Syllabus and Assignments
Problems in red are due on the Tuesday after they are assigned. Problems not in red are candidate exam problems.
Problems in red are due on the Tuesday after they are assigned. Problems not in red are candidate exam problems.
Week 1  TuesdayAugust 21  Vector algebra and geometry
Section 1.11.7 p. 14, Problems 4, 5, 9, 12, 13, 16 p. 23, Problems 1, 2, 5, 8, 9, 1324 
Scans of problem set 1

Week 1  ThursdayAugust 23  Equations of lines
Sec. 1.8 p.29, Problems 1,3,8,9,10,18 
Scans of problem set 2

Solutions to week 1 homework



HW 1  Max points = 21. Average score = 15.45
Week 2  Tuesday
August 28  Dot product, equations of planes, cross product
Sec. 1.91.12 p.34, Problems 3,4,11,13 p.38, Problems 1,2,3,4,13,14 p.51, Problems 2,3,5,11 
Scans of problem set 3

Week 2  ThursdayAugust 30  Triple scalar product, vector identities
Section 1,121.14 p.51, Problems 22, 23, 29, 30, 31 p.57 Problems 8, 9, 11 p. 60 Problems 5, 6, 11 
Additional problem:

Solutions to week 2 homework 

HW 2  Max points = 33. Average score = 21.125
Week 3  TuesdaySeptember 4  Curves, arclength, tangents, and velocity.
Section 2.12.2 p. 70, Problems 1, 2, 3 p. 85, Problems 1, 2, 3, 5 
Solutions to week 3 homework

Week 3  ThursdaySeptember 6  Acceleration, curvature, torsion, and the Frenet formulas
Section 2.3 p. 95, Problems 1, 3,4,5,6,10,13,14,15, 
Additional problem:

Week 4  TuesdaySeptember 11  Vector fields: gradient, flow lines, and divergence
Section 3.13.3 p. 112, Problems 1,3, 9, 10, 20 p. 117, Problems 1, 2 p. 124, Problems 4, 5,6, 8 
Solutions to week 4 homework

Week 4  Thursday
September 13  Divergence, Curl, Laplacian, Vector Identities
Section 3.33.8
No new homework. Review for exam.
Section 3.33.8
No new homework. Review for exam.
Week 5  TuesdaySeptember 18  Exam 1
p. 124, Problems 4, 5, 6 p. 132, Problems 6, 10, 12a p. 135, Problems 1, 2, 3, 7 p. 140, Problems 1, 7, 8 
Week 5 Solutions

Week 5  ThursdayReview of Exam 1

Exam 1  solutions and comments

Week 6  Tuesday
September 25  Vector differential identities, Cylindrical coordinates
p. 150, Problems 8, 9, 10, 11, 13
p. 169, Problems 2, 3, 6 (spherical only), 8,
Extra problem: Derive a formula for the velocity and acceleration of a particle in cylindrical coordinates
p. 150, Problems 8, 9, 10, 11, 13
p. 169, Problems 2, 3, 6 (spherical only), 8,
Extra problem: Derive a formula for the velocity and acceleration of a particle in cylindrical coordinates
Week 6  ThursdaySeptember 27  Cylindrical and Spherical coordinates
p. 170, Problems 12, 13, 14 
Solutions to week 6 homework

Week 7  Tuesday
October 2  Line integrals
Section 4.1
p.190, Problems 5,6,7,8,9,10,13
Extra problem: Let x=uv, y = (u^2v^2)/2, z=z. What are the gradient, divergence and Laplacian in this coordinate system?
Section 4.1
p.190, Problems 5,6,7,8,9,10,13
Extra problem: Let x=uv, y = (u^2v^2)/2, z=z. What are the gradient, divergence and Laplacian in this coordinate system?
Week 7  ThursdayOctober 4  Line integrals, domains, scalar potentials
Section 4.14.3 p.196, Problems 2,4,5,6,8,10 p.204, Problems 2, 4, 5, 6,7 
Solutions to week 7 homework 
Announcement
The Center for Academic Program Support (CAPS) is now offering a study group for students taking Math 311. The study group meets on the third floor of the Zimmerman Library on Mondays from 2 p.m. to 3 p.m. This group is not led by a tutor, but instead gives students in the course the opportunity to work together and share ideas on the homework; however, there is one tutor who has successfully completed the course available in the dropin lab during this time to answer questions.
Week 8  TuesdayOctober 9  Irrotational and solenoidal fields
Section 4.44.5 p. 212, Problems 6, 7, 8, 9b, 11 p. 222, Problems 2, 6, 7 ,8, 9 Homework 8 solutions

