General Information

PLEASE NOTE: All information in this syllabus is subject to change in response to the resurging Covid epidemic. Changes will be noted right here at the top of the syllabus, and will be announced in class.

      Unique ID: 53785  and 53795 

      Instructor: Dave Rusin ( 
      Office hrs: (1) Tuesdays noon-2pm and Wednesdays 4pm-5pm
       Feel free to drop in during those hours to my office, PMA 9.140.
       (2) I am also an academic advisor and hold advising hours 
       Tuesdays 10:30-noon and Wednesdays 10-11:45; if you show up in
       my office I would be happy to talk to you if I am not in an
       advising session.
       (3) I can also arrange additional times to meet; send me email if 
       you'd like to meet with me.

      Text: Vector Calculus 6th Ed., Marsden and Tromba. I will follow the
      book pretty closely (augmenting certain parts of it), and it has plenty
      of exercises for you to practice with before exams. It is available for
      rent or purchase from the publisher and fine booksellers everywhere.
      But you can choose to use any resource that you find helpful.

      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 happened when YOUR section was meeting.
      So as a rule, stick to your assigned times. They are:
       sect. 53795: M W F noon-1pm with me in RLP 0.126
                    T Th  2pm-3pm with the TA in PHR 2.110
       sect. 53785: M W F 3pm-4pm with me in CPE 2.214
                    T Th  12:30pm-1:30pm with the TA in RLP 0.130

      Teaching assistant: TBA

      Please note the time of your final exam:
        sect 53795: Wednesday, May 11, 2:00 pm-5:00 pm
        sect 53785: Wednesday, May 11, 7:00 pm-10:00 pm
      There is no provision for taking the final exam earlier or later,
      and you must take the exam with the rest of your section.

Course webpage: It is unlikely that I will post any important material to Canvas but it does provide access to some of the services mentioned elsewhere in this document, and I encourage you to become familiar with it. When I want so share some additional material I may load it under the Canvas "Files" tab.


(Odds and ends may be added here during the semester.)

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.

I recognize that the pandemic lockdown has interrupted students' education. It is possible that your calculus courses have had to omit material or adopt more relaxed grading policies. Nonetheless the syllabus of this course is unchanged; in order to thrive in M427L, you really will have to have mastered all the material that is normally taught in a full-year college calculus course. Please note that "mastery" is more than "exposure": you need to be able to carry out computations accurately and efficiently.

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.

Homework: 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.

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.

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 longer but you have 3 hours to complete it.

Because my exams tend to be hard, I have a way to curve the exam scores. I will compute both your raw score and your curved score and whichever is higher for you will be the score I use when computing semester grades. The curving method is simple: I compute the mean, mu, and the standard deviation, sigma, of the class's raw scores, and then a person with a raw score of X will get a curved score of

   85 + 10 (X-mu) / sigma
(with a maximum curved score of 105). This way the mean curved score will be 85 and the standard deviation of the curved scores will be 10. I don't record letter grades for individual exams, but as you will see below this curving system effectively gives a person a "B" if their score matches the class average; a person whose exam grade is higher or lower by one standard deviation gets an "A" or a "C".

Textbooks, notes, and electronic devices (including phones and calculators) are not permitted during exams. Any violation of the Academic Integrity rules will result in getting a score of ZERO on the exam.

I expect the dates of the midterms to be March 4 and April 22. The last day of class is Fri, May 6. Please mark on your calendars now the time and date of the final exam.

Semester grades: Your numerical grade for the semester is a weighted average of the components above; specifically it is the dot product

 < 0.30, 0.20, 0.20, 0.30 > . < HW, T1, T2, Final >
This number is converted to a letter grade according to the following scale: Just kidding. I use a pretty standard conversion formula:
97.0-100 A+
0 -59.9F
A majority of students get As and Bs in this class, but every semester there is a significant number of Cs as well as a few lower grades. Of course, this is a hard course, so some low grades are not unexpected, but sadly some students put themselves at risk simply by failing to complete the homework. You have time to do complete it, and permission (even encouragement!) to do it with friends, so it's comparatively easy to get a good grade on the homework. Don't miss this opportunity.

Having said that, please make sure you use the homework to really practice with the material. Do not get in the habit of using friends or a machine to get your answers or check them before submitting. You will not have that luxury during the exams!


Class meetings: Our "lecture" meeting times together are very short so we must make the most of them. Attend daily, with all the materials you need to take notes and work problems. Per university policy, we will hold classes by Zoom for two weeks and then return to in-person classes starting January 31.

For any classes held via Zoom the meeting number will be:

noon class (53795): 
 3pm class (53785): 
The Teaching Assistant will participate in our classes via Zoom. He or she will monitor the "chat" box so that will be a place to ask questions --- the T.A. will either answer your question or draw my attention to it; I can't follow the chat box during the lecture. You should also feel free to interrupt me directly! I will usually see a raised-hand icon if you activate it, but I don't mind at all if you simply speak up. (Within reason, of course.)

Please note that when the class meets live, there will be NO opportunity to attend class via Zoom. There will be NO recordings of the class. I wish I could be more accommodating to students with special needs, but I sadly I have found that many more students did worse in the class in recent semesters because they stayed away from the classroom, and to prevent that this semester I am offering no alternative to the in-person classes. Obviously I will accommodate students who become ill or otherwise must be absent during the semester, but if you know now that you must or prefer to have an online class experience, you must sign up for a different section of M427L.

Attendance is not mandatory. But who are we kidding? We're going to work through the entire textbook in just 45 class meetings. At the pace of this class, any time you miss a class, you are at least a whole section behind! That's hard to make up. Plus, if you are (to take a common example) paying in-state tuition for 12 undergraduate credit-hours in the College of Engineering, the tuition alone costs you $50 for every one of those 45 class meetings. Are you really going to throw away $50 you have already paid, so that you can stay home and take a nap?

Piazza: There is a tab in Canvas that takes you to Piazza, a discussion forum for the students in the class. This is a good place to ask questions when class is not in session. Other students can answer your question(s) when they log in. The TA and I will try to visit the forum occasionally to help out with the discussion (and in particular I may need to improve some student answers a bit for accuracy or clarity). WARNING: As of this writing, the College is deliberating the use of Piazza and may decide not to renew the site license. We may opt instead to use another similar tool.

Make-ups: It is in general not possible to make up missing tests 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 when my trust is violated, I report students to the Dean's office.

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 PMA, and ordinarily I do not admit students who ask to enroll then if they have missed any graded activities).

Drop dates: Jan 21 is the last day to drop without approval of the department chair; Feb 2 is the last day to drop the course for a possible refund; Apr 4 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,

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 PMA 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.

Sharing of Course Materials is Prohibited: No materials used in this class, including, but not limited to, lecture hand-outs, videos, assessments (quizzes, exams, papers, projects, homework assignments), in-class materials, review sheets, and additional problem sets, may be shared online or with anyone outside of the class unless you have my explicit, written permission. Unauthorized sharing of materials promotes cheating. It is a violation of the University’s Student Honor Code and an act of academic dishonesty. I am well aware of the sites used for sharing materials, and any materials found online that are associated with you, or any suspected unauthorized sharing of materials, will be reported to Student Conduct and Academic Integrity in the Office of the Dean of Students. These reports can result in sanctions, including failure in the course.

Sanger Center resources: The Sanger Learning Center offers resources for students seeking academic success. Among them, students may schedule unlimited tutoring appointments in several subjects including M427L.


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


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, a nontrivial fraction 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. In my office I am always happy to talk about mathematics topics beyond what we discuss in class.