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.
| 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 |