MATH 408D: Differential and Integral Calculus II (HONORS)

"Person, Woman, Man, Calculus, TV !"

Disclaimer: Due to the unusual and changing conditions of the pandemic lockdown, it may be necessary to adjust the terms of this syllabus during the semester. Every effort will be made to avoid detrimental effects on any student.

General Information

      Instructor: Dave Rusin (
      Class meets MWF 9:00-10:00 am via Zoom; join at
     (**Note change from first day**)

      Your section also meets Tuesdays and Thursdays with the TA at, respectively,
          Sect 53125:  4:00- 5:00pm via[ ~TBA~ ]
          Sect 53130:  5:00- 6:00pm via[ ~TBA~ ]
      Teaching asst: TBA  (Location: TBA)
      TA Office hrs: Mondays and Wednesdays 4pm-6pm.

      Text: Calculus (8th Edition, "Early Transcendentals" version) by
      James Stewart. You may also use the all-electronic version of
      that same book, or the "special UT edition" at the bookstore.
      Information about buying the electronic version of the text has
      been posted to Canvas.

      Office hrs: I will keep public office hours at these times:
         Mondays noon-2 pm         in my office (PMA* 9.140)
         Wednesdays 12:30-2 pm     via Zoom @ https://utexas/
         Thursdays 11am-1pm        via Zoom @
      I hope also to be available MWF 10-11am via Zoom; details
      depend on technical resources not known at this time.

      If you need to meet me in private please do not use the public
      Zoom invitation: send me email and we can arrange a private Zoom
      meeting or office hour. (Walk-ins to my office can be private if
      no one else is visibly waiting to see me.)

      Your final exam is Saturday, December 12, 9:00 am until noon .
      The exam will be taken remotely.

(*) The building named PMA is listed on older UT maps as "RLM"

Course webpage:

Miscellaneous Updates

The publishers sent me a copy of the student instructions for obtaining the electronic copy of the book.

Catalogue Description

Course description: This is the second semester of the accelerated calculus sequence. The theory and applications of sequences and infinite series, including those involving functions of one variable, and an introduction to the theory and applications of differential and integral calculus of functions of several variables; subjects include methods of integration, parametric equations, sequences, infinite series, power series, functions of several variables, partial derivatives, and multiple integrals. Its objective is to provide students with practical mathematical skills necessary for advanced studies in all areas of science and engineering.

Only one of the following may be counted: Mathematics 403L, 408D, 408M.

Please note that "mathematical skills" here refers to more than algebraic manipulation (although you will be expected to do that kind of thing quickly and accurately). It is an explicit goal of this course to develop your mathematical intuition: many of the problems you will be asked to solve will require much more thought than symbol-moving. I also take it as an important step in your mathematical training that you learn to communicate mathematics well: what you write must hang together logically, and be presented with enough words to make the presentation comprehensible.


Entry to this course is limited to students who have attained a sufficient score on the AP Calculus exams, or have obtained permission from the instructor. This course is, by design, more difficult than the regular sections of Math 408D. If you are looking for an easier or less-conceptual presentation of this material, please sign up for one of the regular sections.

If you have not met the pre-requisites of the class, the Registrar will remove you within the first two weeks of the semester.

Apart from the administrative pre-requisites, let me stress that I will assume you have mastered all the typical material of first-semester Calculus. If you took Calc-1 in Spring 2020, your class probably got interrupted in March, in which case you may not have been given a typical Calc-1 preparation. I will not compound this situation by reducing our syllabus, but that may mean you will struggle a little more with this class, especially at the beginning. Make sure you understand everything there is to learn about Limits and about Differentiation, and about the main ideas of Integration (how it's the limit of Riemann Sums) up through the Fundamental Theorem of Calculus. Along the way make sure you're solid on your algebra and pre-Calculus stuff: review your trig identities, and how to divide polynomials, things like that.

Class structure

There is a cycle of activity that we follow for each section of the book (typically one class meeting per section).

