Sequences, series, and multivariable calculus (M408D): Fall 2014

T I M P E R U T Z
	Sequences, series, and multivariable calculus, AP Honors (M408D) University of Texas at Austin, Fall semester, 2014 Course number: M408D. Unique identifiers: 55080, 55085 (these distinguish different discussion sessions). Classes: MWF 9 - 10 am, CLA 0.130 Discussion sessions with TA: TTh 55080: 8:30 - 9:30 am, NOA 1.102 55085: 5 - 6 pm, PAR 1; Instructor: Timothy Perutz (Assistant Professor) Email: perutz AT math DOT utexas DOT edu Office hours: Wednesday, 10-11 am, 3:45-4:45 pm, RLM 10.136. TA: Nicolas Reyes Email: nreyes AT math DOT utexas DOT edu Office hours: to be announced Textbook: James Stewart, Calculus: Early Transcendentals, 7th Edition. Brooks/Cole, 2012. Available from the University Co-Op bookstore. Note: this text is available in a number of formats. Any format is acceptable. Homework schedule: Quest homework is due on Wednesdays by 11pm and Fridays by 11pm. In addition, there will be problems (typically from Stewart) to be addressed in discussion sessions with the TA. You should work them through before the TA sessions. These questions will not be turned in, but they reappear on tests. I'm happy to answer questions about this course by email or in person (RLM 10.136). However, please read this page first, since it may well answer your query.
	Aims The specific mathematical aims of the course are as follows: (i) To learn techniques of integration, including integration by parts and trigonometric substitutions. (ii) To learn the basics of differential equations. (iii) To learn to work with infinite sequences and series, applying tests to establish their convergence or divergence. (iv) To learn the basics of multivariable calculus (partial differentiation and multiple integrals). Much of this material is highly applicable, part of the working toolkit for physicists, engineers, economists, those who use statistics, and computer programmers. It is also relevant to other sciences, including chemistry and some parts of the biomedical sciences (e.g. epidemiology). Transferable skills developed in this course include: problem-solving skills; the ability to think logically about precisely-defined notions; and precision of expression. Careful definitions and statements of theorems will be emphasized. Explanations of why things work will also be emphasized, but not formal proofs. This course carries the university's Quantitative Reasoning flag. Quantitative Reasoning courses are designed to equip you with skills that are necessary for understanding the types of quantitative arguments you will regularly encounter in your adult and professional life.
	Is this course for you? This is an advanced placement or honors section of M408D. It is restricted to students who have scored well on the AP/BC exam (at least 3), very well on the AP/AB exam (5), are in the Engineering Honors Program, or have the consent of the mathematics adviser. M408D is a fast-paced course which covers a lot of material. In this honors section, there will be a focus on more challenging problems and on explaining why the methods work. To succeed in mastering this material, you will have to make a serious time-commitment to the course, including each week, attending three lectures and two discussion sessions, doing two Quest homeworks, and preparing for discussion sessions by working on designated problems from the textbook. The expectation is that the work you do beyond the five hours of class and discussion will require around 10 hours per week of your time. The coursework is designed so that, if you make this time commitment, you should be able to follow and learn the material through the semester. However, you cannot afford to lose your focus. Please do not take this course if you are not prepared to commit to this workload, or if you feel you would get more out of a non-honors section or slower-paced course (compare M408K/L/M and M408N/S). It will be assumed that you have algebra and trigonometry, differential calculus and basic integral calculus (as in M408C) at your fingertips. By this, I don't mean that you remember every trig formula and every integral in the book, but rather that (for instance) you can handle differentiation problems fairly quickly and comfortably. If you're not in that situation, there will not be time within the course to catch up, so please consider taking a different course. Students who have selected this course because they are in an honors program (e.g. Dean's Scholars) should take special note of the last paragraph. Some students who are exceptionally able in other subjects struggle in this course because they are not fluent in algebra and differential calculus. If you think that may apply to you, please consider carefully whether you are in the right course (I'll be happy to talk it through with you). It's better to change right away than to find yourself struggling later. In lectures, my aim is to explain concepts, writing up the explanation on the blackboard, and to work through a few examples. I recommend that you copy down these explanations in your notes, along with other comments I make verbally that you think are worth recording. Writing helps maintain your concentration in lectures, and will provide you with a set of notes to refer to. If you find the copying a distraction from thinking, an alternative is to photograph each blackboard. There isn't time in lectures to go through a large number of examples, but the discussion sessions will go through more examples and problems.
