MATH
217:101 Multivariable and
Vector Calculus. UBC course page here
Class:
Tue, Th 09:3011:00 & Fri 09:0010:00 at
Buchanan A103
Office hours (subject to
change): Th 2:003:00, Fri 11:1012:10 or by
appointment. Please email at yhkim "at"
math "dot" ubc 'dot' ca
First class: Thursday, Sept. 9. Last
class: Friday, Dec. 3.
Announcements
Nov 22, 2010. Teaching evaluation is NOW available online in the UBC system: https://eval.olt.ubc.ca/science. Pleaes take it seriously and please complete the evaluations before the deadline: 11PM on December 5th, 2010. (Survey results will not be released to instructors until course grades have been submitted.)
Sept 16,
2010.
A copy of the textbook is on reserve (2hr loan) in the library:
You may request the available Stewart book by the call number: QA
303.2 .S735 2008 PRIV.COPY. It is held in the reserve area behind
the circulation desk at IKBLC.
Sept 17,
2010. Office hours are now changed to Th 2:003:00 and Fri
11:1012:10. Of course, you can alway contact me by email, to arrange
meeting me at other times.
Homework
Assignments:
Week  Date  Contents  suggested practive exercises (Please note that we are using Stewart 6th edition. NOT Early transcendental.) 
1  
Sept. 9 (first class)  Overview. coordinate systems. distance. sphere. 13.1  13.1. #11, 15, 19, 33, 38*, 39  
Sept 10 (Fri)  Vectors and dot product. 13.2 3  13.2. #1, 11, 19, 29, 36* 13.3. #1, 11, 13, 19, 23, 41, 49, 50*, 51, 57, 60* 

2  Sept 14 (Tue)  Do product13.3: projections. Cross product. 13.4: cross product. triple product. 
13.4 #7, 9, 11, 13,
15, 19, 29, 36*, 37, 43, 44*, 45, 49. p830, Discovery project #2*, 
Sept. 16 (Thur)  Equations of lines and planes. 13.5. Cylinders and quadric surfaces 13.6 
13.5. #1, 5, 13, 19, 21, 31 13.5 #38*, 41, 45, 49, 55, 59, 61, 62*, 74* 13.6. #3, 7, 11, 19, , 21, 23, 25, 27, 33, 34*, 41, 42*, 43 (also sketch the surface), 46* (also sketch the surface) p848. TrueFalse quiz # 1  18. p851 #3 

Sept. 17 (Fri). HW 1 is due 
Vector functions and space curves 14.1  14.1 #1, 3, 4*, 5, 10*,
14*, 13, 19, 21, 25, 37, 38*, 43 

3  Sept 21 (Tue)  Derivatives and integrals of vector functions. 14.2 
14.2 # 3, 5, 7, 13, 15, 16*, 21,
35, 37, 40*, 47, 49, 50*, 51 
Sept 23 (Thur)  Arc length and curvature 14.3 Position, velocity, and acceleration 14.4. Example 3. Acceleration and curvature: 14.4. p 878  879 
14.3 #3, 5, 11, 13,
15, 16*, 19, 24*, 51, 53, 54*, Read 14.4 Example 3. 14.4. #15, 19, 35, 41 

Sept 24 (Fri) HW 2 is due 
Functions of several variables. 15.1 
Do not use computer or graphic
calculators! 15.1 # 7, 9, 11, 13, 15, 17, 19 

4  Sept 28 (Tue) 
 Functions of several variables. (graphs and level curves) 15.1  Limits and continuity 15.2 
Do not use computer or graphic
calculators! 15.1. # 23, 25, 29, 30*, 34*, 35, 37, 38*, 41, 45, 46*, 49, 55, 57, 59, 60*, 61 15.2 # 7, 9, 10*, 13, 14*, 16*, 18*, 41 
Sept 30 (Thur) 
 Limits and continuity 15.2 
15.2 # 19, 22*, 25, 29, 30*, 33, 37, 45  
Oct 1 (Fri) HW 3 is due 
 Partial Derivatives 15.3 
15.3 #4*, 5, 8*, 37, 40*, 71,
72*, 73, 76*, 81, 82*, 87, 93 

5  Oct 5 (Tue) 
First Midterm. It
includes the materal covered in class for sections up to 15.2 (Limits
and Continuity) inclusive, and corresponding suggested practice
exercises (including homework assignments). 

