MATH 311   VECTOR ANALYSIS    Spring 2008

                                                                 

Instructor: Dimiter Vassilev     Office :  Humanities Bldg, Office 447  Email: vassilev@unm.edu  Phone Number: 505 277 2136

 

Office Hours: TTh 8:00-9:00, W 13:00-14:00  or by appointment                                         

                                                                                   

Text: Introduction to Vector Analysis by H. F. Davies and A. D. Snider, 7th Edition, Hawkes Publishing, ISBN: 0-697-16099-8.

 

Please note the following guidelines for the course:

 

Grades: The final grade will be determined by homework (25%), two midterms( 50%) and a final exam (25%). 

 

Homework:  Homework is due every Thursday. There will be one HW a week. You are encouraged to work together on the homework, but you do need to write up your own solutions in your own words. To help the grader, please write your solutions up neatly and clearly (no points for work that the reader cannot follow- this is true for exams).   The lowest homework grades will be dropped. Please no late homework!

 

The syllabus lists also recommended homework problems.  These are NOT to be handed in. Keep all of your homework together in a folder so that if you are having trouble in the course, you can bring it with you when you go to see your instructor or get tutoring.  The problems used on exams and quizzes are based on these homework problems.  Work as many as it takes for you to understand the material. 

 

- Missed Exams:  Make-up exams can be arranged for exams missed with a VALID excuse (illness, family emergency, active participation in scholarly or athletic activities), and ONLY if prior notice is given. 

 

- 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.  In addition, they should see CATS- Counseling and Therapy Services; Student Health Center (277-4537). (They can help if you suffer from exam anxiety).    

 

 

             Math 311 Syllabus – Spring  2008  (please check after class as advanced postings of homework could change)

 

 week of

Recommended Homework Problems (do NOT hand in)               

Topics Covered

Due Homework – turn in the next Thursday (Th & T due Th after the T)

Solutions are posted on WebCT.

 Jan 21

 

 

 T:  p.14/4,5,13,15  p.23/1,5,9,13-24  

 

 

Th:    p. 29 /1, 3, 11, 12, 13.

         p. 34/ 3, 5, 11, 15,27.

         p. 38 /5, 10.

         

 

Monday Jan. 21 is the Dr. M. L. King Holiday--NO CLASSES

Sections 1.2 – 1.10

·         Vector algebra and cartesian coordinates

·         Geometry and equations of the line.

·         Scalar product and equations of a plane

HW 1   (due Jan 24)

·         T:  p.14/6,12,21    p.23/4,8

 

 

HW 2 (due Jan 31)

·         Th: p.29/7,18   p.34/8,13  p.38/3,11

 

 

·         T: none

 Jan 28

T :   

 

 

 

 

 

Th: p. 51 Section 1.12/  5, 13, 19, 20, 26     

       p. 57 Section 1.13/ 5, 8, 12

       p. 60 Section 1.14/6, 7, 10

Sections  1.11 – 1.14

·         Orientation and Cross product.

·         Triple scalar products.

·         Vector Identities.

HW 3 (due Feb 7)

 

·         Th:  p. 51/2,8,12,14,21,24    p. 57/3, 6,17    p. 60/ 3, 11

 

 

·         T: p.70/ 1, 4, 5(h)(i)  p. 85/2, 5, 6, 9

 Feb 4

  T: p.70  Section 2.1/3
       p. 85 Section 2.2/ 7,8

 

 

Th:  Section 2.3/1,4, 6, 17 

Sections 2.1 – 2.3

·         Curves, tangents, velocity, acceleration.

·         Arclength and curvature.

·         Curvature and torsion, Frenet formulas

HW 4 (due Feb 14)

 

·         Th: p. 95 Section 2.3/2, 5, 9, 13, 15

 

 

·         T: p.113 Section 3.1/1(a), 9, 12, 14,  27     p.117 Section 3.2:/2

 Feb 11

NOTE: Friday Feb. 15 is the last day to change grading options

 

T:  Section 3.1/3, 4, 10, 20  Section 3.2/2*, 3, 4.

 

 

 

 

Th: p.124  Section 3.3/3, 5, 7, 8, 10   p. 132 Section 3.4:/2, 3, 10, 11.

 Sections 3.1 – 3.4

·         Scalar fields, level lines/surfaces, gradient.

·         Directional derivatives, vector fields and flow lines.

·         Divergence and flow tubes.

·         Curl and vorticity.

HW 5  (due Feb 21)

  • Th: p.124 Section 3.3/3, 4, 6, 11    p. 132 Section 3.4/ 4, 9

 

 

  • T: p. 140 Section 3.6/ 2, 4, 5    p. 150 Section 3.8:/6, 10(b, g, i).  NOTE: Problem 13 is removed!

 Feb 18

  

T: p. 140 Section 3.6:  7

.    p. 150 Section 3.8: 9,11, 12

 

Th: p. 170 Section 3.10: 10, 13, 14 (not included in Exam 1)

     

Sections 3.6, 3.8

·         Laplacian.

·         Vector differential identities

·         Polar coordinates, Spherical coordinates, Cylindrical coordinates.

HW 6  (due Feb 28)

 

  • Th:. p.170 Section 3.10/ 6, 7, 8(a, b), 11

 

 

  • T no homework

 Feb 25

NOTE: Friday Feb. 29 is the last day to drop a course without a grade.

