Vector Analysis -- Math 550H

Frank Thorne - Spring 2020

University of South Carolina

Effective March 23: Instruction is moved online because of the COVID-19 outbreak. Please see here for important updates to the syllabus.
Instructor: Frank Thorne, LeConte 317O, thorne [at] math [dot] sc [dot] edu

Office Hours: Tuesdays, 9:00-10:30, and Wednesdays, 3:30-5:00.

Course objectives/learning outcomes:

Successful students will:

Warning. You should expect 5-8 hours of homework a week in this class, which is more than most other instructors assign; in my experience there is no other way to learn the material. Your consistent effort will certainly lead to improved understanding, and it will almost certainly lead to you earning high grades.

  • Text : Susan Jane Colley, Vector Analysis, Third Edition. It is recommended that you buy used online, for example from Amazon. If you buy from the campus bookstore, you will pay much more.

    I anticipate covering the entire text, except for any material which I presume you already know from 241. The text will also be supplemented with additional material, for which lecture notes will be made available. This will be on the homework and exams too.

  • Lectures : LeConte 303B, MWF, 9:40-10:30 am.

  • Exam schedule : There will be two two-hour midterms, and the registrar-scheduled final exam. Midterms will be take home, pledged, and closed-book and closed-notes. Dates that the exams will be passed out will be announced at least one week in advance, and you will have a week to do each midterm.

    The final exam will be two and a half hours, with the same format as the midterms. The final exam will be distributed on Monday, April 27 and is due by the end of the day on Tuesday, May 5.

    Midterm Exam 1, with solutions.

    Midterm Exam 2, with solutions.

  • Grading : On both homework and exams, you will be graded both on correctness and on quality of exposition. Indeed, a major focus of Math 550 is the ability to communicate mathematical ideas clearly. The standard is that someone who doesn't know the answer should be able to easily follow your work. In particular, please write in complete English sentences and draw clear diagrams where appropriate. Any work that is confusing, ambiguous, or poorly explained will not receive full credit.

    Grading scale: You are guaranteed at least an A for 85+, B+ for 80+, B for 70+, C+ for 65+, C for 50+, and D for 40+. These are wider margins that the usual 10-point scale. But be warned that I will be fairly strict, and that some problems will be difficult.

      Grade component     % of grade  
      Two midterm exams     15% x 2  
      Final exam:     25%  
      Homework:     45%  

    Homework will be due approximately once a week. Late homework will only be accepted in case of illness, emergency, or university-sanctioned event (in which case you should clear it with me beforehand).

  • Contacting me : Please contact me if you have any questions about the course, about my expectations, about my lectures, about the homeworks, about the reading, or about anything else. The syllabus is demanding and it is my job to help you succeed. The best ways to get help are to come to office hours (no appointment necessary) or to e-mail me (I will usually reply within 24 hours). If neither of these work for you then please e-mail me to set up an appointment.

    Please note: If you come to office hours, please don't be shy about interrupting me! I'm usually in the middle of something, but it can wait.

  • Other policies :

    Academic honesty and attendance are expected of all students.

    On homeworks, collaboration is encouraged, but you should write up your own solution. The basic guideline is: when writing up your solutions, you should not be looking at another student's solution. If another student explains to you how to solve a problem, that is okay, but you should then reproduce this solution without copying theirs.

    If you have a documented disability, or otherwise need special arrangements, then let me know and I will work to accommodate your needs. If you need any sort of special treatment, you should let me know at least one week in advance.

    Exams should be your own work exclusively.

    Calculators will not be needed or allowed on exams. You may use them sparingly on homeworks -- but don't rely on them!

  • Schedule and homeworks :

    Homework 0, due Friday, January 24.

    Homework 1, due Monday, February 3.

    Homework 2, due Monday, February 10.

    Homework 3, due Friday, February 20.

    Homework 4, due Friday, March 6.

    Homework 5, due Monday, April 6.

    Homework 6, due Monday, April 13.

    Homework 7, due Monday, April 20.

    Homework 8, due Monday, April 27.

    (That's all, folks!)

  • Recommended videos :

    TNB Frame (with animation), by lahvak1.

    The Line Integral, A Visual Introduction, by vcubingx (Vivek Verma).

    Divergence and curl: The language of Maxwell's equations, fluid flow, and more, by 3Blue1Brown (Grant Sanderson).

    Green's Theorem, explained visually, by vcubingx.

    The excellent Khan Academy has a number of outstanding videos on multivariable and vector calculus.