MATH 241 Spring 2005- Course log and homework
Problems in italics have been
discussed in class
1/12 Course policies
Algebraic vectors and
geometric vectors: operations, equivalence
9.2: 3, 4, 7, 9
1/14 Dot product and applications
9.3: 19, 21, 25,
34, 35, 36, 40, 41
1/18 Discussion of problems; vector product
9.4: 15, 17, 23,
26, 27, 33
1/19 triple scalar product; eqns of lines
9.5: 11, 12, 13, 15
1/21 eqns of planes
9.5: 21, 22, 23, 26,
27, 28, 29, 33, 35, 36,
38, 41, 45
1/24 discussion of homework problems
1/25 Quiz 1:
9.3 (35) 9.4(26) 9.5 (22, 38)
discussion of
quiz 1
sketching
parametrized curves in space: 2 examples (10.1)
Policy announcement: the syllabus did not address the
relative weights
of quizzes and exams. The policy is this: each problem proposed in a
quiz/exam
will have the same weight in the final average. Since quizzes
will have 3-4
problems and exams 6-8, it follows that each exam will enter the course
grade
with about twice as much weight as each quiz.
1/26 smooth parametrized curves: tangent
vector, tangent line, product rules
10.1: 19, 28, 29, 30
10.2: 5, 7, 15, 19, 43,
46
1/28 arc length and curvature; unit tangent and
unit normal vectors
10.3: 3, 7, 11, 18, 25,
49
1/31 discussion of homework problems
motion in space (10.4)
10.4: 6, 10, 13, 19, 21, 30
2/1 Quiz
2: 10.1:29; 10.2:46; 10.3: 49
solution of quiz 2
quadric surfaces (start)
2/2
quadric surfaces (9.6)
9.6: 16, 21, 22, 23,
32, 34
partial derivatives and tangent planes (p. 769-771,
p. 779-781): start
partial derivatives: p.777 (11.3): 13, 14, 15, 17, 23, 25, 35, 36
2/4 tangent planes to graphs (end)
11.4: 1, 2, 4;
5, 6 (no graph)
Reading assignments: 9.7 (by 2/7) , 11.1 (by 2/9)
2/7 10.5: parametrized surfaces; tangent
planes
10.5: 2,
4, 17, 18, 20, 24
11.4: 33, 34 (no graph)
2/8 Exam 1 (PDF
file)
2/9
Functions of several
variables: level sets, limits
2/11
implicitly defined functions; higher order partials
11.1 16, 18 22, 39
11.2: 10,
11, 12, 17, 18, 20
11.3: 41, 42, 48, 52, 54
2/14
Linear approximations, differentials
11.4: 9, 10, 12, 20, 28, 30, 31
solution of exam 1
2/15 Discussion of HW
problems (10.5, 11.1-11.4)
2/16 11.6: gradient vector, directional
derivatives
11.6: 4, 5, 10, 20, 23
27, 29, 30, 32, 34
2/18 11.6: geometric applications-
tangent line/plane to level sets
11.6: 35, 36, 42, 44, 46, 49, 52(a)
2/21 Discussion of HW problems,
review
2/22 Exam
2: 9.5, 10.4, 10.5, 11.1 to 11.4, 11.6
(Review also Exam 1 and the quizzes)
Exam 2
(PDF), with answers
2/23
11.5: chain rule, implicit function theorem
11.5: 4, 6, 20, 26, 30, 34
2/25 11.7: max/min in 2 variables
11.7: 6, 8, 24, 25, 29, 30
2/28 max/min (cont'd)
3/1 Quiz 3: Hw for 11.5, 11.7
11.7: 33, 34, 35, 36, 37, 39, 45
3/2
Lagrange multipliers (11.8)
11.8: 5, 6, 9, 10, 15, 17, 18, 19, 24, 36, 37, 38
3/4 Taylor
approximations in 2 variables, with error bounds
(p. 821 and handout including homework problems)
3/7 discussion of HW
problems
3/8
Quiz 4: (HW for 11.7, 11.8,
handout)
solution of quiz 4
3/9, 3/11 iterated integrals: 12.2, 12.3
12.2: 5, 6, 8, 12, 13, 15, 20, 21
12.3: 4, 7, 8, 9, 19, 20, 29, 30, 35, 36, 37, 41
3/14 double integrals in
polar coordinates; center of mass
12.4: 10, 12, 16, 19, 21, 26, 27, 32
12.5: 4, 6, 8, 10, 11
3/15 review
(driven by student questions)
Exam 3: Wednesday 3/16 (sections
11.5, 11.6, 11.7, 11.8, handout, 12.2, 12.3)
Exam 3 (PDF)
3/18
Problems from 12.5
3/28 Triple
integrals
12.7: 5, 6, 15, 18, 35, 36, 38(a)(b)
3/29
Cylindrical/spherical coordinates; discussion of exam 3
12.8: 8, 10, 14, 16, 18, 22 (a)(b), 26, 27, 29, 30
3/30
vector fields
13.1: 3, 4, 5, 6, 11-14, 15-18, 29-32
4/1 line
integrals of vector fields
13.2: 5, 6, 10,
11, 16, 17, 19, 20
13.3: 1, 2, 11
4/4 conservative
vector fields
13.3: 3, 4, 6, 10, 13, 14, 15, 21
discussion of Ch. 12 homework
4/5
Quiz 5: HW from 12.4, 12.5, 12.7, 12.8
solution of quiz
conservative vector fields
4/6
simply-connected regions, conservative v.f. (summary)
problems from 13.2 and 13.3
13.3: 23, 24, 27, 28, 33
4/8
Exam 4: Ch. 12 (12.1, 12.6, 12.9 excluded), Ch.13 up to 4/4 lecture
Exam 4 (PDF)
4/11
Green's theorem
Applications: computation of area, line integrals of d(theta)
13.4: 7, 8, 9, 10, 12, 16, 19, 20, 27
4/12
solution of exam 4
examples from 13.4
integrals with respect to arc length (13.2)
13.2: 2, 4, 7, 8, 26, 28
4/13
surface area and surface integrals (12.6, 13.6)
12.6: 2, 3, 8, 10, 11
13.6: 5, 9, 12, 34
4/15
flux of a vector field; oriented surfaces (13.6)
13.5 divergence of a vector field- the divergence thm in the plane
13.6: 19, 21, 25, 27
13.5: 7-9, 10, 13, 14, 18, 19, 20, 23,
24
4/18
curl of vector fields (13.5)
discussion of HW problems
4/19 Quiz 6 (HW from 13.2, 13.4,
12.6, 13.6)
divergence theorem (13.8)
13.8: 9, 12, 13, 18, 20
4/20 Stokes'
theorem (13.7)
13.7: 7, 8, 9, 10, 11(a)
4/22
Exam 5 (13.1 to 13.6)
Exam 5 (PDF)
4/25
solution of exam 5
discussion of HW problems
4/26
optional quiz 7 (HW from 13.7, 13.8) (will replace lowest quiz
grade, if higher)
Remark: in addition to
being optional, this quiz (like all others) is worth at most 12 pts out of a total
of 300 possible points in the course. That's 4%, and therefore the quiz
is consistent with U policy for the last week
of classes.
solution of quiz 7; course evaluations
ch. 13 review problems ( p. 987): 5, 7, 11, 12, 16,
26, 28, 32, 34
4/27
ch. 13 review problems (even-numbered from list above)
5/2 (Monday) FINAL (= Exam
6): 13.2 to 13.8
Remark: the problems on
the final will be based on the quizzes and exams for
ch. 13 and from the list of problems from p.987 given above (the
specific data
for the problem-functions, vector fields, curves, surfaces, dimension
of
the space, etc.-may be
changed)
Exam 6 (PDF)