MATH 241-FALL 2013-Sections 5,6,7,8-COURSE LOG
Problems listed in boldface
italics are
to be turned in as homework. The remaining recommended problems
will be used in the quizzes.
1. Linear analytic geometry
8/21 W Introduction/ vector addition and scaling/length and
unit vectors/dot product and angle
(12.1) 42, 43, 46, 58,
59
(12.2) 26, 27
(12.3) 23, 28, 31, 45, 46, 48, 49
Lecture
1 scan
8/23 F projections/wedge product in R2 (oriented area)
/cross product in R3 (def)
(12.3) 59, 60,
64, 65,
79, 80
(12.4) 20, 21, 30, 43, 44
Lecture
2 notes
8/26 M HW1 due (8 problems)/area and volume/ equations for
lines and line segments, typical problems.
(12.2) 44,
48, 49, 51,
53, 58, 59, 60, 61, 62
Lecture
3 notes
8/28 W planes, intersections, projections: typical problems
(12. 5) 22, 27,
29, 33, 47, 52, 60,
62
Lecture
4 notes
sections 12.6 and 12.7 are independent
reading assignments: this material will be needed later.
8/30 F parametrized curves in the plane and in space
(13.1) 14,
16, 25, 26,
42
Lecture
5 notes
9/2 M Labor Day (No classes)
9/4 W HW2 due. vector-valued functions; position, velocity and
acceleration vectors/ tangent line at a point/
regular parametrization/ reparametrization, chain rule/ product rules:
dot product, vector product/Examples
(13.2) 36, 40,
45, 55, 56,
58, 60, 64
(13.3) 13,
16, 17, 22, 24, 25, 27, 29
(these 8 problems are HW3, due Monday 9/9)
Lecture
6 notes
9/6 F arc length parametrization/ unit tangent vector
Lecture
7 notes
9/9 M HW3 due/ curvature: plane curves, graphs, curves in
space/examples: ellipse, graph of f(x)=x^n, helix
(13.4) 15,
18, 25, 28, 30,
37, 38, 43, 44, 50, 53
Lecture
8 notes
9/11 W Mechanics examples: tangential and normal components of the
acceleration vector.
(13.5) 16, 17, 18,
21, 23, 24, 27, 29,
48, 49,
51, 52
(problems
from 13.4 and 13.5 due Monday, 9/16: HW4)
Lecture
9 notes
9/13 F two mechanics examples/ graphs and level sets in several
variables (examples)
Lecture
10 notes
(14.1) 20, 29 to 36, 38, 39
9/16 M limits in two variables (14.2)
Lecture
11 notes
(14.2) 13, 14, 16,
17, 21, 24, 29,
31, 32, 36
9/18 W Partial derivatives (14.3)
Lecture
12 notes
(14.3) 58, 60, 63, 73, 74, 76, 79b,d 80, 81, 83
9/20: F Definition of the derivative/ linearization/
differentials
(14.4) 14, 16, 19, 35, 36, 40
Lecture
13 Notes
9/23 M Tangent plane to a graph/ directional derivative/ chain rule for
curves
Lecture
14 Notes
(14.4) 7, 10, 11, 12
(14.5) 15, 19, 25, 26, 28, 31, 32, 37
9/25 W Properties of the gradient, tangent planes
Lecture
15 Notes
(14.5) 42, 43, 46, 51, 52, 61, 66, 68
9/27 F Review
9/30 M Exam 1. Included: Lectures from 8/21 to 9/25
Exam
1
Exam1
solutions
10/2 W Chain Rule in several variables (lecture by Prof.
