Math 241: Vector Calculus.

Section 003

Spring 2009

University of South Carolina

      Instructor  
      Matthew Boylan  
  Office     LeConte 400G  
  Phone     777-8874  
  E-mail     boylan@math.sc.edu  
  Office hours     Tues. 9 - 10  
  Weds. 3:30 - 4:30  
  Fri. 11 - 12  
  And by appointment  

  • University of South Carolina Mathematics Department .

    • Course information :

  • Prerequisite : Qualification through placement or a grade of C or better in MATH 142

  • Text : Calculus: Early Transcendentals, by Anton, Bivens, and Davis.
    8th ed., John Wiley and Sons, Inc. (2005).

  • Course objectives : Students will master concepts and solve problems on vector algebra, geometry of three-dimensional space; lines, planes, and curves in space; polar, cylindrical, and spherical coordinate systems; partial differentiation, max-min theory; multiple and iterated integration, line integrals, and Green's theorem in the plane.

  • Meeting schedule :

          Section 003  
      Lecture     MWF     12:20 - 1:10     LeConte 115  

  • Homework : Homework will be assigned each lecture but not collected.

  • Quizzes: Weekly quizzes will be given based on the homework. Missed quizzes will not be made up.

  • Exam schedule : (3 one-hour exams and a cumulative final exam)

      Exam 1:     Wednesday,     February 11     12:20 - 1:10     LeConte 115  
      Exam 2:     Wednesday,     March 18     12:20 - 1:10     LeConte 115  
      Exam 3:     Wednesday     April 15     12:20 - 1:10     LeConte 115  
      Final Exam:     Saturday     May 2     2:00 - 5:00     LeConte 115  

    Missed exams will not be made up. Exceptions may be made for documented illness/family emergency.

  • Grading :

          Points/650     % of grade  
      Three hour exams:     100 pts. x 3     15% x 3  
      Final exam:     200 pts.     30%  
      Quizzes:     150 pts.     25%  
      Total:     650 pts.     100%  

    Letter grades will be assigned according to the following approximate scale unless otherwise noted:

      A     B     C     D     F  
      90 - 100     80 - 90     70 - 80     60 - 70     0 - 60  

    Note : The deadline to drop without a WF is Monday, February 23.

  • Calculators : Calculators (and computer software such as Maple) may be used homework unless otherwise noted. They may not be used to do quizzes or exams.

  • Student Success Center Tutoring Program : Free tutoring beginning 1/20 in the Student Success Center/Thomas Cooper Library, Mezzanine level. Students are asked to make appointments for tutoring.

  • Other help resources : Math Lab (free drop-in tutoring at various locations on campus, including LeConte 105), Private tutors , On-line materials for courses   (241 websites from past semesters), Math library .

  • Syllabus (which contains all of the above information): (pdf)   (ps)

    • Lectures and Homework :

