Math 13 Fall 2005

Math 13: Calculus of Vector-Valued Functions
Fall 2005

Mon, Wed & Fri 12:30 - 1:35pm
X-Hour: Tues. 1-1:50PM
Location: 102 Bradley Hall

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Instructor: Craig Sutton
Office: 307 Bradley Hall
E-mail: craig.j.sutton AT dartmouth.edu
Phone: 646-1059
Office Hours:
Mon. 3:00 - 4:30 PM
Tues. 1-2PM (when we don't use our X-hour)
Fri. 9 - 10:30 AM
(Also by Appointment)

TA: Paul Kinlaw
Tutorial: 7-9PM (Su., Tu. & Th.)
Location: 104 Gerry Hall

Math 13 Syllabus/Homework

General Information

Textbook: Vector Calculus (3rd Edition), Susan J. Colley. (required)

Course Description: This course is a sequel to Math 8/9 and provides an introduction to the calculus of vector-valued functions. Although this is a topic of intrinsic mathematical interest (especially for those who like geometry & analysis), it should also be of particular relevance to students interested in physics and engineering.

Topics will include some of the following:

differentiation of vector-valued functions and linear approximation
differentiation and integration of parametrically defined functions
double & triple integrals including change of coordinates.
vector fields, curl and divergence
line & surface integrals, Green's theorem and Stoke's theorem.

Prerequisites: Math 8 or the equivalent. If you are unsure about your preparation please speak with me as soon as possible.

Disabilities: If you have a disability and require disability related accommodations please speak to me and Cathy Trueba, Director of Student Disability Services, in the Academic Skills Center as soon as possible, so we can find a remedy.

Office Hours: Office Hours are a good time to flesh out material you're having trouble with or to go beyond the syllabus. Please don't hesitate to stop by in either case.

Tutorials: Starting Sept. 22 Paul Kinlaw will run a tutorial for this course on Su., Tu. & Th. 7-9PM in 104 Gerry Hall.

Homework:

A. Reading: Corresponding to each class there will be a reading assignment which should be completed before coming to class.

B. Daily Exercises: Corresponding to each class there will be daily homework problems which are intended to help you flesh out the material we discussed that day. Although these problems will not be collected or graded, you should complete these problems before the next class.

C. Weekly Homework: There will be weekly homework assignments for this course whihc in general will be assigned on Wednesday and collected the following Wednesday at the start of class. No late homework will be accepted (see "Personal Day" below).

Personal Day: During the course of the term things will come up. You might catch a cold, have a fight with a friend, or perhaps you will have a sudden attack of lethargy. All of these things can temporarily impair your ability and desire to do your work. For this reason each of you will be granted one personal day. That is, I will drop your lowest homework score of the semester in order to smooth out a minor bump during the semester. Therefore, I will not accept late homework except in the event of a major crisis (e.g., family issues, protracted illness, etc.). In this event you should speak with your dean and obtain a note outlining the issue, so we can devise a plan to get you back on track.

Honor Principle:

A. Homework: I encourage you to form study groups to discuss the course material and homework problems. However, the assignments you turn in should be in your own words and handwriting. Also, the names of others you consulted with must appear at the top of your assignment.

B. Exams: You should not give or receive help during exams. All exams are closed book unless otherwise stated.

(Tentative) Grading Policy

Your course grade will probably be determined by the following scheme.

Weekly Homework:     15%
Exam I :                        25%
Exam II :                        25%
Final :                              35%

I will announce the definitive grading guide in the coming weeks.

