MATH 311 - 002 3363  VECTOR ANALYSIS    Spring 2017  

Time MW 1600-1715, Location SMLC-120

               

Instructor: Dimiter Vassilev     Office : SMLC 326  Email: vassilev@unm.edu  Phone Number: 505 277 2136 

Office Hours: M&W 9:30am-10:30am & 2:30pm-3pm  but feel free to stop-by anytime you have a quick question.

MATH311 Course Description. Vector algebra, lines, planes; vector valued functions, curves, tangent lines, arc length, line integrals; directional derivative and gradient; divergence, curl, Gauss’ and Stokes’ theorems, geometric interpretations. Prerequisite: Calculus III.

Final Exam: Monday May 8 5:30‐7:30 p.m. Students having conflicts with this examination schedule must notify the appropriate instructor before Friday, March 31, 2017. Any student having more than three examinations scheduled in any one day may notify the instructor of the last examination listed. If notified before Friday, March 31, 2017, the instructor shall make arrangements to give a special examination. Conflicts arising as a result of scheduling out of normal hours-pattern or day sequences must be resolved by the instructor of the off-pattern courses.        
Semester Deadline Dates: http://registrar.unm.edu/semester-deadline-dates/spring-2017-printable.html                                                                                                             

Please note the following guidelines for the course:

Text: Introduction to Vector Analysis by H. F. Davies and A. D. Snider, 7th Edition, Hawkes Publishing, ISBN: 0-697-16099-8. Additional books of interest: 1. Susan Jane Colley, Vector Calculus, Fourth Edition; 2. M.R. Spiegel, Schaum’s Outlines-Vector Analysis, McGraw-Hill; 3. Paul C. Matthews, Vector Calculus, Springer Undergraduate Mathematics Series, 1998, Springer-Verlag London, eBook ISBN 978-1-4471-0597-8, Softcover ISBN, 978-3-540-76180-8

Grades: The final grade will be determined by homework (10%), two midterms( 50%) and a final exam (40%).  The Final Exam score will replace all midterm scores that are lower than the Final Exam score. All grades will be posted on UNMLearn. Although a small curve might be used, 90% , 80% or 70% of the possible maximum points guarantees at least an A, B or C, respectively.

Homework:  Homework is due every Monday at the beginning of the class. You are encouraged to work together on the homework, but you are required to write up your own solutions in your own words. Links to solutions to most of the homework problems can be found on UNMLearn. Please note the Academic dishonesty section below. To help the grader, please write your solutions up neatly and clearly (no points will be given for work that the reader cannot follow- this is also true for exams).   The two lowest homework grades will be dropped. Please no late homework! The syllabus also lists recommended homework problems.  These are NOT to be handed in. Work as many as it takes for you to understand the material.  Keep all of your homework together in a folder for an easy reference.  You should see me as early and as often as necessary if you are having difficulties with the homework problems.

Reading: You are expected to read the textbook. Since class time is short, there will be theorems and examples that you will need to read on your own. Reading sections in the book before they are discussed in class will help you to get the most out of class time and to stay on top of the material. This is especially true for the material marked in the schedule as "review from Calculus III". I will almost exclusively only do problems and go beyond what you learned in Calculus III in these sections.

Academic dishonesty includes, but is not limited to, dishonesty in quizzes, tests, or assignments; claiming credit for work not done or done by others; hindering the academic work of other students; misrepresenting academic or professional qualifications within or without the University; and nondisclosure or misrepresentation in filling out applications or other University records. Each student is expected to maintain the highest standards of honesty and integrity in academic and professional matters. The University reserves the right to take disciplinary action, up to and including dismissal, against any student who is found guilty of academic dishonesty or who otherwise fails to meet the expected standards. Any student judged to have engaged in academic dishonesty in course work may receive a reduced or failing grade for the work in question and/or for the course.

Exams: The exam dates are given in the schedule below. No makeup exams will be given unless you contact your instructor ahead of time with a documented “university authorized absence” (illness, family emergency, active participation in scholarly or athletic events).  All exams can include some multiple-choice questions.  The exams will be based on the homework problems. 

Disability Statement: We will accommodate students with documented disabilities. During the first two weeks of the semester, those students should inform the instructor of their particular needs and they should also contact Accessibility Services in Mesa Vista Hall, Room 2021, phone 277-3506. 

 Math 311 Spring  2017 homework and schedule

 

Day

Class Date

Topics                                                                                   

Due Homework (turn in following Monday) For available Solutions see UNMLearn

 Extra Problems (do NOT hand in)

M

1/16

 MLK - no class

 HW1:
  • 1.5/6,12,21   
  • 1.7/4,8
  • 1.8/7,18  
  • 1.9/8,12a,13 
  • 1.10/3,4,13

1.5/4,5,13,15 1.7/1,5,9,13-24
1.8/1, 3, 11, 12, 13.
1.9/ 3, 5, 11, 15,27.
1.10 /5, 10.

W

1/18

Sections 1.2 – 1.10 (Review from Calculus III) 

  • Vector algebra and cartesian coordinates
  • Geometry and equations of the line.
  • Scalar product and equations of a plane

 

 

 

 

 

M

1/23

Sections  1.11 – 1.14 (Review from Calculus III)

  • Orientation and Cross product.
  • Triple scalar products.
  • Vector Identities.

