MATH 408S: Integral Calculus for Science

General Information

      Instructor: Dave Rusin ( 
      Office hrs: MWF 11-12, MF 1-2, and by appointment, in RLM 9.140 .
      (I am usually in my office during ordinary business hours but if you
      want to be sure I'm available, let me know in advance.)

      Text: Calculus (7th 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.

      Class meets MWF in JGB 2.216, noon-1:00 pm. Plan now so that you 
      will have time to eat lunch at some other time than in class!

      Teaching assistant: Alex Moody  ( 
      These sections meet Tuesdays and Thursdays with him at, respectively,
          Sect 55445: 8:30-9:30am in UTC 1.132
          Sect 55450: 3:30-4:30pm in BUR 208
      Your TA will also be available for questions in the Calc Lab

      Registration in both sections is closed. I can't put anyone into
      the course or move people between sections. If you think you will
      probably drop the course, please do so promptly and allow another
      student to take your place.

      Your final exam is Monday, December 15, 2:00-5:00 pm. It may not be
      in the regular classroom; I will announce the location when I know it.
      There is no provision for taking the final exam earlier or later.

Course webpage: It is unlikely that I will post any important material to Blackboard or Canvas; for any additional information I want to give you outside of class you should come to this webpage.


I promised I would put online the homework I announced in class. Here is a separate web page that lists the written homework I am asking you to turn in.

Here is an answer key to the first midterm.

Some of you didn't seem to realize that you can, without any real creativity, compute the integrals of any product of basic trig functions. The book shows how you can do them all -- there are various special cases. You might to have a look at a slight variation of this iprocedure I wrote up (kind of flow-chart style).

Would you like to practice some trig integrals? Here are the integrals of sin(x)^i*cos(x)^j for some small values of i and j : The cases with i and j both positive, i positive and j negative, and i and j both negative. To see how to evaluate some of these you might want to see the results of using trig substitutions to integrate some combinations of 1 / (1+u^2)^j, and to see the results of using partial fractions to expand u^i/(1-u^2)^j and u^i/(1+u^2)^j.


408S INTEGRAL CALCULUS FOR SCIENCE: Introduction to the theory of integral calculus of functions of one variable, and its applications to the natural sciences. Subjects may include integration and its application to area and volume, and transcendental functions, sequences, and series and their application to numerical methods.

May be counted toward the quantitative reasoning flag requirement.


The prerequisite is a grade of at least C- in Mathematics 408C, 408K, or 408N. 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 assistants.

Registration is restricted to students in the College of Natural Sciences. Only one of the following may be counted: Mathematics 403L, 408L (or 308L), 408S.

Class structure

Every day (more or less) I will ask you to review some material online BEFORE coming to class. I will use the following web site (possibly to be changed later): Please note that I do NOT intend to repeat, in class, what is in the videos and the web pages shown there; rather, I want you to come in with questions and to be ready to work on problems. This is not only more efficient but you will be more involved and so will learn better.

Each day I will ask some of you to come to the front of the class and explain something about the material you are supposed to have learned, or to show us how you worked out a problem that I give you in class.

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: As of this moment I have not arranged the homework process but there will be homework due weekly. My intention is that at least some of them will be 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! I will also collect some written homework which will be graded by a human being. The two portions of the homework together will be combined and scaled 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.

Exams: There will be 2 mid-term exams, to be held during the usual class period, and a comprehensive final exam. Each midterm is worth 100 points and the final is worth 200 points. I expect the dates of the midterms to be September 29 and October 27. Please also mark on your calendars now the time and date of the final exam. (I don't know yet what room the final exam will be held in.) Textbooks, notes, and electronic devices (including phones and calculators) are not permitted during exams. The exams will be a mix of multiple-choice and free-response questions; the ratio will change as the semester progresses.

Attendance: I will be at class every day and expect you to be, too. Please note that we WILL have class the day before Thanksgiving. Sorry. The last day of class is Dec 5. We will use the class time to work problems together and I *WILL* call you to come forward and explain things to the class. In particular: I'll notice if you're not there...

Letter Grades

Your semester grade is based only on the number of points accumulated from the above mix of 600 possible points. I will use this conversion table:
Point total Semester grade
550-600 A
530-549 A-
510-529 B+
490-509 B
470-489 B-
450-469 C+
430-449 C
410-429 C-
390-409 D+
370-389 D
350-369 D-
0-349 F
If for some reason there is a deviation from this scale it will be applied uniformly to the whole class, and it will be announced in class. I promise that if anything, I will only make the scale more generous! WARNING While the letter grade distributions in my classes tend to look like those of other instructors, students often report that my tests tend to be difficult and long, and so the numerical scores are not high. Here is what the mean scores were in a recent semester: (Standard deviations shown in parentheses.)

You will notice that this mean score roughly separates the A's and B's from the C's, D's, and F's above; after all A and B are supposed to mean "above average", right? (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.)

No letter grades will be assigned to the midterms, quizzes, or homeworks, but you should keep track of where you stand: I will advise you of the class averages and you can use this data from other semesters as a rough guideline.


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.

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: Sept 2 is the last day to drop without approval of the department chair; Sept 12 is the last day to drop the course for a possible refund; Nov 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,

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.

Assistance with course work

CalcLab: Starting this Fall, the Mathematics Department will offer 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 open Monday through Friday, from 2:00PM to 7:00PM, starting Tuesday, September 2nd. The Lab is almost always in PAI 5.39. If you go there during those hours you will 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 M408S):

A further description of the Sanger Learning Center services can be found here:


This semester we will cover most of chapters 5,6,7,11,and 15 of the text, following this pattern (subject to minor variation):



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 408S 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.