Fall 2003

Calculus III M2057 Section 2

Professor James J. Madden

Lecture topics and homework assignments

Date
Section
Topics
Notes
Homework Problems Assigned
8/25
14.1
 Functions of two or more variables; graphs; level sets.   5,30,35
8/27
14.3

Meaning of partial derivatives

   11 -- 15
8/29
14.3
 Computing partial derivatives   5,21,13,27,36,45,47,49
9/3
14.4
 Tangent plane to graph of z = f(x,y)   1,3,5
9/5
14.4
 Linear approximation Page a, Page b 9,11,13,35,36,37,42
9/8
14.5
 Chain rule   1,3,5,7,9,11,19,37,41,48,49
9/10
14.6
 Directional derivative, gradient   3,5,7,9,11,13,15,21,23,25
9/12
14.6
 Gradient (cont.); tanget lines/planes to level sets Announced test on Sept. 22 35,37,39,45,55
9/15
14.7
 Finding local maxima and minima   3,5,7,9,13,17,19,25
9/17
14.8
 Lagrange multipliers   3,5,7
9/19
review
 Practice test Solutionst: 1-5, 6-10  
9/22
ch. 14
 TEST TEST solutions: p1, p2, p3  
9/24
15.2
 double integrals, Fubini's theorem, iterated integrals Retest Monday 9/29, 7PM, Prescott 213.

5,7,9,11,13,15,17,21,25.
Hand in: 22, 26.
9/26
15.3
 integrals over general plane regions   5,7,9,13,33,35,37,39,41.
Hand in: 36, 42.
9/29
15.4
polar coordinates
  
9,11,13,17
10/1
15.4
examples
  
no HW assigned
10/6
15.5,
15.7
Moments of mass (in 2-dimensions);
Triple integrals
  
15.5:11,13;
15.7:10,26
10/8
15.7
Examples
Announced test on 10/22
29
10/10
15.8
Cylindical and spherical coordinates
  

2,4,5,6;
Hand in: (page 1035) 7,8,9,10,11
10/13
15.8
Examples
  
35 (page 1024)
10/15
15.9
Change of variables (theory)
  
no HW assigned
10/17
15.9
 Examples   7,9,11,13,15
10/20
review
 Practice test probs 1-6, probs 7-8  
10/22
Ch 15
 TEST    
10/24
16.1, 16.2
 Vector fields; line integrals w.r.t. a vector field    
10/27
16.2
 line integrals w.r.t. a scalar field    
10/29
16.2
 line integrals: examples   16.2: 3,11,17,19,23,31
10/31
16.3
 a gradient field is: 1) exact and 2) path independent   16.3: 3,5,9,11
11/3
16.3
 path-independent fields are gradient fields.   16.3: 13,21,23,27,33,34;
11/5
16.4
 Green's theorem   16.4: 1,3
11/7
16.4
 Green's theorem    
11/10
   Loose ends    
11/12
   Review    
11/14
   Practice quiz 1 2 3 4 5    
11/17
QUIZ
    

Extra Credit (20 pts)
Hand in before Thanksgiving
p. 1120: 2-16 (even)
11/19
16.5
 Operations on vector fields   16.5: 3,5,9,10,11,12
11/21
16.6
 Parametric surfaces; normals Normals to the sphere 16.6:3,11-16,17,19,31,33,39;
Hand In 11/24: 21, 29
11/24
16.7
Surface Integrals
  
11/26
16.7
Examples
  
16.7:5,7,9,11,19,21,23(hint),25(hint)
12/1
16.8
Divergence Thm. and Stokes Thm.
  
12/3
  
Review
 Sample Final.
Answers:
1a(corrected version), 1b, 2a, 2b, 2c, 3, 4, 5-6, 7-8, 9, 10
TAKE HOME TEST.
Due before Fri. Dec 12, 5PM
This take-home test consists of the following:
P. 1120: 18, 25, 26a+c, 28, 32, 34