 

 

Polar coordinates, Spherical coordinates, Cylindrical coordinates.

Exam 1 - Sections 1.2 - 3.10.

See WebCT for Practice Problems.

 

HW 7  (due March 6)

 

  • Th: Exam 1, February 28

 

  • T: p.191 Section 4.1/ 6, 7, 10, 12, 14, 18, 20

            Exam 1  (solve and turn in  the problems again, this time at home)

 Mar 3

T: Ch 4.1  Line integrals. p.191 Section 4.1: 1, 2, 3, 4
         

 

Th: Ch 4.2 Domains.   p.196 Section 4.2:  3, 5, 6, 7, 10.   

       Ch 4.3 Conservative fields: potentials. p.204 Section 4.3: 2, 8.

Sections 4.1 – 4.4

·         Line integrals.

·         Domains

·         Conservative fields: potentials.

 

HW 8  (due March 13)

 

  • Th: Section 4.3/2, 4, 5 6, 7.

             

 

 

 

  • T: p.196 Section 4.2/ 2, 4, 8  

            

           

 Mar 10

T: Ch  4.2 Domains.   p.196 Section 4.2:  3, 5, 6, 7, 10.   

   Ch. 4.3 and 4.4  Conservative fields

   Ch.  4.5 Divergence free or solenoidal fields

 

 

 

 

Th:  Ch.  4.5 Divergence free or solenoidal fields

       Ch. 4.6 Oriented surfaces.  p.236 Section 4.6: 3, 4,

Sections 4.2, 4.3, 4.4, 4.5, 4.6

·         Conservative fields: Irrotational fields.

·         Scalar and vector potentials: two-dimensional fields.

·         Oriented surfaces.

 

 

.

HW 9   (due March 27)

 

·    Th: p.212 Section 4.4/ 1( b,  d, e), 3, 7, 9

           p. 222: Section 4.5/ 4, 9

            p.236 Section 4.6/ 1, 2,  5, 6

 

 

·       T: p.246 Section 4.7/ 1, 6, 11, 14, 16, 21.

 

 

 Mar 17

SPRING BREAK  3/17 - 3/23  NO CLASSES

 

 Mar 24  

  T:     Surface Integrals.  p.246: 2, 4, 5, 15, 20, 21.

 

 

Th:                                                                                                              

Sections  4.7

·         Surface Integrals.

 

 Mar 31

 T:

 

 Th:  Thursday, April 3  (Practice Problems on WebCT)

 

 

 

Exam 2

HW 10 (due April 10)

 

 

 

 

T: p.256 4.8/1, 3, 5a, 6  p. 181 3.11/ 4, 13

 Apr 7


T: Ch 4.8 Volume integrals. p.256:  4

     Ch 3.11 Curvilinear Coordinates

 

 

Th: Ch 4.9 Introduction to Divergence and Stokes theorem

 

 

Section 4.8, 4.9

·         Volume integrals.

 

·         Curvilinear Coordinates.

·         Introduction to Divergence and Stokes theorem.

HW 11 (due April 17)

·  Th: p. 262 4.9/ 4, 5, 10, 11, 23, 34

 

 

 

 

 

·  T:  p. 277 5.1/ 6, 7, 8, 9, 10.

 

 Apr 14

 

T: Ch 5 (Sec 1)- Divergence Theorem.

 

Th:

 

NOTE:  Friday Apr. 18 is the last day to withdraw from the course without Dean’s approval.  Grade of WP or WF is required.

 

 

 

 

 

 

 

Section 5.1

 

·         Divergence Theorem   solid angles, heat conductivity, Gauss’ law, law of bouyancy.

·         Divergence formula in 2-D.

 

 

 

 

 

HW 12 (due April 24)

 

·  Th:  p. 265 4.9/ 6, 13, 16, 26

 

 

 

 

 

·  T: p. 294  5.4/5,  7,  9, 12  p. 299 5.5/1, 2, 3  

 

 

 

 

 

 

 

 Apr 21  

T: Ch 5 (Sec 4) - Green's  Theorem.

   Ch 5 (Sec 5) - Stoke's Theorem.  p. 299: 5, 6, 7.

 

 

 

Th:  Ch 5 (Sec 2) - Potential Theory: Green's formulas, Solving Poisson's Equation



Section 5.2, 5.4, 5.5

·         Example of a solenoidal field that is not a curl.

·         Green's formula

·         Proof of Stoke's Theorems

 

HW 13 (due May 1)

·  Th:  p. 284  5.2/ 1, 2, 6, 8  

 

 

 

 

·  T:  p. 284  5.2/ 9, 10

Apr 28 

T:  Ch 5 (Sec 2) - Potential Theory: Green's formulas, Solving Poisson's Equation

 

 

 

 

Th: Ch 5 (Sec 3) - The Helmholtz decomposition.

 

·         Potential Theory: Green's formulas.

·         The Helmholtz decomposition.

 

 

 

 

 

 

 

 

·  Th: p. 290 5.3/1, 3, 4.

 

 

 

 

 

 

·  T:

 

May 5

 

 

 

T:

 

 

 

 

Th:

 

Note: Friday May 9 is last day to withdraw with Dean’s approval

 

REVIEW FOR FINAL

 

 

MAY 13

Final Exam  - Tuesday May 13 in regular class room

Time: See Calendar on WebCT.

FINAL EXAM