General Information

      Unique ID: 52845, 52850

      Instructor: Dave Rusin ( 
      Office hrs: I will be in my office (RLM 9.140) at these times for you:
         Mondays and Wednesdays 1-2 pm and 3-4pm
         Fridays 9:30-11 am and 1-2 pm.
      I will hold additional office hours near exam times, and can also
      be available by appointment; talk to me or send email to arrange it.
      UPDATE: I will keep the same office hours through Zoom.
      Those meetings are open to all; if you need to speak to me privately
      (e.g. to discuss a grade or personal issue) please send an email and
      I will arrange a time to meet you privately (by Zoom, phone, skype, etc.)

      UPDATE: There will be one final office-hour session: Monday May 11, 11am-1pm.
      The zoom invitation is

      Text: Vector Calculus 6th Ed., Marsden and Tromba.

      I am teaching two sections of this course this term. They should run in
      parallel, so if you have to miss your class one day, you can *probably*
      make it up by attending the other class. But please be aware that the
      classes are organic things, and I will probably adjust the exams for
      YOUR section to match what happens when YOUR section is meeting. So as
      a rule, stick to your assigned times and places. They are:
       sect. 52845: M,W,F 11am-12  in WAG 101  with me
                    T,Th   4-5pm   in ETC2.108 with the TA
       sect. 52850: M,W,F 12-1 pm  in WAG 101  with me
                    T,Th   2-3pm   in CAL 100  with the TA
      UPDATE: We will convene MWF at the same time by Zoom.
      The Zoom links for the 11am classes are:
      The Zoom links for the noon classes are:
      Those class meetings will be recorded and uploaded to YouTube at
      (The YouTube channel is called "rusin.2020a")
      The T/Th Discussion Sections with the TA have been cancelled. 

      Teaching assistant: TBA

      Please note the time of your final exam:
        sect 52845: Saturday, May 16, 7:00 pm-10:00 pm
        sect 52850: Wednesday, May 13, 9:00 am-12:00 noon
      There is no provision for taking the final exam earlier or later,
      and you must take the exam with the rest of your section.
      I expect the exam to be in your regular class room but that may change.
      UPDATE: The final plan for the final exam is this: I will make some
      free-response questions available to you right here link by
      Wednesday May 13 at 9am. You will have to submit your responses to me
      by Saturday May 16 at 10pm on Canvas. Separately, you will find a
      multiple-choice Quest exam will be available during the same period.
      You must finish it within 4 hours after you start. The final will
      be conducted under the same terms as midterm 2

The second midterm exam is now available. You may start the Quest portion any time between 1pm Thursday and noon Friday; you will have two hours to finish it after you start. The free-response questions are now available here; you may start when you wish but must finish by Friday at 2pm. Please review the email message I sent yesterday, which lays out the requirements for taking this exam. An answer key is now available too.

Course webpage: It is unlikely that I will post any important material to Canvas; for any additional information I want to give you outside of class, you should come to this webpage, right in this next section:


The class is currently waitlisted. If you are trying to enroll, you will have to wait -- I cannot and will not allow students into the class except those who enrol through the online system or through the advising office (RLM 4.101). If you are in the class but think you might drop, please try to decide promptly: there are students who are eager to take your place soon if you don't intend to keep it.

Catalogue Description

Matrices, elements of vector analysis and calculus of functions of several variables, including gradient, divergence, and curl of a vector field, multiple integrals and chain rules, length and area, line and surface integrals, Green's theorems in the plane and space, and, if time permits, complex analysis.


The prerequisite is a grade of at least C- in Mathematics 408D or 408M. Please note that if you had a C- in one of those courses, you have the weakest background in the class and so you should be working hardest and getting the most help and feedback from me and the teaching assistant.

Graded material

Your semester grade will be based on a number of components. This structure is designed to encourage you to stay actively involved in the course all the way through the semester. Any adjustments to the schedules or policies will be announced multiple times in lecture and via email and on the course website shown above.

Homeworks: There will be homework due weekly, done online using the Quest system, located at This will enable you to get constant feedback on how well you are understanding the material. The homework must be completed online by the date posted, typically about one week after it becomes available. Note that Quest will subtract points for wrong answers, so think carefully before you answer or you could end up with a negative score! (Why?)

I will drop the lowest homework grade and average the rest to give you a "Homework Score" of up to 100 points for the semester.

Quizzes: There will be a quiz (almost) every week. As with the homeworks, this will be scaled to give you a semester "Quiz score" of up to 100 points. The Teaching Assistant will give further information about how the quizzes will be totalled.

UPDATE: Your quiz grade will be the average of the five quizzes already taken. You may request an additional quiz to replace your lowest score among those five.

