Sequences, series, and multivariable calculus M408D

Transcription

1 Sequences, series, and multivariable calculus M408D T. Perutz University of Texas at Austin, Spring Semester Basics Course number: M408D. Unique identifiers: 55720, 55725, (these distinguish different discussion sessions) Classes: Tuesday, Thursday, 11-12:30 pm, ECJ Discussion sessions with TA: Monday, Wednesday 55720: 12 1 p.m., PAR : 3 4 p.m., RLM 5.120; 55730: 4 5 p.m., RLM Instructor: Timothy Perutz (Assistant Professor) perutz AT math DOT utexas DOT edu Class webpage: Office hours: Tuesday, Wednesday 5-6 p.m., RLM TA: Will Carlson wcarlson AT math DOT utexas DOT edu Office hours t.b.c. Textbook: James Stewart, Calculus: Early Transcendentals, 7th Edition. Brooks/Cole, Available from the University Co-Op bookstore. I m happy to answer questions about this course by or in person (RLM ). However, please read this page first, since it may well answer your query. 1

2 2 Aims The specific mathematical aims of the course are as follows: (i) To learn to work with infinite sequences and series, applying tests to establish their convergence or divergence. (ii) To learn to work with vectors in 3-dimensional space, including the dot and cross products. (iii) To learn differential calculus for functions of several variables, including partial differentiation, the notion of differentiability, and the method of Lagrange multipliers. (iv) To learn the beginnings of multivariable integral calculus. 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. 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, but not 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. 3 Is this course for you? This is the second part of the M408C/D calculus sequence. The prerequisite is a grade of C- or better in M 408C, M 408S, M 408L or the equivalent. M408D is a fast-paced course which covers a lot of material. If you took 408C and found it uncomfortably fast, you will likely find this one very fast. To succeed in mastering this material, you will have to make a serious timecommitment to the course, including attending twice-weekly lectures, twiceweekly discussion sessions, doing twice-weekly homework, and preparing for quizzes in the discussion sessions. 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. 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 slower-paced course (compare M408K/L/M and M408N/S). It will be assumed that you have algebra and trigonometry, differential calculus and integral calculus (as in M408C) at your fingertips. If you do not, there will not be time within the course to catch up, so please consider taking a different course. 4 Syllabus and schedule We shall cover material (mostly) from chapters from Stewart. 2

3 The schedule is given on the last page of this document. Warning: the schedule is approximate! This is my first time teaching M408D, so I can only estimate how long things will take. The section references are to Stewart s Calculus: Early Transcendentals, 7th edition. 5 Assessment 5.1 Exams Exam dates: Midterm Exam 1: Thursday, February 21, 2013, in class Midterm Exam 2: Thursday, April 4, 2013 in class Final Exam: Friday, May 10, 9:00-12:00 noon (to be confirmed) Exam rules: You must bring a valid photo ID to all exams. Notes, books, phones, and calculators cannot be used or even visible during exams. Your final exam grade will replace the lower of your two midterm exam grades, if the final exam score is higher than either of them. 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 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. If the time of the final exam is inconvenient, consider switching to another section. 5.2 Quizzes There will be a quiz in each discussion session. The Wednesday quiz will ask you to solve a problem already solved in Tuesday s class, while the Monday quiz will ask you to solve a new problem based on material from Thursday s class. One quiz per week will be graded. 3

4 No make-up quizzes will be given. To account for legitimate reasons to miss a discussion session, or unusually poor performances, the two lowest graded quiz scores will be dropped. 5.3 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 at 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, quest.billing@cns.utexas.edu. Homework assignments will become available on Quest by 3 p.m. on each class day (Tuesday and Thursday) and will be due at 9 a.m. on the following class day. No homework will be due on midterm exam days. There are approximately 25 online assignments for this class; the highest 20 scores will count towards your grade. No late work will be accepted. We will drop some of the assignment scores to allow for legitimate reasons for not turning in an assignment. 5.4 Grading The course components will be assigned the following weights: Homework: 15% Quizzes: 10% Midterm 1: 20% Midterm 2: 20% Final exam: 35% