple tutorial. Please see the section on Examples from Multivariable Calculus.
  5. Tools 2: For those who like crib sheets, I've placed on the web a pdf file continaing the basic calculus rules. (calcrulz.pdf) You may use this as a help for homework and studying but you won't be allowed to use it during in-class quizzes or exams.
  6. There will be weekly quizzes (no matter how much material is covered), a one-hour midterm and a two-hour cumulative departmental final. Otherwise, the final course grade will be calculated as follows:

     
    Homeworks           8%
    Weekly Quizzes28%
    Midterm Exam24%
    Final Exam40%
  7. Cheating: Those who choose to cheat should consult the appropriate section their Student Handbook or read the university's Academic Integrity Policy prior to doing so. Note that in this class, collaborating on homeworks is not considered cheating but each person much turn in their own write-up.
  8. If you have any questions, please feel free to talk to me. If my office hours are not convenient for you, please contact me and we can find some other time to meet.