MATH 408D: Differential and Integral Calculus II

General Information

      Instructor: Dave Rusin ( 
      Office hrs: I will be in my office (RLM 9.140) at these times for you:
         Tuesdays 11-2 pm
         Wednesdays noon-2:30 pm
         Thursdays 11-2 pm
      Other times available by appointment.

      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.

      Class meets Tuesdays and Thursdays in CPE 2.214, 9:30-11:00am.

      Teaching asst: TBA
      TA Office hrs: TBA
      These sections meet Mondays and Wednesdays with the TA at, respectively,
          Sect 52435: 12:00- 1:00pm in CPE 2.206
          Sect 52440:  2:00- 3:00pm in CPE 2.206

      Your final exam is Saturday, December 14, 7:00 pm-10:00 pm. in GDC 2.216 ---
      this is NOT the regular classroom!
      There is no provision for taking the final exam earlier or later.

Course webpage:

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

Here is the summary of integration techniques that I told you in class I would prepare for you. It also summarizes the trig identities you may need.

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.

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, 408L, or 408S, or suitable performance on an entrance exam (AP, IB, or CLEP). Please note that if you had a C- in Math 408C/L/S, you have the weakest background in this class and so you should be working hardest and getting the most help and feedback and the teaching assistant.

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

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

Class structure

Every day (more or less) I will ask you to learn some material online BEFORE coming to class. This is presented in a "learning module" at the Quest site. There will be pages to read, short videos to watch, and some straightforward questions. Follow the instructions and make notes of your questions; you can bring these to me (or the T.A.) in class.

That way we can use our very limited time together to be more productive by getting you to do things rather than sit passively listening to me drone on and on. We will work individually or in groups, and some of you may present your work for the rest of the class to see.

There will then be some traditional homework for you to complete, also through Quest. You can and probably should work with your friends on these assignments.

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.

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.

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.

Learning Module, 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 ratio will change as the semester progresses. 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.

I will use the scale above to convert your raw score to a letter grade, but because my exams tend to be hard, I will also use an alternative method and then whichever method gives you the better letter grade will be the one I record for you for that exam. Here's the alternative method: 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) :
In this way 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 11% of the letter grades were D's and F's.)

Note that in this example any student whose raw score was 87 or higher would get a higher letter grade based on the traditional 90-80-70-60 scale shown earlier, and thus for those students the traditional scale will be used.

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

I expect the dates of the midterms to be October 3 and November 12. Our last day of class is Thursday, December 5. You can mark on your calendars now the time and date of the final exam.

Letter Grades

Your final semester grade is simply a weighted average of the components: learning module, homework, quiz, and midterm grades count equally (1/7 each) and the final counts double (2/7 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!

Note that in this way your weekly homework grades and so on are giving you approximations to your eventual semester grade. If you don't like the grades you are getting, please see me (or the T.A.) before a bad pattern sets in. For most people the LM and HW grades pull their average up and their tests pull their average down, but the deviation is not typically large. 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. Please silence your cell phones. I will always assume that any talking I hear is about the course material so I may ask you to share your conversations with the class.

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: Sep 3 is the last day to drop without approval of the department chair; Sep 13 is the last day to drop the course for a possible refund; Oct 31 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 instructional material for this coursei which is mandatory, 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.

Bennett exam: The Bennett contest exam is a competition held at The University of Texas Mathematics Department at the end of every regular semester. (This semester that will be Tuesday, Dec 10.) 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!

Assistance with course work

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 RLM 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):

Students can now enroll in refresher classes and register for tutoring support by going directly to the Student Login portion of the Sanger website.


We meet 30 times this semester. 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 29:  7.1, 7.2
Sep  3:  7.2,3    Sep  5:  7.4
Sep 10:  7.5      Sep 12:  7.8  
Sep 17: 11.1,2    Sep 19: 11.3     
Sep 24: 11.4      Sep 26: 11.5     
Oct  1: 11.6,7    Oct  3: *EXAM 1*
Oct  8: 11.8      Oct 10: 11.9,10  
Oct 15:  11.11    Oct 17:  9.1,2
Oct 22:  9.2,3    Oct 24:  9.4
Oct 29:  9.5      Oct 31: 10.1,2
Nov  5: 10.3,4    Nov  7: 10.5,6
Nov 12: *EXAM 2*  Nov 14: 14.1,2,3  
Nov 19: 14.5      Nov 21: 15.1
Nov 26: 15.2      Nov 28: Thanksgiving Holiday
Dec  3: 15.3,4    Dec  5: 15.4,9

Attendance is not mandatory. But who are we kidding. At the pace of this class, any time you miss a class, you are a couple of sections 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 $47 for every one of those 30 class meetings. Are you really going to throw away $47 you have already paid, so that you can sit home and eat Cheetos on the couch?


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 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 talk in my office about mathematics topics beyond what we discuss in class.