Homework and Quiz scores will be treated as letter grades using the following scale:

Exams: There will be 2 mid-term exams, to be held during the usual class period, and a comprehensive final exam. The exams will be a mix of multiple-choice and free-response questions. The midterms will be 8-12 questions long; the final is twice as long (and counts twice as much) but you have 3 hours for it.

UPDATE: Exam 2 will be purely multiple-choice. It will be administered under the same rules as the Final Exam (see above). Please accept my apologies as I think this makes for a less complete learning experience, but circumstances beyond our control make anything else hopelessly complicated. Take this as a signal that you should put more emphasis on your day-to-day learning of the material. I'll Zoom with you all day if it helps :-)

I will use the scale above ("scale 1") to convert your exam raw score to a letter grade, but my exams tend to be hard, so I will also use an alternative method and then whichever method gives you the better grade will be the one I record for you for that exam. Here's how I construct the alternative scale ("scale 2"): After I compute the mean and the standard deviation of the class grades, I will determine how many standard deviations above or below the mean your grade is. If your score is greater than the mean by less than one standard deviation, you will get a B (or B+ or B-, as appropriate); higher scores get A's, lower scores get C's, D's, and F's. For example, suppose the class average on the exam was 78.3 points and the standard deviation was 14.4 points. Then the conversion from raw scores to letter grades will be based on these brackets (of width 14.4/3 = 4.8 up and down from 78.3) :

SAMPLE! based on mean=78.3, standard deviation 14.4
letter gradeA+AA-B+BB-C+CC-D+DD-F
scale 197+94-9690-9387-8984-8680-8377-7974-7670-7367-6964-6660-630-59
scale 2103+98-10293-9788-9284-8779-8374-7869-7364-6860-6355-5950-540-49
most generous97+94-9690-9387-8984-8679-8374-7869-7364-6860-6355-5950-540-49

In this scale I am literally giving grades of "above average" (A's and B's) exactly to students whose scores are above the class average. (Mean is not the same as median; most of the students last semester got A's and B's; only 5% of the letter grades were D's and F's.)

The final scale that determines what letter grade you get on that exam is then the one that gives each person the more generous grade. So for example in the above sample, any student whose raw score was 87 or higher would get a higher letter grade based on the traditional 90-80-70-60 scale ("scale 1"), and thus for those students the traditional scale will be used; other students benefit from the other "scale 2", and so I use that scale for them. Everybody wins!

Textbooks, notes, and electronic devices (including phones and calculators) are not permitted during exams.

UPDATE: Yes they are.

I expect the dates of the midterms to be March 6 and April 24. The last day of class is May 8. Please mark on your calendars now the time and date of the final exam.

UPDATE: This does not change. In particular, please note that we thus have one less week of the semester because of this. We might try to pick up the pace a little so as not to miss the great theorems at the end of the course.

Semester Grades

Your final semester grade is simply a weighted average of the components: homework, quiz, and midterm grades count equally (1/6 each) and the final counts double (2/6 of the total). I do the arithmetic as is done for high-school GPAs: A=4.0, B=3.0, etc; "+" and "-" are one-third of a letter grade up or down. An average of 3.83 rounds down to an A- (4-1/3) while 3.84 rounds up to an A (4.00), etc. Sadly, the university does not permit me to report scores of "A+" but internally I do track those terrific students whose semester average is 4.17 or above!

If for some reason there is a deviation from this scale it will be applied uniformly to your lecture section, and it will be announced in class.


Classroom activity: Our meeting times together are very short so we must make the most of them. Come to class daily and ask questions; this is greatly facilitated by reading ahead each day and doing the homework problems as they are assigned. Please silence your cell phones. I will always assume that any conversations I hear are about the course material so I may ask you to speak up.

UPDATE: The TA will be present at the Zoom meetings and will monitor the Chat box. Please also take advantage of the Raise-Hand icon in Zoom (If you open the Participant List from the bottom icons, you should see the Raise-Hand button.) I will definitely engage questions from the class.

UPDATE: On the other hand the TA will not meet you in Discussion Sections any more. You have two new ways to get help from them. First, the TAs have agreed to hold office hours via Zoom. Second, the TA will monitor the Piazza conversations and provide expert commentary on the questions posed there. Piazza is a forum where M427L students can pose and answer questions. Each of these URLs should get you there: The TA will delete inappropriate questions and remarks. ("Can anyone help me with the test?" is inappropriate!) Ask the crowd at large for help when you need it, but you will also gain much from answering questions when you are able.

Attendance: I will be at class every day and expect you to be, too, through the last day of our class. We will use the class time to work problems together, and as I work with people in class, I'll notice if you're not there...

Make-ups: It is in general not possible to make up missing quizzes or homework assignments after the due date. If you believe you will have to miss a graded event, please notify me in advance; I will try to arrange for you to complete the work early.

Students with disabilities: The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.

Religious holidays: If you are unable to participate in a required class activity (such as an exam) because it conflicts with your religious traditions, please notify me IN ADVANCE and I will make accommodations for you. Typically I will ask you to complete the required work before the religious observance begins.

