MATH 331 L02 (Winter 2010)
"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; F:11:00am-12:00pm

Teaching Assistant:
Vanessa Dixon

E-mail:
vrdixon@ucalgary.ca
Office: MS 382
Tel.:
(403) 220-6323

Place:  SB 142
Lectures Schedule and Tutorials 
Lectures schedule (L02)
Tutorials  schedule (tut4-tut5)
Monday/Wednesday/Friday  13:00-13:50  (SB 142)
 Monday (tut4) 10:00-10:50am (MS371)-A. Swishchuk
 Tuesday (tut3) 13:00-13:50am (MS427)-V. Dixon

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
Course Information Sheet

 Important Class Dates:
First day of class: 13:00, Monday, January 11, 2010;
Quiz # 1: 10:00-10:50am/13:00-13:50, Monday/Tuesday, January 25/26,  2010; Tut 4/3, MS 371/427; 
Quiz # 2: 10:00-10:50am/13:00-13:50, Monday/Tuesday, February 8/9,  2010; Tut 4/3, MS 371/427;
Midterm: 13:00-13:50, Friday, March 12, 2010, SB 142
Quiz # 3: 10:00-10:50am/13:00-13:50, Monday/Tuesday, March 1/2,  2010; Tut 4/3, MS 371/427;
Quiz # 4: 10:00-10:50am/13:00-13:50, Monday/Tuesday, March 22/23,  2010; Tut 4/3, MS 371/427;
Quiz # 5: 10:00-10:50am/13:00-13:50, Monday/Tuesday, April 5/6,  2010; Tut 4/3, MS 371/427;
Last day of class: April 16, 2010.
Winter Session Final Examinations: April 19-29, 2010;
Final Exam: Thursday, April 22, 8:00-11:00am, ST 141

Recommended texts:

  1) 'Calculus. A Complete Cours' by Robert A. Adams, Fifth Edition, 2003, Pearson Education Canada Inc., Toronto, Ontario
2) 'Elementary Differential Equations' by William F. Trench, 2000, Brooks/Cole, 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://math.ucalgary.ca/~aswish/math331W10.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 12, 2010) 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%
13:00-13:50, Friday, March 12, 2010, SB 142
Quizzes (5)
20%
#1-Jan25/26; #2-Feb8/9; #3-Mar 1/2; #4-Mar22/23; #5-Apr5/6 (Mon/Tue,10:00-10:50am/13:00-13:50, MS371/427)
Final Exam 50%  Thursday, April 22, 8:00-11:00am, ST 141


Tentative Lectures Schedule for MATH331 and Lecture Notes
Month
Day
Monday
Day
Wednesday
Day
Friday
Jan
11
Lec1: Course Outline. Linear Systems of Ordinary Differential Equations (LSODE). Introduction.
Review of Linear Systems.
Examples and Exrcises.
13
Lec2: Basic Theory of Homogeneous   LSODE.
Here: Example
Exercises.

15
Lec3: Constant Coefficients Homogeneous LSODE.
Here: Example
Exercises
Jan
18
Lec4: Constant Coefficients Homogeneous LSODE. Symmetric Matrix 3x3. 20
Lec5: Constant Coefficients Homogeneous LSODE. Repeated Eigenvalues.
Exercises.

22
Lec6: Constant Coefficients Homogeneous LSODE. Complex Eigenvalues.
Example.
Example (continuation)
Exercises
Jan
25
Lec7: Variation of Parameters of LSODE.
Here: Example
Example (cont.)
Example and Exercises
27
Lec8: Geometric Properties of Solutions of LSODE when n=2.
Phase Plane Analysis
29
Lec9: Functions of Several Variables.
Feb
1
Lec10: Examples: Domain, Range, Graphs, Level Curves, Limits and Continuity.
3
Lec11: Partial Derivatives, Tangent Planes, Examples.
5
Lec12: Linear Approximation, Differentiability, Differentials, Higher-Order Partial Derivatives, Examples.
Feb
8
Lec13: The Chain Rule, Examples.
10
Lec14: Gradients and Directional Derivatives I, Examples.
Review of Vector Geometry in 3D
12
Lec15: Gradients and Directional Derivatives II, Examples.
Feb
15
Reading Week 17
Reading Week 19
Reading Week
Feb
22
Lec16: Implicit Functions, Taylor Formula. 24
Lec17: Examples of Partial Differential Equations I. 26
Lec18: Examples of Partial Differential Equations II.

Mar
1
Lec19: Double Integrals. Exercises.
3
Lec20: Repeated (Iterated) Integrals.
5
Lec21: Double Integrals in Polar Coordinates.
Mar
8
Lec22: Line Integrals I.
10
Lec23: Line Integrals II.
12
Midterm
Mar
15
Lec24: Standard Version of Green's Theorem. 17
Lec25: Triple Integrals I (By Inspection).
19
Lec26: Triple Integrals II (By Iteration).
Mar
22
Lec27: Triple Integrals with Cylindrical Coordinates.
24
Lec28:  Triple Integrals with Spherical Coordinates I.
26
Lec29. Triple Integrals with Spherical Coordinates II.
Mar-Apr
29
Lec30: Vector Fields.
31
Lec31: Surface Integrals. Evaluation.
2
Good Friday-No Lecture
Apr
5
Lec32: Surface Integrals II, Examples.
7
Lec33: Oriented Surfaces and Surface Integrals. 9
Lec34: Vector Calculus: Gauss Theorem
Apr
12
Lec35: Gauss TheoremII.
14
Lec36: Stokes Theorem I.
16
Lec37: Stokes Theorem II.


Announcements:
1) Marks for Final Exam and Unofficial Final Grades

2)
Final Exam: Thursday, April 22, 8:00-11:00am, ST 141
(Bring in your ID)

3) USRI is running Online this term between April 1 and April 16. Please, evaluate this course. Thank you.

4) Official Formula Sheet
 
Tutorials:
1. Tutorial #1 (Tut4/3, Mon/Tue, Jan 18/19, 10:00-10:50/13:00-13:50, MS371/427)
2. Problems based on Lectures 1-6.

3. Tutorial #2 (Tut4/3, Mon/Tue, Jan 18/19, 10:00-10:50/13:00-13:50, MS371/427)
4. Problems based on Lectures 7-11.
5. Tutorial #3 (Tut4/3, Mon/Tue, Feb22/23, 10:00-10:50/13:00-13:50, MS371/427)
6. Problems based on Lectures 12-18.
7. Midterm Exam_Winter_2006
8. Tutorial #4 (Tut4/3, Mon/Tue, Mar 8/9, 10:00-10:50/13:00-13:50,MS371/427)
9. Tutorial #5 (Tut4/3, Mon/Tue, Mar15/16, 10:00-10:50/13:00-13:50,MS371/427)
10. Problems based on Lectures 19-26.
11. Tutorial#6 (Tut4/3, Mon/Tue, Mar29/30,10:00-10:50/13:00-13:50,MS371/427)
12. Problems based on Lectures 27-31
13. Tutorial#7 (Tut4/3, Mon/Tue, Apr 12/13, 10:00-10:50/13:00-13:50,MS371/427)
14. Final Exam Winter 2005


This page was updated on April 27, 2010.