Lecture topics and homework assignments. Last updated May 7, 2004.
Date 
Section 
Topics 
Notes 
Homework Problems Assigned 
1/21 
14.1 
Functions of two or more variables; graphs; level sets.  23, 27, 29, 35  
1/23 
14.3 
Meaning of partial derivatives 
Geometric meaning and symbolic meaning  5,1116 (all) 
1/26 
14.3 
Computing partial derivatives  Examples; higher derivatives; mixed partials.  21,23,27,36(done in class),45,47,49,51,59 
1/28 
14.4 
Tangent plane to graph of z = f(x,y)  Differentiability at (a,b) means having a good linear approxiamtion at (a, b). Formula for this linear approximation.  1,3,5; hand in 6. 
1/30 
14.4 
More on linear approximation  differentials  11,13,31,33,35 
2/2 
14.5 
Chain rule  1,3,5; hand in 6.  
2/4 
14.5 
Chain rule (continued)  Exercise 50 was done in class.  7,9,11,19,21,41; hand in 42. 
2/6 
14.6 
Directional derivative, gradient introduced.  3,5,7,9,11,13,15; hand in 12 (or 16).  
2/9 
14.6 
Gradient (cont.)  Meaning of of gradient; tanget lines/planes to level sets  37,39,41,45; hand in 56. Help on 56. 
2/11 
14.7 
Finding local maxima and minima  Brief introduction  3,5,7,9 (find critical points only); hand in 8 from last semester's practice test. 
2/13 
14.78 
Maxima and minima (cont.)  Local extremes and global extremes. Methods for one variable generalize. Second derivative test. Global extremes on closed bounded sets.  5,7,9,13,17; hand in 16. 
2/16 
14.8 
Lagrange multipliers  14.7: 29,31,33 (done in class); hand in 32; 14.8: 3,5,7; p963: 57  
2/18 
Review 
Suggestion. Work the practice test without looking at the answers. Attempt to do it all in 50 minutes. If you miss a question, practice on some similar questions. Then attempt the 9/22 test, again allowing yourself only 50 minutes.  
2/20 
ch. 14 
TEST  Answers: Page1, Page 2, Page 3  
2/27 
15.115.2 
Double integrals and volume. Iterated integrals and Fubini's theorem. Computing iterated integrals using Fundamental Theorem of Calculus.  15.2: 5,7,9,11 

3/1 
15.215.3 
More on double integrals over rectangular regions. Integrals over general plane regions  Some solved problems from 15.2.  15.2: 13,15,17,19,21,25 
3/3 
15.3 
general plane regions (cont.)  15.3: 3,7,9,11,13,17,33,35,37,39,41  
3/5 
No class. (A makeup class will be scheduled later this semester.)  Complete HW from 3/3!!!  
3/8 
15.3 
examples 

3/10 
15.4 
polar coordinates 
15.4:117 (odd); hand in 15.4:14 on 3/15 

3/12 
15.4 
polar coordinates 
15.4: 19,21,23,25 hand in 15.4:26 on 3/17 

3/15 
15.7 
triple integrals 
Express in all 6 orders: the triple integral of f(x,y,z) over the tetrahedron with vertices at (0,0,0), (a,0,0), (0,b,0), (0,0,c) 

3/17 
15.7 
triple integrals 
15.7: 13,15,29,30  
3/19 
15.8 
cylindrical and spherical coordinates  hand in 15.7: 32 on 3/22 15.8: 3,5,11,13,17,19,21,35; hand in 15.8: 22, 36 on 3/24 

3/22 
16.2, 16.6 
Integrals on parametric curves 
Lecture notes  Do the three exercises in the lecture notes. Solutions 
3/24 
16.6, 16.7 
Integrals on parametric surfaces 
See pp. 10835, 10937.  
3/26 
Review 1  Practice test. Picture for #6.  
3/29 
Review 2  
3/31 
Integration 
TEST  
4/2 
16.1 
Vector fields  
4/54/9  Spring Break  
4/12 
16.2 
line integrals and work  16.2: 17,18,19,20  
4/14 
16.3 
A gradient field is: 1) exact and 2) path independent.  16.3: 3,5,7,9  
4/16 
16.3 
Finding potential functions. Pathindependent fields are gradient fields  16.3: 19,21,23,25  
4/19 
16.4 
Green's Theorem  16.4: 1,3,7,9; hand in 10  
4/21 
16.5 
Operations on vector fields    16.5: 3,5,7 
4/23 
16.5 
Divergence and curl    16.5: 9,10,11,12,15, 2329 
4/26 
16.7 
Parametric surfaces (again; see 3/24) 
  16.7:5 
4/28 
16.7 
Flux integrals 
  16.7: 19,21,23,25 
4/30 
16.8 
Stokes Theorem / Takehome exam 
Get a copy of the takehome   
5/3 
 
review/discussion 
   
5/5 
 
review/discussion 
   
5/7 
 
Takehome exam DUE. 
   
5/10 
FINAL 
In ususal classroom, 3PM5PM 
To review for final, see review for Fall 2003 
 