Our "lecture" meeting times together are very short so we must make the most of them. Log in daily, with all the materials you need to take notes and work problems. If possible, please choose a distraction-free environment and connect to the Zoom session with your camera on and your microphone off. (Why your camera should be on:

During each of these regular sessions I will answer any questions that you may have from the Learning Module, and then present some more examples or some more of the underlying theory. Then I will put you into break-out Zoom rooms with a few other students, and give you a few minutes to try some examples on your own. After we come back together I will again answer questions or point out some fine points about the ideas that emerged from those examples. We will repeat this cycle a couple of times up to the end of class. Please plan to interact with the other students. I will drop in to the breakout rooms at random.

It is very important to me that the class feel like a live interaction despite being conducted remotely --- I believe that will help you learn more effectively, not to mention keeping me energized! The recording studio where I face the camera gives me a display monitor showing the faces of students in the Zoom session. In order to see the faces more clearly I will ask the engineers to pick a couple dozen students to be on my display each day. On any given day, whether you are in that group or not, you should feel free to speak up whenever you have a question. You may use the raise-hand icon, or type a question into the chat box, or simply unmute your microphone and politely interrupt me. I or the TA will try to answer all questions as soon as they arise.

Graded material

Your semester grade will be based on a number of components:

Learning modules: Quest will assign you a grade for these and at the end of the semester it will provide me your average score (0 to 100). I will adjust this a bit by dropping your lowest two learning module scores. Note: Doing the Learning Modules well is your easiest route to improving your semester grade!

Homeworks: There will be questions for you to answer on Quest after each class. This will enable you to get constant feedback on how well you are understanding the material. 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 two lowest homework grades 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 for 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. That is, the average grade is a "B" and being off by one standard deviation raises or lowers your grade by one letter grade.

Letter Grades: Your final semester grade is simply the average of the components: learning module, homework, and exam grades count equally (1/5 each). This number is converted to a letter grade according to the following scale: Just kidding. I use a pretty standard conversion formula:
For most people the LM and HW grades pull their average up and their tests pull their average down, so you will cause yourself unnecessary grief if you neglect to do all the LM and HW assignments!


We meet 40 times this semester (plus exams). That's not much time, and we have a lot to do! I mean, really. You're going to feel exhausted by the pace. I intend to follow this schedule; it is subject to minor adjustment without notice:
                    Aug 26:  7.1       Aug 28:  7.2
Aug 31:  7.3        Sep  2:  7.4       Sep  5:  7.5       
Sep  7: Labor Day   Sep  9:  7.8       Sep 11:  7.8       
Sep 14: 11.1        Sep 16: 11.2       Sep 18: 11.3       
Sep 21: 11.4        Sep 23: 11.5       Sep 25: 11.6       
Sep 28: 11.7        Sep 30: Review     Oct  2: *EXAM 1*   
Oct  5: 11.8        Oct  7: 11.9       Oct  9: 11.10    
Oct 12: 11.11       Oct 14:  9.1       Oct 16:  9.2       
Oct 19:  9.3        Oct 21:  9.4       Oct 23:  9.5       
Oct 26:  9.5        Oct 28: 10.1       Oct 30: 10.2       
Nov  2: 10.3,4      Nov  4: 10.4,5     Nov  6: 10.5,6     
Nov  9: *EXAM 2*    Nov 11: 14.1,2     Nov 13: 14.2,3   
Nov 16: 14.5        Nov 18: 15.1       Nov 20: 15.2       
Nov 23: 15.3        Nov 25:  --Thanksgiving Holiday--
Nov 30  15.4        Dec  2: 15.9       Dec  4: 15.10 
Dec  7: Review

Assistance with course work

Your primary sources of human help this semester should should be your instructor and your teaching assistant, either in class or in office hours. But there are two other ways to get help here at UT:

Piazza: We will set up a Piazza forum for this course. Piazza provides a discussion forum, not unlike reddit or slack or the comments section of a website. The TA will monitor the forum on a periodic visit to give authoritative answers (and I might stop by as well) but any other student is welcome to respond at any time. This could be helpful if you have waited until the last minute to complete a homework assignment (not that you would ever do that, of course...)