Ken Stephenson)
(14.6) 4, 5,
12, 13,
17, 25, 26, 31, 36, 37 (HW6)
10/4 F Implicit differentiation/ max-min, critical points, 2nd
derivative test (lecture by Prof. Ken Stephenson)
(14.7) : 3, 4,
5, 7, 33, 34, 35, 37 (HW6)
Lecture
17 Notes (by Ken Stephenson)
10/7 M Optimization in several variables
Lecture
18 Notes
(14.7) 39, 41,
44, 46, 48,
50 (HW7)
10/9 W Optimization with constraints, Lagrange multipliers/ HW6
due
Lecture
19 Notes
(14.8) 6, 7,
8, 11, 16,
17, 20,
35, 36, 37, 39, 40
(HW7)
10/11 F Optimization: examples (lecture by Prof. Ken Stephenson)
10/14 M Double integrals over rectangles
Lecture
21 Notes
(15.1) 18, 24, 30, 35,
36, 40, 42,
44, 45 (HW 8)
10/16 W Double integrals over general regions
(15.2) 21, 22,
25, 26, 29, 32,
49, 52,
53, 56 (HW 8)
Lecture
22 Notes
10/18 F FALL BREAK (no
classes)
10/21 M HW8 due/ polar coordinates/ applications of double
integrals
Lecture
23 Notes
(15.4) 15, 16 (symmetry), 17, 18, 19 (symmetry), 20 (symmetry), 21, 22
(15.5) 4, 5, 8/ 11, 12, 13 16/ 24, 25/ 50, 51, 54
10/23 W Problems on double integrals (review)
10/25 F Review
Lecture
25 notes
(solutions to review problems done in lecture on 10/23 and 10/25)
10/28 M Exam 2 (chain rule,
optimization, double integrals)
Exam
2 (with solutions)
10/30 W Triple integrals
(15.3) 10, 14, 16,
21, 23, 25,
26, 29, 35
(HW9)
Lecture
26 Notes
11/1 F Triple integrals: cylindrical/spherical coordinates,
applications
(15.4) 29,
32, 35, 44, 45,
49, 52 (HW9)
(15.5) 21, 22, 27
(HW9)
Lecture
27 Notes
11/4 M Class canceled
11/6 W Change of variable (15.6)/ HW9 due
(15.6) 21, 34, 35,
38, 39, 40,
41 (HW10)
Lecture
28 Notes
11/ 8 F: Parametrized surfaces/ surface integrals of functions (16.4)
(16.4) 7, 8,
20, 23, 25, 26,
34, 36, 37 (HW10)
Lecture
29 Notes
11/11 M HW
10 due/ Line integrals of functions and vector fields/flux-type
integrals across curves or surfaces
Lecture
30 Notes
functions on curves (plane, space): 9, 11 (16.2)
functions on surfaces: see 16.4
line integrals in the plane: 22, 24 (16.2)
line integrals in space: 35, 36, 52 (16.2)
flux integrals in the plane: 62, 65 (16.2)
flux integrals across surfaces: 5, 7, 8 (16.5)
(highlighted problems are for HW11, due 11/18)
11/13 W Conservative vector fields (16.3) (16.1: independent reading)
Lecture
31 Notes
(16.3) 12,
17, 21, 22,
27, 28 (HW11)
11/15 F Green's theorem (17.1)
Lecture
32 Notes
Practice problems from 17.1: 10, 11, 12, 17, 21, 24, 25, 36, 3
11/18 M Stokes' theorem (17.2)
Lecture
33 Notes
Practice problems from 17.2: 12, 13, 17, 19, 20, 21, 22, 26
11/20 W Problems from Chapters 16, 17
11/22 F Problems from Chapter 15 and sect 16.4
11/25 M Exam 3
(triple integrals, change of variable, conservative vector fields/
line integrals and flux integrals, theorems of Green and Stokes)
Exam
3 (with solutions)
11/27 W Divergence theorem in the plane and in space. Example: flux of
a configuration of "point charges" in
the plane or in space. Identities curl (grad V)=0, div (curl F)=0, div
(grad u)=Laplacian of u.
Lecture
34 Notes
Problems from 17.3: 13, 15, 16, 17, 20, 22, 33
This is HW 12 (4 problems, optional, due Monday 12/2)
12/2: HW 12 due (last day)/ discussion of exam 3
FINAL EXAM: Thursday, December
12, 2:45-4:45 (in the usual classroom; blue books not needed)
Structure of the
final exam: 8 problems
3 chosen from exam 1 or exam 2 (with specific data changed): 36%
1 problem on Lagrange multipliers: 14%
3 chosen from exam 3 (with specific data changed): 36%
1 problem on the divergence theorem: 14%
Final
Exam (with solutions)