MATH 311 - 003 67897 VECTOR ANALYSIS   Fall 2021

 

Scheduled Meeting Times

Type

Time

Days

Where

Date Range

Schedule Type

Instructors

Face-to-Face Plus

8:00 am - 9:15 am

T

DSH-223 (room was changed late Monday night on 08/23/21 from SMLC 102)

Aug 23, 2021 - Dec 18, 2021

Lecture

Dimiter Vassilev E-mail

Remote Set Day/Time

8:00 am - 9:15 am

R

Remote Instruction Microsoft Teams

(In addition to your emails, Teams and the class notebook in OneNote you can find on UNMLearn the link to join the class and/ or office hours using Teams.)

Aug 23, 2021 - Dec 18, 2021

Lecture

Dimiter Vassilev E-mail

               

You need to be registered for the course with a @unm.edu email. Any other email will disable features of Microsoft Teams. I have sent you by email a link to join the MATH311 team. Please follow it in order to request access. You can find the link to join the team in UNM Learn as well. After you join the class MS Team I will also give you access to Overleaf. The latter will be used to collaborate on writing the findings of your respective research projects. I will drop from the class all students who do not request access to Microsoft Teams by Friday, September 3.

 

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

Office Hours: I will have office hours through Microsoft Teams on Monday 3:30pm-4:30pm and Thursday 2:30pm-3:30pm. You can also send me an email to arrange a meeting.

 

MATH311 Catalog 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: Undergraduate level MATH 2531 Minimum Grade of C or Undergraduate level MATH 2530 Minimum Grade of C or Undergraduate level MATH 264 Minimum Grade of C.

 

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

 

Learning goals

·       Acquire a more in-depth knowledge of vector calculus and vector analysis.

·       Become familiar with some applications of vector calculus.

·       Be able to express mathematically using vector calculus various objects and concepts from other subjects.

·       Collaborate on a Research Topic.

·       Learn/Practice collaboration work.

 

Learning objectives

·       Learn concepts and acquire computational capability involving the topics listed in the course description.

·       Become familiar with the structure, preparation and collaboration leading to a scientific paper.

·       Use vector calculus and seek a solution to a particular problem in mathematics, physics, CS/Machine Learning or in an area of your choice. Learn to use standard mathematics and physics resources for references and known results.

·       Learn how to use latex and contribute to the writing of a “scientific” paper as a member of a collaborative group.

 

Semester Deadline Dates: http://registrar.unm.edu/semester-deadline-dates/fall-2021-printable.pdf       and Fall 2021 Semester deadline dates 

                                                                                                     

Please note the following guidelines for the course

You are expected to be courteous.  We would like to have a welcoming atmosphere where all are comfortable speaking, regardless of any aspect of their background.    Please keep in mind that students are entering this class with various degrees of prior knowledge of mathematics and/ or general interests and concentration.

 

Vaccination Policy. All students, staff, and instructors are required by UNM Administrative Mandate on Required Vaccinations to be fully vaccinated for COVID-19 as soon as possible, but no later than September 30, 2021, and must provide proof of vaccination or of a UNM validated limited exemption or exemption no later than September 30, 2021 to the UNM vaccination verification site. Students seeking medical exemption from the vaccination policy must submit a request to the UNM verification site for review by the UNM Accessibility Resource Center. Students seeking religious exemption from the vaccination policy must submit a request for reasonable accommodation to the UNM verification site for review by the Compliance, Ethics, and Equal Opportunity Office. For further information on the requirement and on limited exemptions and exemptions, see the UNM Administrative Mandate on Required Vaccinations.

 

UNM Requirement on Masking in Indoor Spaces. All students, staff, and instructors are required to wear face masks in indoor classes, labs, studios and meetings on UNM campuses, see the masking requirement. Qualified music students must follow appropriate specific mask policies issued by the Chair of the Department of Music and the Dean of the College of Fine Arts. Students who do not wear a mask indoors on UNM campuses can expect to be asked to leave the classroom and to be dropped from a class if failure to wear a mask occurs more than once in that class. Students and employees who do not wear a mask in classrooms and other indoor public spaces on UNM campuses are subject to disciplinary actions.