HW2:

  • 1.12/2,8,12,14,21
  • 1.13/3, 6,17   
  • 1.14/ 3, 11

 

 1.12/ 5, 11,13, 19, 20, 26
1.13/ 5, 8, 12
1.14/6, 7, 10
 

W

1/25

 

 

 

 

 

M

1/30

Sections 2.1 – 2.3

  • Curves, tangents, velocity, acceleration. (Review from Calculus III)
  • Arclength and curvature. (Review from Caluclus III)
  • Torsion and the Frenet formulas

HW3:

  • 2.1/ 1, 4,3a, 5(h)
  • 2.2/2, 5, 6, 9
  • 2.3/2, 5, 9, 13, 15

2.1/3

2.2/ 7,8
2.3/1,4, 6, 17
 

W

2/1

 

 

 

 

 

M

2/6

 Sections 3.1 – 3.4 (Review from Calculus III)

  • Scalar fields, level lines/surfaces, gradient.
  • Directional derivatives, vector fields and flow lines.
  • Divergence and Curl.

HW4:

  • 3.1/1(a), 9, 12, 14,  24  
  • 3.2:/2
  • 3.3/3, 4, 6, 11
  • 3.4/ 4, 9

3.1/3,4,10,20,27 3.2/2, 3, 4.
3.3/3,5,7,8,10 3.4:/2, 3, 10, 11.
 

W

2/8

 

 

 

 

 

M

2/13

 Sections 3.6, 3.8

  • Laplacian.
  • Vector differential identities

HW5:

  • 3.6/ 2, 4, 5
  • 3.8:/6, 10(b, g, i)

3.6: 7

3.8: 9,11, 12

W

2/15

 

 

 

 

 

M

2/20

 

Exam I extra credit (due Wednesday March 1

  

W

2/22

Exam 1 - covers Sections 1.2 - 3.8. See UNMLearn for Practice Problems. Exam I Solutions

 

 

 

 

 

M

2/27

Sections 4.1, 4.3 (Review from Calculus III)

  • Line integrals.
  • Domains
  • Conservative fields: potentials.

HW6:

  • 4.1/ 6, 7, 10, 12, 14, 18, 20
  • 4.3/2, 4, 5 6, 7.
4.1: 1, 2, 3, 4
4.3: 2, 8.
 

W

3/1

 

 

 

 

 

M

3/6

Sections 4.2, 4.3, 4.4, 4.5 (review from Calculus III)

  • Conservative fields: Irrotational fields.
  • Scalar and vector potentials: two-dimensional fields.

HW7:

  • 4.2/ 2, 4, 8
  • 4.4/ 1( b,  d, e), 3, 7, 9
  • 4.5/ 4, 9
 4.2: 3, 5, 6, 7, 10. 

W

3/8

 

 

 

 

 

M

3/13

Spring Break

 

 

W

3/15

Spring Break

 

 

 

 

 

M

3/20

 Sections  4.6, 4.7

  • Oriented surfaces
  • Surface Integrals.

HW8:

  • 4.6/ 1, 2,  5, 6
  • 4.7/ 1, 6, 11, 14, 16, 21.

4.6: 3, 4

4.7: 2, 4, 5, 15, 20, 21.

W

3/22

 

 

 

 

 

M

3/27

Section 4.8, 3.10, 3.11, 4.9

  • Volume integrals. (Review from Calculus III)
  • Curvilinear Coordinates. Polar coordinates, Spherical coordinates, Cylindrical coordinates.

HW9 (corrected):

  • 4.8/1, 3, 5a, 6
  • 3.10/2, 6 (do it only for cylindrical working as in class for polar coordinates), 7, 8, 11
  • 3.11/ 4, 13
 3.10: 10, 13, 14

W

3/29

 

 

 

 

 

M

4/3
  • Introduction to Divergence and Stokes theorem.

 

Exam 2 on all sections covered since Exam 1. Exam II solutions

(See UNMLearn for practice problems).

 

W

4/5

 

 

 

 

 

M

4/10

Section 5.1, 5.2

  • Divergence Theorem. Applications - solid angles, conservation of mass, heat conductivity, Gauss’ law, electricity and Maxwell's equations.

HW10:

  • 5.1/ 6, 7, 8, 9, 10
  • 4.9/ 13, 16, 
  

W

4/12

 

 

 

 

 

M

4/17

Section 5.4, 5.5

  • Green's formula: Laplace's and Poisson's equations, integration by parts, applications.

Math/Stats Students: you are invited to attend our Department's Ice Cream Social, Friday 4/21, at 2pm, in SMLC Lounge/356 so you can meet your fellow students and your faculty; find out about opportunities for math/stats majors; freshmen-juniors: hear advice from senior students; seniors: give any advice you have for the junior students. Schedule:

  • 2:00-2:15 introductions/icecream (SMLC 3rd floor Lounge)
  • 2:15-2:45 faculty introductions, including opportunities for
    undergrad research, internships, more (SMLC 356)
  • 2:45-3:15 discussion led by senior students (SMLC 356)
  • 3:15-3:30 wrapup

HW11(corrected)

  • 5.2/ 1, 2, 5,8, 9, 10

  

 

W

4/19

 

 

 

 

 

M

4/24

Sections 5.4 &5.5

  • Example of a solenoidal field that is not a curl.
  • Divergence formula in 2-D & (proof of) Stoke's Theorem

 

HW12:

  • 5.4/5, 7, 9, 12
  • 5.5/1, 2, 3 

 

  • take home part of final (due Wednesday 5/3; note the correction on Problem 5a - the surface is the unit sphere, so the 4 should be 1)
 5.5: 5, 6, 7

W

4/26

 

 

 

 

 

M

5/1

 

REVIEW FOR FINAL - will go over questions you have on the Practice Problems

 

 

  

W

5/3

F

5/8

 

Final Exam  Monday May 8 5:30‐7:30 p.m. in the usual room