CalcLab: The Mathematics Department offers assistance to all students taking Calculus courses in our new Calc Lab. Here's the department's web page about this: The Calculus Lab is in PMA 8.136 and is staffed most weekday afternoons. (This semester's schedule will appear on the preceding web page.) If you go there during those hours you will typically find two graduate Teaching Assistants and some undergraduate Learning Assistants whose job it is to help you learn the material, perhaps clarifying some point from our class or the textbook, perhaps giving hints on homework. Please take advantage of their help!

In addition to visiting the instructor or the teaching assistant during office hours, you might want to make use the services of the Sanger Learning and Career Center. The Sanger Center offers several forms of tutoring to students throughout the semester (for students in select math courses, including M408D).

All Sanger Learning Center services are free for currently enrolled UT students.


Online learning: Please ensure that you have the tools necessary to participate in the Zoom sessions with me, the discussion sessions with the TA, and the exams. A good resource to check your readiness is at In a pinch, you can join any Zoom meeting if you know the Meeting Number shown in the URL; select a local phone number from this list If you believe you do not have the necessary resources, please apply for assistance from the Dean of Students Emergency Fund. I cannot guarantee that they will get you what you need, but their goal is to prepare every student for success.

Everyone at UT learned this past Spring that, in a nutshell, online education sucks. I will do my very best and hope you will too, but if you don't make the effort to really decide that you are going to learn this material, you won't. Make a committment now, or do yourself a favor and withdraw from this course.

Class Recordings: The class "lectures" will be recorded and made available on Canvas so you can refer to them later. Student faces and breakout room sessions will not be recorded, but we are dedicated to protecting your privacy. Class recordings are reserved only for students in this class for educational purposes and are protected under FERPA. The recordings should not be shared outside the class in any form. Violation of this restriction by a student could lead to Student Misconduct proceedings.

Exams: The exams will be taken during the designated class times. You must take your exam in front of your Zoom camera. The exams will be administered through Quest. (The questions will be very similar to the homework questions, though the formatting of the exam will be a little different.) There will also be a couple of free-response questions; you will have to write out your answers and scan them, then upload your answers through Canvas. These will have to be completed the following hour; I will work out alternative plans in advance for everyone who has another commitment in that hour. We will have a dry-run ungraded exam before the first midterm, to make sure everyone has all the right technology and understands the rules.

Textbooks, notes, and electronic devices (including phones and calculators) are not permitted during exams. I will be available to answer questions during the test, by way of the Zoom chat feature. I will also monitor my email during the test: if you experience technical difficulties ("my dog ate my keyboard") please notify me immediately by Zoom or email and we will work something out.

Make-ups: it is in general not possible to make up missing assignments or exams 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.

Late course entry: 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).

Course drop dates:

October 29 is also the last day to change your enrollment to or from a pass/fail basis. (The special blanket extensions granted in the Spring no longer apply.) 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 instructional material for this coursei which is mandatory, just as is your textbook, etc. For payment questions, email

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. In case you are unfamiliar with the UT Honor code, please allow a governor, a first lady, and Mr. "Alright alright alright!" to remind you: UT Honor Code

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.

Covid-19 Safety and Class Participation/Masks: Since this is an online-only course, it is sadly true that you and I may never be in the same room. I would love to meet you in person for office hours if that is possible but please remember to wear a mask in my office. It's a small office; to observe social-distancing guidelines only one student can join me at a time. Also note that the PMA elevators are now limited to 3 people at a time, and masks are expected whenever you are in our building.

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

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.

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.

Bennett exam: The Bennett contest exam is a competition held at The University of Texas Mathematics Department at the end of every regular semester. Participation is limited to students who are finishing the Calculus sequence that semester. That includes you! The questions are based on the topics covered in the Calculus courses, but require more than the usual amount of persistence and cleverness. There are cash prizes for the top scorers. Please plan to participate! (Exactly how the contest will be conducted this semester is yet undetermined.)


Attendance is not mandatory. But who are we kidding? 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 $53 for every one of those 40 class meetings. Are you really going to throw away $53 you have already paid, so that you can turn off Zoom and take a nap?

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, as many as a quarter of these 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 the learning modules give you a lot of trouble, 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 408D 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 chat about mathematics topics beyond what we discuss in class.