MATHEMATICS 189-222A (CALULUS III)
 
 
Section 1
Section 2
Section 3
Instructor
Prof. J. A. Toth
Prof. J. Labute
Prof. A. Zaharescu
Lectures
MWF 10:30
MWF 9:30
MWF 10:30
Office
BURN 1213
BURN 1112
BURN 1243
Telephone
398-3847
398-3819
398-3803
Office Hours
MW 1:00-2:30
MWF 10:30-12:30
MWF 10:30

Drop-in Center: Wednesdays, 6:00 pm - 8:00 pm in BURN 911.

Tutorials: Bi-weekly on Wednesdays, 4:30-5:30 pm in BURN B45. First tutorial September 23.

Prerequisite: 189-121 or 189-123 or CEGEP 201-203.

Exclusions: 189-151 or CEGEP 201-303.

Textbook: Calculus with Analytic Geometry, 5th edition, by C. Edwards and D. Penney (Prentice Hall) OR
Multivariable Calculus with Analytic Geometry, 5th edition, by C. Edwards and D Penney (Prentice Hall).

Calendar course description:
       Taylor series, Taylor's theorem in one and several variables. Partial differentiation, directional derivatives.  Extrema of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.

Objectives:
  a)  To familiarize the student with the techniques of the differential and integral calculus of functions of several variables and to enable her or him to solve a variety of problems using these tools.
  b) To supplement the material on infinite series treated in Calculus II to enable the student to use power series with some facility.

Course Requirements and Evaluation Method:  There will be six hand-in problem assignments which will be graded. It must be emphasized that mastery of the material requires working MANY more problems than are assigned. You should devote a significant amount of time after each lecture to working problems from the text relevant to the material being discussed. Because of the strongly cumulative nature of the material, it would be highly ill-advised not to do so conscientiously.
      The final grade in the course (F) will be determined from the assignment score (A) and from the grades in a midterm test (T) and in a three hour final examination (E) according to the formula:

F = max ( .15 A + .2 T + .65 E, .15 A + .85 E).
Please note} Assignments are collected  in class on the due date. Late assignments will be corrected, but will be assigned a grade of zero.

Midterm Examination: Thursday, November 5, Leacock 132, 6:30 pm - 8:00 pm . Please note that there will be no ``make-up'' midterm test. Students who miss the midterm will have there final grade determined by F= .15 A + .85 E.

Final Examination: To be scheduled by the Faculty of Science.
 

Principal Topics

1. Review of sequences and series. (Chapter 11)
2. Power series, Taylor series, Taylor polynomials, Taylor's Theorem with remainder. (Chapter 11)
3. Analytic geometry and vectors. Matrix formalism. (Chapter 12)
4. Vector-valued functions, curves and parametrizations. (Chapter 12)
5. Functions of several variables, partial derivatives, higher order derivatives. (Chapter 13)
6. The chain rule, differentials and differentiability. (Chapter 13)
7. Gradients and directional derivatives. (Chapter 13)
8. Implicitly defined functions. (Chapter 13)
9. Extreme values. (Chapter 13)
10. Double integrals, iteration in rectangular and polar coordinates. (Chapter 14)