 

Academic Honesty. Please note the Regents' Policies: "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.

 

Title IX. The University of New Mexico prohibits discrimination on the basis of sex (including gender, sex stereotyping, gender expression, and gender identity). If you have experienced sexual harassment, including sexual assault as defined in this policy, you have a variety of options available to you. You may report this crime to the police, pursue administrative investigative options, seek supportive measures and seek confidential resources. Please see https://loborespect.unm.edu/faculty--staff/index.html and https://policy.unm.edu/university-policies/2000/2740.html for more detailed information. Any report of gender discrimination, which includes sexual harassment, sexual misconduct and sexual violence made to a faculty member, TA, or GA must be reported to the Title IX Coordinator at the Office of Equal Opportunity (oeo.unm.edu).

 

Academic accommodation will be made for any student who notifies me of the need. Please take the initiative to let me know of your needs and contact Accessibility Services in Mesa Vista Hall, Room 2021, phone 277-3506. 

 

Collaboration.  I encourage you to work with your peers and me on the homework, provided you write up and submit your own solutions in your own words. I will have in-person office hour if you prefer to stop by my office. I will also have an office hour through Microsoft Teams.

 

Research Project. The class will split into collaboration teams based on the chosen Research Projects. You will work on the chosen problem with your respective teams throughout the semester. Each team will have their own “space” in the class notebook of Microsoft Teams and in Overleaf. Only the respective team members and I will be able to see and edit this space. Each team should set-up an hour long meeting every week throughout the semester. The meeting could be in Microsoft Teams or in-person or a combination of both, alternating each week for example. The general guide for the research projects can be found in the class OneNote notebook or at this link.

 

Homework.  Homework is due every Tuesday at the beginning of the class. I encourage you to work on the homework with your classmates, 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 in Microsoft Teams. To help the grader, please write your solutions neatly using correct grammar and mathematical notation (no points will be given for work that the reader cannot follow).   The ten best homework grades will be used in computing the homework score. Please do not turn-in 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.

 

Exams. The exam dates are given in the schedule below. The Final Exam date is set by UNM, see https://schedule.unm.edu/final-exams/final_exam/fall2021.pdf. No makeup exams will be given unless you contact me ahead of time with a documented “university authorized absence”, including, but not limited to illness, family emergency, active participation in scholarly or athletic events. Exams may include some multiple-choice questions testing very specific skills or concepts. The exams will be predominantly based on the homework and in-class problems. Students having conflicts with the examination schedule must notify me before TBD. Any student having more than three examinations scheduled in any one day may notify the instructor of the last examination listed. If notified before TBA, I 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.        

 

Assessment (including grading). You should think of most of the work during the semester including homework, midterm exams, and the research project(s) as means for feed-back and learning. This will be reflected in the grading policy where I will drop about 25%-30% of the lowest homework and quiz scores. The Final Exam will be an opportunity for a major grade change by  showing a cumulative  achievement of the course objectives. The “score” for the research project will be a purely bonus score. Writing is one of the most important skills.  You should use the homework and the research project as the main tools for writing-to-learn. The final grade will be determined using the following weights: homework (30%), one midterm (35%) and a final exam (35%).  The Final Exam score will replace the midterm score if the latter is lower than the Final Exam score. All grades will be posted on UNMLearn. The research group project will be a bonus of at most 20%.

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.

 

 

Math 311 Fall 2021 schedule. The current homework and schedule are posted in the OneNote class notebook.

NOTE: You need to be registered for the course with a @unm.edu email in order to use all features of MS Teams and OneNote. Any other email will disable features of Microsoft Teams. I have sent you by email a link to join the MATH311 team. Please follow it in order to request access. In addition to your emails, Teams and the class notebook in OneNote you can find on UNMLearn the link to join the class and/ or office hours using Teams.

 

Week

Day

Class Date

Topics                                                                                   

T

  Aug 24

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

Research Project:  begin reviewing the research projects, ECURE survey

R

  Aug 26

 

 

 

 

T

  Aug 31

Sections  1.11 – 1.14 (Review from Calculus III)

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

Research Project:   discussion of projects.

R

  Sep 2

 

 

 

 

T

  Sep 7

Sections 2.1 – 2.3

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

Research Project: discussion of projects and creation of teams.

R

  Sep 9

 

 

 

 

T

  Sep 14

 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.

Research Project:

  • Critical points, the Hessian, Taylor expansion;
  • Latex, overleaf, and the writing of math paper.

R

  Sep 16

 

 

 

 

T

  Sep 21

 Sections 3.6, 3.8

  • Laplacian.
  • Vector differential identities 

Research Project:

  • The Helmholtz decomposition of a vector field on Euclidean space; Cauchy-Schwarz inequality in various settings; Heisenberg uncertainty inequality;
  • discussion of questions on projects.

R

  Sep 23

 

 

 

 

T

  Sep 28

Sections 4.1, 4.3

  • Line integrals. (Review from Calculus III)
  • Domains and simply connected domains
  • Conservative fields: potentials.

Research Project:  discussion of questions on projects.

R

  Sep 30

 

 

 

 

T

  Oct 5

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

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

Research Project:  discussion of questions on projects.

R

  Oct 7

 

 

 

 

T

  Oct 12

    • Curvilinear Coordinates. Polar coordinates, Spherical coordinates, Cylindrical coordinates.

R

  Oct 14

Fall Break

 

 

 

T

  Oct 19

 Sections  3.10, 3.11, 4.6, 4.7

  • Continue curvelinear coordinates - the Jacobian matrix
  • Surface Integrals.

Research Project:  discussion of questions on projects.

R

  Oct 21

 

 

 

 

T

  Oct 26

    

  • Continue Surfaces and Surface Integrals.

Section 4.9

  • Introduction to Stokes' theorem.

R

  Oct 28

 

Research Project:  discussion of questions on projects.

 

 

 

T

  Nov 2

Exam on Nov. 2, on all sections covered to this point except 4.9. (See the OneNote class notebook for practice problems Practice problems for the midterm exam).

Section 4.8

  • Volume integrals. (Review from Calculus III)

Exam solutions

R

  Nov 4

Research Project:  discussion of questions on projects.

 

 

 

T

 Nov 9

Section 4.9, 5.1

  • Divergence and Stokes' Theorems. Applications - solid angles.

Research Project:  discussion of questions on projects. First draft due Nov. 9.

R

  Nov 11

 

 

 

 

T

  Nov 16

Section Appendix D, 5.1, 5.2, 5.5

  • Another look at the meaning of div and curl.
  • Applications-conservation of mass (p.123, heat conductivity (p. 242), electricity and Maxwell's equations (App. D).
  • Green's formula: Laplace's and Poisson's equations, integration by parts, applications.

Research Project:  discussion of questions on projects.

R

  Nov 18

 

 

 

 

T

  Nov 23

Sections 5.3, 5.4

  • One more look at the Helmholtz decomposition of a vector field
  • Divergence formula in 2-D

Research Project:  discussion of questions on projects. Second draft due.

R

Nov 25 Thanksgiving

 

 

 

 

T

  Nov 30

  Sections 5.1, 5.4, 5.5

  •  (proofs of) Divergence theorem and Stokes' Theorem

Research Project:  discussion of questions on projects. 3rd draft due

R

  Dec 2

 

 

 

 

T

  Dec 7

 

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

 Research Project:  discussion of questions on projects. Final draft due.