Syllabus/Homework

WEEK 1

Sept. 21

Topics: Course Mecahnics/Overview, Review of Vectors
Reading (Due Today): 1.1-1.7
Daily Exercises (Due Next Class): 1.2 #11, 13 & 19; 1.3 # 5, 9, & 11; 1.4 # 1, 3, 7, 15; 1.5 # 1, 5 & 13; 1.6 # 5 & 7
Weekly Homework: HW1 (due Sept. 28, last updated Fri. Sept. 23 3PM)

Sept. 23

Topics: Vector Wrap-up, Matrices & Linear Maps
Reading: 1.1-1.7 & 2.1
Daily Exercises (Due Next Class): 1.7 # 1, 5, 7, 11, 15, 17 & 19; 2.1: # 1, 3, 5 & 9

WEEK 2

Sept. 26

Topics: Matrices, determinants and area; Review of Limits
Reading (Due Today): 2.1-2.4 (Skip Newton's method in Sec. 2.4)
Daily Exercises (Due Next Class): 2.2: # 1, 3, 5, 17, 22, 34 & 37; 2.3: #1, 3, 5, 11, 15, 17, 21, 23, 29

Sept. 27 (X-Hour)

Topics: Good Linear Approximations: Partial Derivatives and the Tangent Plane
Reading: 2.2-2.4 (Skip Newton's method in Sec. 2.4)
Daily Exercises: 2.2: # 1, 3, 5, 17, 22, 34 & 37; 2.3: #1, 3, 5, 11, 15, 17, 21, 23, 29

Sept. 28

Topics: Chain Rule
Reading (Due Today): 2.5 & 2.6
Daily Exercises (Due Next Class): 2.4:#9, 11, 18; 2.5: # 15 , 19 & 21
Weekly Homework: HW2 (Due Oct. 5)

Sept. 30

Topics: Directional Derivatives & the Gradient
Reading (Due Today): 2.5& 2.6
Daily Exercises: 2.6: # 1, 3, 5, 9, 23, & 24

WEEK 3

Oct. 3

Topics: Vector Fields: Gradient, Divergence & Curl
Reading (Due Today): 3.3 & 3.4
Daily Exercises (Due Next Class): 3.3: # 1, 3, 5, 9, 11, 23, 17 & 27; 3.4: # 1, 3, 5, 7, 9, 11, 13

Oct. 4 (X-hour)

Topic: More Vector Fields, Catch Up
Reading: Chp. 1, Chp 2 (w/o Newton's method), 3.3 & 3.4
Daily Exercises:

Oct. 5

Topics: Volume & Double Integrals: Integrals over Rectangles.
Reading (Due Today): 5.1-5.2
Daily Exercises (Due Next Class): 5.1: 3 1, 3, 5, 11, 13 & 15
Weekly Homework: HW3 (Due Oct 14, extra time because of exam, etc.)

Oct. 7

Topics: Double Integrals: Beyond Rectangles & Order of Integration
Reading (Due Today): 5.1, 5.2 & 5.3
Daily Exercises (Due Next Class): 5.2: # 1-15 (odd)

WEEK 4

Oct. 10

Topics: Double Integrals: Change of Variables
Reading (Due Today): 5.3 & 5.5 (p. 322-335)
Daily Exercises (Due Next Class): 5.3:#1, 3, 5, 9, 11

Oct. 11 Exam I: 7-9PM (Rockefeller 2)

Oct. 12

Topics: Double Integrals: Change of Variables
Reading (Due Today): 5.5 (p. 322- 335)
Daily Exercises (Due Next Class): 5.5: # 1-5, 9, 13-17

Oct. 14

Topic: Application: The Gaussian Integral
Reading (Due Today): 5.4 & 5.5 (p. 335-341)
Daily Exercises (Due Next Class): 5.4: 1-18 (odd), 23 & 25; 5.5: # 24, 25, 27 & 29
Weekly Homework: HW4 (Due Oct. 19)

WEEK 5

Oct. 17

Topic: Triple Integrals
Reading (Due Today): 5.4 & 5.5 (p. 335-341)
Problems:

Oct. 19

Topic: Change of Variables (Wrap-up), Summary of 2D & 3D Integrals, Applications of Integration
Reading (Due Today): 5.6
Daily HW (Due Next Class): 5.6: 1-21 (odd), 27 & 33
Weekly Homework: HW5
Mid-Semester Survey (Due Friday, Oct 21)

