University of Toronto

MAT 291F (Calculus III)
Course Outline
2007

Instructors:
    Lec 01 - S. Abou-Ward
    Lec 02 - R. Sasyk
    Lec 03 - M. Krishnapur

    Each student will be assigned to one lecture section and one tutorial section. You can view the Course Timetable on the Web at: http://www.ecf.utoronto.ca/apsc/registrar

Course Description:
    This is a second year calculus course.  It will assume that the student already possesses a comprehensive knowledge of single variable calculus and basic concepts of linear algebra.  The course will cover most of the classical topics of differential and integral calculus of several variables.  The emphasis will be placed on the concepts, properties and typical procedures.  Theorems will be stated precisely, mostly without proof, but with indications and understanding of the mathematical ideas involved.

    Applications will be presented and discussed during lectures.

Textbook:
    SALAS, HILLE and ETGEN, "Calculus Several Variables" 9th edition.

Tutorials:
    In addition to the lectures you are required to attend a two hour tutorial each week, during which you will have the opportunity to go over problems and receive help from your tutor, as well as take the weekly quiz.

    Tutorials will begin the week of Sept. 18.

Marking Scheme:
    The course mark will be computed as follows:

3 one hour quizzes             25%  (10% for the best two, and 5% for the worst)
1 term test                         25%
final examination               50%

      The quizzes will be very close to the homework problems. There will be no make-up tests or exams. Please note that calculators or any other aids will not be allowed during tests or exams.

     To learn and understand the material, and performe well in the course, you must work through the assigned homework problems.

Course Schedule:
   This is the tentative schedule for the semester. Please check announcements for more precise updates.


WEEK  #
TOPICS COVERED
HOMEWORK
QUIZZES or TESTS
MIDTERMS


DUE DATE
% of FINAL GRADE
DATE
% of FINAL GRADE
DATE
1

Sep 11- 15
Functions of Several Variables, Quadric Surfaces, Graphs and  Level Sets, Partial Derivatives, Open and Closed Sets
Sept. 19

§ 14.1- 14.5




2

Sep 18- 22
Limits and Continuity, Differentiability and Gradients
Sept. 26

§ 14.6- 15.1




3

Sep 25- 29
Directional derivatives, Chain Rule, Tangent lines and Tangent Planes
Oct. 3

§ 15.2- 15.4




4

Oct. 2- 6
Double Integrals, Iterated Integrals, Integration Using Polar Coordinates
Oct. 10

§ 16.2- 16.4




5

Oct. 9- 13
(Thanksgiving) Mass, Center of Mass, Triple Integrals
Oct. 17

§ 16.2- 16.4




6

Oct. 16- 20
Calculation of Triple Integrals, Cylindrical and Spherical Coordinates
Oct. 24

§ 16.7- 16.9




7

Oct. 23- 27
Change of Variables in Multiple Integration, Jacobians, Line Integrals
Oct. 31

§ 16.10- 17.2




8

Oct. 30- Nov. 3
Integrals with Respect to Arclength, Green’s Theorem, Surface Area
Nov. 7

§ 17.4- 17.6





9

Nov. 6- 10
Surface Integrals, Divergence, Curl, The Divergence Theorem
Nov. 14

§ 17.7- 17.9




10

Nov. 13- 17
Stokes’ Theorem, Local Extrema
Nov. 21

§ 17.10, 15.5





11

Nov. 20- 24
Absolute Extrema, Maxima and Minima with side conditions
Nov. 28

§ 15.6- 15.8





12

Nov. 27- Dec. 1
Differentials, Review
Dec. 5




     For the purposes of this form, Week 1 is interpreted as the week starting September 11, 2006. Week 12 corresponds to the week starting November 27, 2006, which is the last week of classes for the fall term.

Suggested Homework Problems (subject to change):

Chapter 14  
Section 14.1 # 5, 8, 9, 11, 12, 17, 19, 22, 23, 27, 31, 36
Section 14.2 # 2, 6, 9, 11, 15, 23, 30, 38, 39, 41, 46, 50, 51
Section 14.3 # 5, 6, 9, 15, 16, 21, 22, 23, 30, 32, 38, 40, 41, 43
Section 14.4 # 3, 11, 12, 19, 21, 27, 30, 36, 39, 41, 42, 45, 46, 49, 50, 53, 58, 60, 62
Section 14.5 # 3, 5, 6, 7, 8, 9, 10, 11, 20
Section 14.6 # 7, 10, 12, 19, 21, 23, 26, 27, 29, 30, 31, 33
   
Chapter 15  
Section 15.1 # 13, 15, 21, 29, 35, 36, 37, 41, 43
Section 15.2 # 7, 8, 13, 16, 19, 21, 25, 26, 28, 29, 32, 33, 36, 37
Section 15.3 # 1, 3, 17, 23, 25, 27, 29, 36, 37, 43, 45
Section 15.4 # 5, 7, 9, 11, 15, 19, 25, 27, 29, 31, 33, 35
Section 15.5 # 5, 7, 9, 11, 15, 21, 23, 25, 28, 29, 30
Section 15.6 # 1, 7, 13, 19, 23, 25, 27, 29, 31, 35, 37, 39
Section 15.7 # 5, 9, 11, 15, 17, 20, 29, 31, 33, 38, 41
Section 15.8 # 3, 5, 9, 11, 17, 19, 21, 23, 25, 26, 27, 35, 39, 41
Section 15.9 # 3, 7, 17, 19, 23, 25, 27, 28, 31
   
Chapter 16  
Section 16.2 # 1, 5, 7a, 8a, 10, 17
Section 16.3 # 5, 7, 11, 13, 15, 17, 19, 21, 23, 25, 29, 31, 32, 33, 35, 37, 39, 47, 49, 51
Section 16.4 # 13, 14, 16, 17, 19, 21, 23, 25, 27, 32
Section 16.5 # 3, 5, 9, 31
Section 16.6 # 1, 7
Section 16.7 # 5, 7, 9, 13, 14, 15, 17, 18, 19, 25, 29, 41, 43, 47, 51
Section 16.8 # 3, 5, 11, 13, 15, 17, 21, 23, 25, 27, 28
Section 16.9 # 3, 5, 9, 10, 11, 12, 13, 14, 18, 19, 21, 25, 27, 33, 34, 35, 37
Section 16.10
# 3, 11, 13, 15, 17, 19, 22, 23, 24, 25, 27, 28, 30
   
Chapter 17  
Section 17.1 # 7, 9, 13, 15, 17, 19, 21, 22, 25, 26, 27, 28, 30, 31, 33
Section 17.2 # 6, 7, 9, 11, 13, 15, 21, 22, 25, 27, 29
Section 17.4 # 9, 10, 11, 12, 13, 14, 15, 21, 22, 23, 25, 26, 27, 29a, 32, 33a, b, 35
Section 17.5 # 2, 3, 7, 9, 20, 21, 22, 23, 24, 27, 29, 31, 34, 35
Section 17.6 # 5, 7, 11, 12, 15, 16, 17, 21, 25, 27, 30, 31, 36, 37
Section 17.7 # 5, 9, 11, 13, 17, 21, 25, 31, 32, 35, 37, 38, 39, 45, 47
Section 17.8 # 9, 11, 16, 17, 19, 21, 25, 30, 31, 34
Section 17.9 # 1, 5, 7, 9, 11, 13, 17, 19, 20, 21, 22, 23
Section 17.10 # 3, 5, 7, 9, 11, 13, 15, 17