Practice exam

Week 9  TuesdayOctober 16  Exam 2
Week 9  ThursdayOctober 18  Review of Exam 2

Exam 2 and solutions

Week 10  TuesdayOctober 23  Class cancelled
Week 10  ThursdayOctober 25  Oriented surfaces and surface integrals
Section 4.64.7 p. 236, Problems 1, 2, 3, 4, 5, 6 
Solutions to week 10 homework

Week 11 Tuesday
October 30  Surface and volume integrals
Section 4.74.8
p. 246 2,3,8,9,11,12,14,19
Section 4.74.8
p. 246 2,3,8,9,11,12,14,19
Week 11  ThursdayNovember 1  Surface and volume integrals, divergence theorem
Section 4.74.9 p. 257, Problems 4, 6 p. 262, Problems 3, 4, 5, 6 
Solutions to week 11 homework

Week 12  Tuesday
November 6  Divergence theorem
Section 4.9
p. 263, Problems 11, 12, 13, 17, 18, 19, 20 (Without using Stokes' Theorem)
Section 4.9
p. 263, Problems 11, 12, 13, 17, 18, 19, 20 (Without using Stokes' Theorem)
Week 12  ThursdayNovember 8  Stokes' Theorem
Section 4.9, Problems 7, 9, 10, 11, 13, 16, 17 
Solutions to week 12 homework

Week 13  TuesdayNovember 13  Review for exam 3  Surface and Volume integration

Note: There is a typo in problem 2. The plane is x+y+z=0. A solution for both this case and x+y+z=1 has been provided.

Week 13  ThursdayNovember 15  exam 3


Week 14  Tuesday
November 20  Review of exam 3. Green's Formula's: Laplace and Poisson equations.
Section 5.2, Problems 1, 2, 5, 6, 7  Due Tuesday, December 4.
Hint on problem 5: The usual strategy to show uniqueness of a solution is to suppose there are two different solutions and try to show that the difference between them has to be zero.
Section 5.2, Problems 1, 2, 5, 6, 7  Due Tuesday, December 4.
Hint on problem 5: The usual strategy to show uniqueness of a solution is to suppose there are two different solutions and try to show that the difference between them has to be zero.
Week 15  Tuesday
November 27  Green's functions, fundamental theorem of vector analysis, Green's theorem
Section 5.4, Problems 5,6,7,8,9
Section 5.4, Problems 5,6,7,8,9
Week 15  ThursdayNovember 29  Matrix techniques in vector analysis, linear orthogonal transformations
Section 5.7, Problems 1, 6, 10, 14, 15, 18, 19 Section 5.8, Problems 2, 4, 5, 11, 12 
Homework 13 solutions

Week 16  TuesdayDecember 4  Review for fourth exam. Work through practice exam 4.

12/5/12  corrected typos in problems 4 and 6.

Week 16  ThursdayDecember 6  exam 4

There was a typo in problem 5. It should read x^33xy+y^3=0, however, this equation is not used in the solution of the problem and the parametric form given is correct.

Exam 4 will take place in class on December 6. As with the previous exams, you may use one page of notes. There will be five problems:
 One problem based on section 1.12.4
 One problem based on section 3.13.11
 One problem based on section 4.14.5
 One problem based on section 4.64.9
 One problem based on sections 5.25.5, 5.78