MATH 408D: Differential and Integral Calculus II

Spring 2011 (Unique IDs 55565, 55570, 55575, 55580)


You can now have a look at some possible answers to both test 1 and test 2 and now also the final exam.

General Information

      Instructor: Dave Rusin ( 
      Office hrs: T, Th 2pm-3pm; W 11am-3pm; and by appointment, in RLM 9.140 

      Teaching assistants: Mark Norfleet and Giovanni Franklin.
      Mark lives in RLM 10.106 and is available for his students there on
        Mon 11-12am  and  Wed 3:30-5:30pm
      Giovanni lives in RLM 11.112 and is available for his students there
        Mon 1-2pm  and  Wed 10-11am, and Mondays 7:30pm-8:30pm in Kinsolving
      Please work only with your assigned Teaching Assistant.

      Class meets TTH  3:30pm - 5:00pm  in MEZ 1.306 

      You will also meet every Monday and Wednesday with the teaching assistant:
        section 55565 meets 10-11am in RLM 6.118 with Mark Norfleet
        section 55570 meets 12- 1pm in RLM 6.118 with Mark Norfleet
        section 55575 meets  3- 4pm in RLM 5.118 with Giovanni Franklin
        section 55580 meets  4- 5pm in RLM 5.118 with Giovanni Franklin
      These meetings start Wednesday, January 19.

      Text: Calculus (6th Edition) by James Stewart

Course webpage:


This course is a continuation of M408C and covers a variety of topics in the theory of functions of one or more variables: indeterminate limits, improper integrals, infinite sequences, power and Taylor series, parametric curves, and derivatives and integrals of vector and multivariable functions with applications. Its objective is to provide students with practical mathematical skills necessary for advanced studies in all areas of science and engineering. The prerequisite is a grade of at least C in Mathematics 408C or 408L.

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.


The prerequisite is a grade of at least C in Mathematics 408C or 408L.


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 on Blackboard and on the course website shown above.

Homeworks: You will have regular assignments on the Quest homework 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. You will accumulate points during the semester, and your "Homework score" will be the number of points earned divided by the possible number of points you could have earned, times 100.

Quizzes: There will be a quiz (almost) every Wednesday. As with the homeworks, this will give you a "Quiz score" of up to 100 points.

Exams: There will be 3 mid-term exams, currently scheduled for February 15, March 10, and April 19, during the usual class period. Each is worth 100 points. The final exam will be Tuesday, May 17, 2011, from 2:00-5:00 pm; it is worth 200 points. (That is the last day of the exam period; plan your early-summer activities accordingly.) Textbooks, notes, and electronic devices (including phones and calculators) are not permitted during exams.

Your semester grade is based only on the number of points accumulated from this mix of points (100 from homework + 100 from quizzes + 100 from each mid-term + 200 from the final). Your grade will be no lower than what is indicated from this table:
Percentage Semester grade
93-100 A
90- 92 A-
87- 89 B+
83- 86 B
80- 82 B-
77- 79 C+
73- 76 C
70- 72 C-
67- 69 D+
63- 66 D
60- 62 D-
0- 59 F
The instructor reserves the right to award more generous letter grades but it will be done uniformly: student X can only have a higher letter grade than student Y if X has a higher point total than Y at the end of the term.


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.

Drop dates: Feb 2 is the last day to drop a class for a possible refund. March 28 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. March 28 is also the last day a student may change registration in a class to or from the pass/fail or credit/no credit basis. For more information about deadlines for adding and dropping the course under different circumstances, please consult the Registrar's web page,

Assistance with course work

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 assistance to students throughout the semester: A further description of the Sanger Learning and Career Center services can be found here:

More assistance with course work!

Another service, offered free to students with majors in the College of Natural Sciences, is RHSG, the Residential Halls Study Groups. These are tutoring groups that meet weekday evenings at Jester and Kinsolving dorms. I encourage you to participate if you are looking for additional resources to succeedd in this course.

Even more assistance with course work!

The School of Engineering also offers help to its majors: tutoring and study groups in Jester and Kinsolving, plus tutors from the departments and the engineering Honor Society. Please see "Engineering-wide Tutoring Optionsi" for more information, and avail yourself of this resource.

Video capture

Calculus goes high tech! This semester, Liberal Arts Instructional Technology Services (LAITS) has arranged to capture the projected images and sounds of our classroom and put them on the web. This is intended as a METHOD FOR REVIEW, not as a substitute for going to class, and here are two good reasons why. (1): There will be no video showing your instructor as he goes through his little dances on the stage. Seriously. This course involves a fair amount of 3D geometry, and in my experience this is very difficult to capture in a 2D medium. Come to class and experience 3-dimensional objects. And (B): although this is a large lecture class, there is a certain amount of interaction with the students; in particular, people ask questions. Asking questions is VERY, VERY important for success in a math class. You have to be in class to do it!

OK, so now you know you have to be in class. But if you later want to review one of the examples or something, you can watch the video. To access it, go to Blackboard, click on your section of this course, and then (on the left) look under Course Documents for the video clip.

Here is the official LAITS blurb:

This class is taking part in a lecture capturing experiment. As part of this experiment, audio and projected material presented in class will be recorded and made available to you for review via Blackboard.

To watch a recording, simply click on the link for the recording, enter your UTEID information and select the version of the recording you want to watch (use High Speed if you have a fast internet connection and Low Speed if you have a slower connection). You will need Flash installed on your computer to view these recordings (

Please remember that this is a trial of the lecture capturing system, so an issue might arise that could prevent material from being made available in a timely fashion or at all. Although every effort will be taken to keep the system running, UT does not guarantee the availability of these recordings. Attending class is the only way to insure your viewing of the professor's presentation.

You can find additional information about the lecture capture system as well as report technical issues at:


This semester we will cover most of chapters 11-16 of the text (starting anachronistically with chapter 12), following a brief interlude of topics from sections 7.8 and 8.8

The schedule shown below is subject to change without warning (although any changes to exam dates will be announced repeatedly 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 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 talk in my office about mathematics topics beyond what we discuss in class.