Oct 7 (Thur) 
Partial Derivatives 15.3  
Oct 8 (Fri) HW 4 is due 
Tangent planes and linear approximations 15.4 
15.4 #5, 6*, 13, 15, 19,
21, 42*, 45, 46* 

6  Oct 12 (Tue) 
Chain Rule 15.5 
15.5 #5, 11, 14*, 23, 34*, 36*,
39, 43, 49 
Oct 14 (Thur) 
Directional derivatives and gradient 15.6 
15.6 #11, 14*, 22*, 23, 25, 34*,
35, 37*, 44*, 48*, 52*, 55, 59 

Oct 15 (Fri)  gradient 15.6 Maximum and Minimum 15.7 Lagrange Multipliers 15.8  15.7 #34*, 55, 56* 15.8 #1, 10*, 11, 14, 19, 20*, 25, 26* 

7 
Oct 19 (Tue) 
Lagrange Multipliers 15.8. Second derivative test 15.7.

15.7 #1, 3, 6*, 11, 15, 18*, 19,
and 42* (apply the second derivative test). 
Oct 21 (Thur) 
Double integrals over rectangles 16.1 Iterated integrals 16.2 
16.1 #11, 12*, 14*, 18* 16.2 #3, 9, 12*, 17, 21, 22*, 24*, 26*, 36* 

Oct 22 (Fri)  Double integrals over general regions 16.3. 
16.3 #5, 6*, 9, 13, 15, 19, 22, 24*, 25, 28*,  
8 
Oct 26 (Tue) 
Double integrals over general regions 16.3. Double integrals in polar coordinates 16.4 
16.3 #33, 34*, 45,
46*, 47 16.4 #6*, 9, 11, 15, 18*, 19, 21, 27 
Oct 28 (Thur) 
Triple integrals 16.6 Triple integrals in cylindrical coordinates 16.7 
16.6 #9, 11, 15, 16*, 17, 21,
22*, 28*, 32*, 33, 38* 

Oct 29 (Fri)  Triple integrals in cylindrical coordinates 16.7 Triple integrals in spherical coordinates 16.8 
16.7 #9, 12*, 16*, 18*, 21, 25,
27 

9 
Nov 2 (Tue) 
Triple integrals in spherical coordinates 16.8 Change of variables 16.9 
16.8 #9, 13, 18*, 20*, 21,
25, 28*, 33 (a), 34*, 36*, 39, 44* 
Nov 4 (Thur) 
Change of variables 16.9 
16.9 #7, 10*, 13,
14*, 22*, 23, 24* 

Nov 5 (Fri)  Vector fields 17.1 Line integrals 17.2 
17.1 # 5, 6*, 11, 13, 17, 18,
23, 29, 31, 35, 36* 17.2 # 4*, 7, 8*, 15, 16*, 17, 21, 36*, 40*, 45 

10  Nov 9 (Tue) 
Second
Midterm. 

Nov 11 (Thur) 
No Class (Remembrace Day) 

Nov 12 (Fri) HW 8 due 
17.3 Fundamental Thoerem for Line integrals 
17.3 # 1, 23, 27 

11  Nov 16 (Tue) 
17. 3 Fundamental Theorem for Line integrals 
17.3 # 5, 7, 19, 20*, 29, 31,
31*, 33, 34(a)* 
Nov 18 (Thur) 
17.4 Green's thoerem 
17.4 # 2*, 4*, 8*, 10*, 13, 18*, 21, 22, 23,  
Nov 19 (Fri) HW 9 due 
17. 5. Curl and Divergence 
17.5 # 9, 10*, 11, 12*, 14*,
16*, 19, 20*, 21 (irrotational = zero curl), 22* (incompressible = zero
divergence), 25, 26*, 30 (a)* (b)*, 31 (b) 

12  Nov 23 (Tue) 
17. 5 Curl and Divergence 17. 6 Parametric Surfaces and their areas 
17. 6 #4, 13, 14, 15, 16, 17, 18, 19, 20, 23, 25, 26, 34 (Just the tangent plane), 
Nov 25 (Thur) 
17.6 Parametric Surfaces and their areas 
17.6 # 38, 40, 43, 44, 46,
58, 60 (a) (c) 

Nov 26 (Fri) HW 10 due 
17.7 Surface Integrals 
17.7 #7, 10, 11, 16,
38, 40 (a) 

13  Nov 30 (Tue) 
17.7 Surface Integrals of vector fields 17.8 Stokes' theorem 
17.7 # 19, 21, 22, 28 (with
outward normal direction), 41 
Dec 2 (Thur)  17.8 Stokes' theorem 17.9 The divergence theorem 
17.8 # 1, 4, 5, 6, 7, 8, 9, 12
(a), 17, 18, 19 

(Fri)  17.9 The Divergene theorem 
17.9 # 8, 12, 13, 17, 18, 23,
24, 25, 26, 27 

Ch.
17 Review questions (page 1142  1144): Concept check: all the problems TrueFalse quiz: all the questions Review Exercises: #1, 4, 6, 7, 8, 10, 11, 13, 16, 17, 18, 19, 21, 24, 25, 26(a), 27, 28, 29, 30, 32, 33, 34, 37 (Hint: first, check curl F), 38, 39, 40 

Dec 16th at NOON 
Final
Exam (150 minutes) AT MATH 100 