Oct. 21

Topic: Applications of Integration; Vector Line Integrals & Work
Reading (Due Today): 3.2 & 6.1
Daily HW (Due Next Class): 6.1: 1-25 (odd),

WEEK 6

Oct. 24

Class: Vector & Scalar Line Integrals, Conservative Vector Fields
Reading (Due Today): 6.2 & 6.3
Daily HW (Due Next Class): Catch up on old Daily HW

Oct. 26

Class: Conservative Vector Fields & the Conservative Litmus test, Finding potential functions
Reading (Due Today): 6.2 & 6.3
Daily HW (Due Next Class): 6.3: # 1-25 (odd); 6.2 # 1,3, & 5
Weekly Homework: HW6

Oct. 28

Class: Conservative Vector Fields & Green's Theorem
Reading (Due Today): Chp. 6
Daily HW (Due Next Class): 6.2: # 1- 25 (odd);

WEEK 7

Oct. 31

Class: Green's Theorem Wrap-up; Parametrized Surfaces
Reading (Due Today): 7.1 & 7.2
Daily HW (Due Next Class):

Nov. 2

Class: Parametrized Surfaces
Reading (Due Today): 7.1
Daily HW (Due Next Class): 7.1: # 1-11 (all)
Weekly Homework: Review for Exam II

Nov. 4

Class: Surface Area; Scalar & Surface Integrals
Reading (Due Today): 7.2
Daily HW (Due Next Class):

WEEK 8

Nov. 7

Class: Scalar & Surface Integrals
Reading (Due Today): 7.2
Daily HW (Due Next Class): 7.2: # 1-13 (odd)

Pre-Exam Office Hours:

Mon. 3-5PM
Tues. 12:30-2:30PM

Nov. 8 Exam II 7-9 PM (Carson L01)

Nov. 9

Class: Exam II Discussion
Reading (Due Today): 7.2
Daily HW (Due Next Class):
Weekly Homework: HW7

Nov. 11

Class: No Class
Reading:
Daily HW (Due Next Class):

WEEK 9

Nov. 14

Class: Surface Integrals; Orientation
Reading (Due Today): 7.3
Daily HW (Due Next Class):

Nov. 16

Class: Orientation; Stokes' Theorem
Reading (Due Today): 7.3
Daily HW (Due Next Class): 7.3: #1-5; REVIEW FOR FINAL
Weekly Homework (Due Nov. 21): HW8

Nov. 18

Class: Stokes' & Gauss's Theorem
Reading (Due Today): 7.3
Daily HW (Due Next Class): 7.3: # 6-9; REVIEW FOR FINAL

WEEK 10

Nov. 21

Class: Gauss' Theorem; Conservative Vector Fields Revisited
Reading (Due Today): 7.4
Daily HW (Due Next Class): REVIEW FOR FINAL
Weekly Homework: HW9

Nov. 23

Class: No Class
Reading (Due Today):
Daily HW (Due Next Class): REVIEW FOR FINAL

Nov. 25

Class: No Class
Reading:
Daily HW (Due Next Class): REVIEW FOR FINAL

WEEK 11

Nov. 28

Class: Stokes' & Gauss' Theorem Wrap-up, Applications
Reading (Due Today): 7.4
Daily HW (Due Next Class): REVIEW FOR FINAL

Nov. 30

Class: Electric Fields; Wrap-up
Reading (Due Today):
Daily HW (Due Next Class): REVIEW FOR FINAL

Pre-Exam Office Hours

Mon., Nov. 28 3-4:30PM (as usual)
Tues., Nov. 29 1-2PM (as usual)
Wed., Nov. 30 4-6 PM
Thu., Dec. 1 9-11 AM
Fri., Dec. 2 3-5 PM

Saturday, Dec. 3 8-11AM Final Exam (102 Bradley)