Academic Integrity. Please read the message about Academic Integrity from the Dean of Students Office. I very much prefer to treat you as professionals whose honesty is beyond question; but if my trust is violated I will follow the procedures available to me to see that dishonesty is exposed and punished.

Campus safety: Please familiarize yourself with the Emergency Preparedness instructions provided by the university's Campus Safety and Security office. In the event of severe weather or a security threat, we will immediately suspend class and follow the instructions given. You may wish to sign up with the campus alert programs.

Counseling: Students often encounter non-academic difficulties during the semester, including stresses from family, health issues, and lifestyle choices. I am not trained to help you with these but do encourage you to take advantage of the Counselling and Mental Health Center, Student Services Bldg (SSB), 5th Floor, open M-F 8am-5pm. (512 471 3515, or

Add dates: If you enroll within the first four class days of the semester, and have missed any graded material, I will adjust the weighting of your graded sections accordingly so that you are not penalized. No such accommodation is made for students who enroll on the 5th day or later. (Such students must enroll through the MPAA advising center in RLM, and ordinarily I do not admit students who ask to enroll then if they have missed any graded activities).

Drop dates: Jan 2 is the last day to drop without approval of the department chair; Feb 5 is the last day to drop the course for a possible refund; Apr 6 is the last day an undergraduate student may, with the dean's approval, withdraw from the University or drop a class except for urgent and substantiated, nonacademic reasons. For more information about deadlines for adding and dropping the course under different circumstances, please consult the Registrar's web page,

UPDATE: Please note that the Deans are extending the deadlines during which you may Q-drop the course or change from graded- to pass-fail options. Please consult with me or an academic advisor to determine the most up-to-date rules. The University wants you to have the fullest possible educational experience but recognizes that current circumstances may force students to make unexpected enrollment decisions.

Quest: This course makes use of the web-based Quest content delivery and homework server system maintained by the College of Natural Sciences. This homework service will require a $30 charge per student per class for its use, with no student being charged more than $60 a semester. This goes toward the maintenance and operation of the resource. Please go to to log in to the Quest system for this class. After the 12th day of class, when you log into Quest you will be asked to pay via credit card on a secure payment site. Quest provides mandatory instructional material for this course, just as is your textbook, etc. For payment questions, email

Computers: We don't make use of sophisticated software in this class, but if you find this interesting, you are welcome to use the department's computer facilities. Our 40-seat undergrad computer lab in RLM 7.122, is open to all students enrolled in Math courses. Students can sign up for an individual account themselves in the computer lab using their UT EID. We have most of the mainstream commercial math software: Mathematica, Maple, Matlab, etc., and an asortment of open source programs. If you come to my office you will see me use some of this software to help illustrate concepts. Please see me if you would like more information.

UPDATE: Sadly the computer lab is shuttered for now. Nonetheless if you have a reasonably modern computer you might enjoy using it to help you visualize some of the complicated curves and surfaces we explore this semester. I encourage you to take up this topic on Piazza.


We have a LOT to do this semester --- we'll work through the entire book toghether! So expect to fly through about three sections every week.

UPDATE: We must push back the syllabus for the second half of the semester. For this particular course the material of the final week is of great importance so I will try to select other topics along the way to drop when necessary. Please pay close attention to the discussions in class.


You may have spent most of your mathematical life working on problems by yourself. This is a good thing; you become self-reliant. However, I strongly encourage you to work with one or two other students in this class on a regular basis. Challenge each other to solve the problems, to explain the concepts, and to ask each other for help. This is the way mathematics is done in the real world, and practicing this now can help you this semester and beyond.

Since you are adults, I leave it to you to monitor your level of understanding on your own, and to seek help when you need it. But please allow me to share my experience. Every student who starts this class has met the pre-requisites and has the expectation that he or she will succeed. Nonetheless, every semester, about one-fourth of this group of bright, hard-working students ends up with a D or F, or withdraws. No one likes this outcome. Please be attentive to your progress on homeworks and quizzes and midterms. If you find you are always asking other people for help while studying; if you find that it takes you hours and hours to complete every homework set; if your quiz grades are low, or you score less than half the possible points on a midterm exam: in these cases, you CAN succeed, but ONLY if you change your patterns immediately. Optimism is a wonderful thing but it alone cannot bring the results you may want. Please see me early in the semester if you think you may have trouble during this course. I can try to help you with the material, or with your study habits, or else advise you to withdraw. Let's make this the first-ever 100% successful Math 427L class!

One more suggestion: have fun this semester! Some of us think math is so cool that we end up doing it for a living. I will try to convey to you some of what's kewl, and invite you to consider majoring (or minoring) in math, joining the math club, or simply taking more math classes. I am always happy to talk in my office about mathematics topics beyond what we discuss in class.