Department of Mathematics, Louisiana State University, Baton Rouge

Math 2057 Calculus III

Spring 2004 Section 1

Professor James J. Madden

First Day Announcements

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 5,11--16 (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
14.7-8
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

See the practice test and solutions and the actual test and solutions from last semester. (Look on lines 9/19 and 9/22.)

Get a blank copy of the 9/22/2003 test.

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
15.1-15.2
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
15.2-15.3
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 make-up class will be scheduled later this semester.)   Complete HW from 3/3!!!
3/8
15.3
examples
   
3/10
15.4
polar coordinates
  15.4:1-17 (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. 1083-5, 1093-7.  
3/26
  Review 1 Practice test. Picture for #6.  
3/29
  Review 2    
3/31
Integration
TEST    
4/2
16.1
Vector fields    
4/5-4/9   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. Path-independent 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, 23--29
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 / Take-home exam
Get a copy of the take-home --
5/3
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review/discussion
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5/5
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review/discussion
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5/7
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Take-home exam DUE.
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5/10
FINAL
In ususal classroom, 3PM--5PM
To review for final,
see review for Fall 2003
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