	Syllabus We shall cover material from chapters 7, 9, 10, 11, 14 and 15 from Stewart. A revised schedule is available in PDF format here.
	Assessment Exams There will be three midterm tests. Each will consist of several multiple choice questions and one or two free-response questions (in which you are expected to explain your answer as clearly as possible). Midterm Exam 1: Monday, September 22, in class Midterm Exam 2: Friday, October 17, in class Midterm Exam 3: Monday, November 17, in class Final Exam: Friday, December 12, 9:00-12:00 noon (to be confirmed). This information is from the university registrar; you can find updates, including the exam venue, at that site. You must bring a valid photo ID to all exams. Notes, books, phones, and calculators cannot be used or visible during exams. Students will be excused from the exams only because of a serious illness or another emergency of similar gravity. In such a case you must contact me via email before the exam, if physically possible. I will insist on documentation indicating your inability to take the exam at the scheduled time. If you are excused from a midterm, its grade weight will be shifted to the following exams in the most advantageous way for the student. If you are excused from the final, a make-up exam will be given. Enter the exam dates and times in your calendar now. Please note that I will generally not grant a make-up final for non-emergencies such as routine medical check-ups, sporting engagements or family events. Don't arrange to travel home before December 12, or take on a job that requires your presence on that date! If the time of the final exam is inconvenient, consider switching to another section. In tests, you will be expected to remember or derive trig formulas as you need them. Here's a short note about how to do that. Homework 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 $25 charge per student for its use, which goes toward the maintenance and operation of the resource. Please log in to the Quest system for this class using your EID. 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. You have the option to wait up to 30 days to pay while still continuing to use Quest for your assignments. If you are taking more than one course using Quest, you will not be charged more than $50 per semester. Quest provides mandatory instructional material for this course, just as is your textbook, etc. For payment questions, email quest.billing@cns.utexas.edu. There will be two homework assignments per week, both to be submitted using Quest. No homework will be due on midterm exam days. These are multiple choice assignments. You can receive a positive or negative score for each question, depending on how many tries you need (so don't guess wildly). However, your score for an assignment can never be negative, and you get a bonus for attempting all the questions in an assignment. The lowest 3 grades will be dropped. There will be homework assignments due by Wednesday at 11:00 p.m. These assignments will become available by the previous Saturday (typically, they will cover material from the Wednesday and Friday lectures of the previous week). There will also be homework assignments due by Friday at 11:00 p.m. These assignments will become available by the previous Monday (typically, they will cover material from the Monday lecture). Grading The course components will be assigned the following weights: Quest homework: 20% Midterm 1: 16% Midterm 2: 16% Midterm 3: 16% Final exam: 32% BUT: If your final exam grade is higher than your lowest midterm score, then the final exam will instead be worth 40% and the lowest midterm 8%. Plus/minus grades will be assigned for the final grade in this course. All your grades will be posted on Quest (not on Canvas!). It is your responsibility to ensure that your grades are recorded correctly on Quest. If an error occurs you must alert the instructor within two weeks from the date when the correct grade should have appeared. Your grades for assignments will be recorded as percentages. At the end of the course, your weighted total will be computed using the weights and rules described above. Your letter grade is determined by your weighted total. I will decide the grade cutoffs at the end of the semester, based partly on class performance (so there will be some "grading to the curve"). I will take into account the fact that this is an honors section. The cutoffs will be no stricter than the following: D for 60 or above, C- for 70 or above, C for 73 or above, C+ for 77 or above, B- for 80 or above, B for 83 or above, B+ for 87 or above, A- for 90 or above, and an A for 93 or above. The scale is likely to be more lenient than that, but that is at my discretion. These are lower bounds for your grade!
