MATH 331 (Winter 2005)
"Multivariate 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:14:00pm-15:00pm
Teaching Assistant:
Garth Boucher
E-mail: garth@math.ucalgary.ca
Office: MS348
Tel.: (403) 220-4819

Place:  ST  147
Lectures Schedule and Tutorials 
Lectures schedule (lec2)
Tutorials  schedule (tut3-tut5)
Monday/Wednesday/Friday  13:00-13:50  (ST 147)
 Monday (tut5) 10am-10:50am (MS319)
 Tuesday (tut3) 13:00-13:50 (MS427)
 Tuesday (tut4)  13:00-13:50 (MS317)
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: 13:00, Monday, January 10, 2005;
Quiz # 1: January 31 (tut5,M,MS319)/February 1 (tut3,T,MS427;tut4,T,MS317), 2005; 
Quiz # 2: February 28 (tut5,M,MS319)/March 1 (tut3,TMS427;tut4,T,MS317), 2005;
Midterm: 13:00, Friday, March 11, 2005, ST 147;
Quiz # 3: March 14 (tut5,M,MS319)/March 15 (tut3,TMS427;tut4,T,MS317), 2005 
Quiz # 4: March 28 (tut5,M,MS319)/March 29 (tut3,T,MS427;tut4,T,MS317), 2005
Quiz # 5: April 11 (tut5, M,MS319)/April 12 (tut3,TMS427;tut4,T,MS317), 2005
Last day of class: April 15, 2005.
Winter Session Final Examinations: April 19-30, 2005;
Final Exam: April 28, 2005, 8:00am-11:00am, ST147.

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

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.ucalgary.ca/~aswish/math331.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 11, 2005) and 5 Quizzes.

Final Exam:
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 11, 2005
Quizzes (5)
20%=5x4% (4% for each quiz)
#1-Jan31/Feb01/05; #2-Feb28/Mar01/05; #3-Mar 14/Mar15/05; #4-Mar28/29/05; #5-Apr11/Apr12/05
Final Exam 50%  April 28, 2005, 8:00am-11:00am, ST147


Tentative Lectures Schedule for MATH331
Month
Day
Monday
Day
Wednesday
Day
Friday
Jan
10
Lec1: Course Outline. Linear Systems of Ordinary Differential Equations (LSODE). Introduction.
Examples and Exercises.
2
Lec2: Basic Theory of Homogeneous   LSODE.
Examples and Exercices
4
Lec3: Constant Coefficients Homogeneous LSODE. I.
Here: Examples and Exercises
Jan
17
Lec4: Constant Coefficients Homogeneous LSODE.I. 19
Lec5: Constant Coefficients Homogeneous LSODE.II.
Here: Exercises
21
Lec6: Constant Coefficients Homogeneous LSODE.III.
Here: Examples and Exercises.
Jan
24
Lec7: Variation of Parameters of LSODE.
Here: Examples and Exercises.
26
Lec8: Geometric Properties of Solutions of LSODE when n=2. Review of Lectures 1-7.
28
Lec9: Functions of Several Variables.
Jan-Feb
31
Lec10: Examples: Domain, Range, Graphs, Level Curves, Limits and Continuity.
2
Lec11: Partial Derivatives, Tangent Planes, Examples.
Figures.
4
Lec12: Linear Approximation, Differentiability, Differentials, Higher-Order Partial Derivatives, Examples.
Feb
7
Lec13: The Chain Rule, Examples.
9
Lec14: Gradients and Directional Derivatives I, Examples.
11
Lec15: Gradients and Directional Derivatives II, Examples.
Feb
14
Lec16: Implicit Functions, Taylor Formula.
16
Lec17: Examples of Partial Differential Equations I.
18
Lec18: Examples of Partial Differential Equations II.
Review of Lectures 9-17.
Feb
21
Reading Week
23
Reading Week
25
Reading Week
Feb-Mar
28
Lec19: Double Integrals. Exercises.
2
Lec20: Repeated (Iterated) Integrals.
4
Lec21: Double Integrals in Polar Coordinates.
Mar
7
Lec22: Line Integrals I.
9
Lec23: Line Integrals II.
11
Midterm
Mar
14
Lec24: Standard Version of Green's Theorem. 16
Lec25: Triple Integrals I.
18
Lec26: Triple Integrals II.
Mar
21
Lec27: Triple Integrals with Cylindrical Coordinates.
23
Lec28:  Triple Integrals with Spherical Coordinates I.
25
Good Friday (no classes)
Mar-Apr
28
Lec29: Vector Fields.
30
Lec30: Surface Integrals. Evaluation.
1
Lec31: Evaluating of Surface Integrals II.
Apr
4
Lec32: Oriented Surfaces and Surface Integrals. 6
Lec33: Vector Calculus: Gauss Theorem  8
Lec34: Gauss Theorem II.
Apr
11
Lec35: Stokes Theorem I.
13
Lec36: Stokes Theorem II.
15
Lec37: Course Review


Announcements: 
1) Final Exam's Marks are Available
2) Unofficial Final Grades are Available
 
Here you can find your mark for Final Exam
Here you can find your Final Grade
This page was updated on May 4, 2005.