MATH 331 (Winter 2006)
"Multivariable Calculus"
Course Outline
Instructor:
Anatoliy Swishchuk
E-mail: aswish@math.ucalgary.ca
Office: MS552
Tel.: (403) 220-3274
Office Hours: M: 11:00am-12:00pm; W:11:00pm-12:00pm
Teaching Assistants:
Holder, Cody (T01): clholder@math.ucalgary.ca
MS446,Tel.: 220-4044
Chou, James (T02): james@math.ucalgary.ca
MS 342, Tel.: 220-4541

Place: TRB 101

Lectures Schedule and Tutorials 
Lectures schedule (L01)
Tutorials  schedule (T01/T02)
Tuesday/Thursday  12:30-13:45  (TRB 101)
   T01: W, 12:00pm, MS 371, 50min
   T02: M, 2:00pm, SB 105, 50min

Syllabus:
1)   Systems of linear ordinary differential equations;
2)   Functions of several variables, graphs and level curves;
3)   Partial derivatives, differentiability and gradient;
4)   Repeated partial derivatives, the chain rule;
5)   The tangent plane, directional derivatives;
6)   Examples of partial differential equations;
7)   Double integrals, repeated integrals;
8)   Polar coordinates;
9)   Green's theorem, line integrals;
10) Triple integrals;
11) Cylindrical and spherical coordinates;
12) Vector fields;
13) Gauss theorem;
14) Stockes theorem
 Important Class Dates:
First day of class: 12:30, Tuesday, January 10, 2006;
Quiz # 1: January 23(T02)/January 25(T01), 2006;
Quiz # 2: February 13(T02)/February 15(T01), 2006;
Midterm: 12:30, Thu, March 9, 2006, TRB 101;
Quiz # 3: March 13(T02)/March 15(T01), 2006
Quiz # 4: March 27(T02)/March 29(T01), 2006
Quiz # 5: April 10(T02)/April 12(T01), 2006
Last day of class: April 13, 2006.
Winter Session Final Examinations: April 17-28, 2006;
Final Exam: April 22nd (Saturday), 8:00am-11:00am, Place-ST 127.

Recommended texts: 
1) "Calculus. A Complete Course" by Robert A. Adams, Fifth Edition, 2003, Pearson Education Canada Inc., Toronto, Ontario (Chapters 10-16);
                              2) "Elementary Differential Equations" by William F. Trench, 2000, Brooks/Cole, Pasific Grove, USA (Chapter 10).

Course Web Page:
The current official syllabus for this course is available in the wall pockets across from MS 476 and
on the webpage at www.math.ucalgary.ca Course Listing-Undergraduate.
There is also a web page for this course which contains the course outline, tentative course schedule,  grading scheme, important class dates, etc.
Announcements made in class will be posted there (see end of this web-page). The address of this web page is: http://www.math.yorku.ca/~aswish/math331W06.html/

Class work:
In-class lectures with typical examples (lecture notes will be posted on the webpage in the form of pdf-files
);
your computer must have an Adobe Acrobat reader (for free downloading see www.adobe.com).

Midterm and Quizzes:
There will be 1 Midterm (March 9, 2006) and 5 Quizzes.

Final Exam:
April 22(Saturday), 2006, 8:00-11:00am, ST 127
It will cover all the materials covered in this course.
Grading scheme (Course Evaluation):
 Exam, Midterm and Quizzes
Value (% of your final mark)
Dates
Midterm
30%
March 9, 2006, TRB 101
Quizzes (5)
20%=5x4% (4% for each quiz)
Q#1-Jan23(T02)/Jan25(T01); Q#2-Feb13(T02)/Feb15(T01); Q#3-Mar 13(T02)/Mar15(T01); Q#4-Mar27(T02)/Mar29(T01); Q#5-Apr10(T02)/Apr12(T01)
Final Exam 50% April 22nd (Saturday), 8:00am, Place-ST 127


Tentative Lectures Schedule for MATH 331
Month
Day
Tuesday
Day
Thursday
Jan
10
Lec1: Course Outline. Linear Systems of Ordinary Differential Equations (LSODE). Introduction. Basic Theory of Homogeneous LSODE.
12 Lec2: Basic Theory of LSODE II and Constant Coefficients Homogeneous LSODE.I
Jan
17
Lec3: Constant Coefficients Homogeneous LSODE. II. Repeated and Complex Eigenvalues.
Appendix (Real Distinct, Repeated and Complex Eigenvalues, Matrix 3x3)
19
Lec4: Variation of Parameters of Nongomogeneous LSODE. (Examples, matrix 2x2).
Jan
24
Lec5: Functions of Several Variables. Examples: Domain, Range, Graphs.I. (ppt)

Review: Vectors, Surfaces, Planes and Curves in 3D-spaces.
26
Lec 6: Domains, Range, Graphs, Level Curves, Limits and Continuity, Examples. (pdf)
Jan-Feb
31
Lec7: Partial Derivatives, Tangent Planes, Examples. Linear Approximation, Differentials, Hirgher-Order DEs. I. 2
Lec8: Partial Derivatives, Tangent Planes, Examples. Linear Approximation, Differentials, Hirgher-Order DEs. II (continuation of Lecture 7).
Feb
7
Lec9: The Chain Rule, Examples. Gradients.
9
Lec10: Gradients and Directional Derivatives. Examples.
Feb
14
Lec11: Implicit Functions, Taylor Formula, Examples.
16
Lec12:  Taylor Formula, Examples.II. Examples of Partial Differential Equations. 
Feb
21
Reading Week (no classes)
23
Reading Week (no classes)
Feb-Mar
28
Lec13: Double Integrals. Exercises. Repeated (Iterated) Integrals. Examples.
2
Lec14: Double Integrals in Polar Coordinates.
Mar
7
Lec15: Line Integrals, Evaluating Line Integrals, Examples.
9
Lec16: Midterm.
Mar
14
Lec17: Standard Version of Green's Theorem. Triple Integrals I.
16
Lec18: Green's Theorem and Triple Integrals. II. Examples.
Mar
21
Lec19: Triple Integrals with Cylindrical and Spherical Coordinates, Examples.
23
Lec20: Vector Fields. Surfaces in 3D spaces. Examples.
Mar
28
Lec21: Surfaces Integrals. Evaluating of Surface Integrals. Examples
30
Lec22: Evaluating of Surface Integrals. II.
Apr
4
Lec23: Oriented Surfaces and Surface Integrals. 6
Lec24: Vector Calculus: Gradient, Divergence, Curl, Gauss Theorem, Examples.
Apr
11
Lec25: Stokes Theorem, Examples. I
13
Lec26: Stokes Theorem, Examples. II. Course Review.


Announcements: 

 

This page was updated on April 26, 2006.