	Further information and policies Optional Materials Calculators and Wolfram Alpha may be used to check the accuracy of your homework. However, neither will be available in exams. Since the main role of homework is to learn the material well enough to take the quizzes and exams, you are strongly advised to work through the problems by hand. Special concerns Students with special concerns, such as athletes who might miss class meetings, students with religious observances that interfere with class meetings, or students with disabilities who need special accommodation, should all notify the instructor by the 12th class day, that is, Friday September 12, about these special needs. Disabilities Students with disabilities may request appropriate academic accommodations from the Division of Diversity and Community Engagement, Services for Students with Disabilities (SSD), 512-471-6259. If you think this may apply to you, please take action as early as possible. If SSD recommends that accommodations be made, please alert me immediately so that there is time to implement the accommodations effectively. One standard accommodation is extra time in exams. If you are granted extra exam time, you will need to book a place in SSD to take those exams (you can't take them in class, because the room will be in use), and I will need to sign a form and arrange delivery of your exam. Book early, because SSD fills up! If you don't set things up with SSD and me in good time, we may not be able to offer the accommodation. Deadlines for Dropping a Course If you drop a class on or before September 12, the class will not show up on your transcript. If you drop a class after that date, the course will show up on the transcript with a Q grade. After November 5, it is not possible to drop a course except for extenuating (usually non-academic) circumstances. Attendance This course is structured with the expectation that you will attend every lecture and discussion session, and your grade will benefit from your attendance. If absence from a class is necessary, you should contact a classmate to get notes, due dates and other information for the class you missed. Just in case, please introduce yourself to, and note down contact information of, at least three classmates. Please don't ask me for notes or for a summary of what you missed. Please come to class on time. Coming and going during class is distracting to your fellow students. Please do not talk or otherwise disturb students in the class who are trying to learn. All computers, cell phones and other electronic devices must be silenced and put away out of sight during exams. They should also be silenced and put out of sight during class, unless they are being used for the class (e.g., it's OK to use a camera to photograph the blackboard). Academic dishonesty Academic dishonesty, such as cheating in tests or plagiarizing work, will not be tolerated, and may result in a failing grade and other measures under the rules of UT. Resources The following resources may help you with this course: Calc Lab: The Math Department Calculus Lab is open M-F 2-7 in PAI 5.42, starting Tuesday, September 2. This is a joint TA session for all calculus classes taught at UT, and will be staffed at all times by at least two TAs and 3 undergraduate Learning Assistants. No matter what your question, you can always get help at Calc Lab. Drop-in tutoring and exam reviews (free) and private tutoring (not free) for this class are available in the UT Sanger Learning Center in Jester A332. There are also some free workshops and classes. Residential Halls Study Groups are (free) tutoring groups that meet at the study tables in Jester West and Kinsolving dorms on Sunday - Thursday nights 7:30 - 10:30pm. Both your TA and I have office hours, and are happy to meet with you. Come as soon as you have questions - if you wait, it will be hard or impossible to catch up. The mathematics department undergraduate computer lab is located in RLM 7.122, has 40 computers, and 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. Emergencies The following recommendations regarding Emergency Evacuation are from the Office of Campus Safety and Security: Occupants of buildings on The University of Texas at Austin campus are required to evacuate buildings when a fire alarm is activated. Alarm activation or announcement requires exiting and assembling outside. Familiarize yourself with all exit doors of each classroom and building you may occupy. Remember that the nearest exit door may not be the one you used when entering the building. Students requiring assistance in evacuation shall inform their instructor in writing during the first week of class. In the event of an evacuation, follow the instruction of faculty or class instructors. Do not re-enter a building unless given instructions by the following: Austin Fire Department, The University of Texas at Austin Police Department, or Fire Prevention Services office. Behavior Concerns Advice Line (BCAL): 512-232-5050 A link to information regarding emergency evacuation routes and emergency procedures can be found here.