    Lectures Homework
      Dates     Sections     Topics     Problems     Quiz date  
      January  
      Week 1     12     M     12.1     Rectangular coordinates, spheres, cylindrical surfaces.     3, 7 - 13 odd, 17, 21 - 27 odd, 31, 33, 35, 41 (12.1).     1/21.  
      14     W     12.2     Vectors.     1 a, d, 3 a, c, 7 a, 9 a, 11 a, d, 13 a, d, 15 a, c, 17, 19, 29, 31, 33, 35 a, c, 53 (12.2).     1/21.  
      16     F     12.3     Dot product; projections.     1c, d, 3, 5, 9, 10, 13, 27, 28, 29 (12.3).     1/28.  
      Week 2     19     M         No class.     Martin Luther King Jr. Day      
      21     W     12.4     Cross product; Quiz 1 on 12.1, 12.2. Solutions.    1, 3, 11, 13, 15, 25a, b, 33, 34 (12.4).     1/28.  
      23     F     12.4, 12.5     Parametric equations of lines (12.5).     1 - 9 odd, 13 - 17 odd, 21, 25 -33 odd, 39, 51a, c (12.5).     1/28.  
      Week 3     26     M     12.5             2/4.  
      28     W     12.6     Planes in 3-space; Quiz 2 on 12.3, 12.4. Solutions.    1, 3, 9 - 17 odd, 21 - 31 odd, 41 - 47 odd (12.6).    2/4.  
      30     F     12.6             2/4.  
      February     Week 4     2     M     13.1     Vector-valued functions.     1, 3, 7, 11, 13, 15, 19, 21, 25, 27 (13.1).      
      4     W     13.2     Calculus of vector-valued functions; Quiz 3 on 12.5, 12.6. Solutions.     1, 5, 7, 9, 11, 15, 21, 25, 35, 37, 39, 43 (13.2).      
      6     F     13.2, 13.3     Change of parameter; arc length (13.3).     1 - 11 odd, 21 - 25 odd, 29 (13.3).      
      Week 5     9     M     13.3             2/18.  
      11     W     Review (optional): Tues., 2/10 at 7:00 pm in LC 115. Exam 1 Guide     Exam I. Solutions.     Covers:   Information and Homework from Sections 12.1 - 12.6, 13.1 - 13.2; Class Notes: 1/12 - 2/6; Quizzes: 1 - 3.     
      13     F     13.4, 13.6     Unit tangent, normal, and binormal vectors (13.4); Motion along a curve (13.6).     5, 7, 9 (13.4); 5, 7, 17, 19 (13.6).     2/18.  
      Week 6     16     M     14.1     Functions of two or more variables (14.1).     1 - 7 odd, 13, 15, 17 a, 19 - 33 odd (14.1).     2/25.  
      18     W     14.2     Limits and continuity (14.2); Quiz 4 on 13.3, 13.4. Solutions.     1 - 7 odd, 13 - 19 odd (14.2).     2/25.  
      20     F     14.3     Partial derivatives (14.3).     1, 3, 13, 17, 19, 25, 35, 69, 77, 79 (14.3).     2/25.  
      Week 7     23     M     14.3, 14.5     The chain rule (14.5).     1, 5, 9, 11, 13, 19, 21, 23, 31 (14.5).     3/4.  
      25     W     14.5     Quiz 5 on 13.6, 14.1, 14.2. Solutions.        3/4.  
      27     F     14.6     Directional derivatives and gradients (14.6).     1, 15, 19, 29, 37, 51, 55, 61, 65, 71. (14.6).      
      March     Week 8     2     M     14.6              
      4     W     14.7     Tangent planes and normal vectors (14.7); Quiz 6 on 14.3, 14.5. Solutions.     1, 7, 9, 11, 17, 21, 23 (14.7).      
      6     F     14.7              
        8 - 15           No Class.     Spring Break.      
      Week 9     16    M     14.8     Maxima and minima of a function of two variables (14.8).     1, 3, 9, 13, 17, 23, 27, 31, 33, 35 (14.8).     3/25.  
      18     W     Review (optional): Tues., 3/17 at 7:00 pm in LC 115. Exam 2 Guide     Exam II. Solutions.     Covers:   Information and Homework from Sections 13.3, 13.4, 13.6, 14.1 - 14.6; Class Notes: 2/9 - 3/6; Quizzes: 4 - 6.     
      20     F     14.8             3/25.  
      Week 10     23     M     14.9     Lagrange multipliers (14.9).     5, 7, 9, 11, 15, 17 (14.9).     4/1.  
      25     W     14.9     Quiz 7 on 14.7. Solutions.        4/1.  
      27     F     15.1     Double integrals (15.1).     1, 5, 9, 13, 21, 23 (15.1).     4/1.  
      Week 11     30     M     15.1             4/8.  
      April     1     W     15.2     Double integrals over non-rectangular regions (15.2); Quiz 8 on 14.8. Solutions.     1, 3, 7, 11, 13, 17, 21, 25, 29, 33, 35, 39, 41, 45, 47, 53, 55 (15.2).     4/8.  
      3     F     15.2             4/8.  
      Week 12     6     M     15.3     Double integrals in polar coordinates (15.3).     1, 9, 11, 15, 21, 23, 25, 27, 29, 33 (15.3).     
      8     W     15.3     Quiz 9 on 14.9 and 15.1. Solutions.          
      10     F     15.3              
      Week 13     13     M     15.5     Triple integrals (15.5).    3, 7, 9, 11, 15, 19, 23, 25 a, c (15.5).      
      15     W     Review (optional): Tues., 4/14 at 7:00 pm in LC 115. Exam 3 Guide     Exam III. Solutions.     Covers:   Information and Homework from Sections 14.7 - 14.9, 15.1 - 15.3; Class Notes: 3/16 - 4/10; Quizzes: 7 - 9.      
      17     F     15.5              
      Week 14     20     M     15.7     Triple integrals in cylindrical and spherical coordinates (15.7).     1, 3, 5, 7, 9, 13, 19, 23 (15.7).      
      22     W     15.7              
      24     F     15.8     Change of variables in multiple integrals; Jacobians (15.8).     3, 5, 17, 19, 31 (15.8).      
      Week 15     27     M     15.8              
      May     Finals week     May 2     Sat.     Review (optional): Thurs., 4/30 at 6:00 pm in LC 112. Note that the room is different than usual. Review sheet     Final Exam, 2 - 5 pm.     Cumulative.