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)