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)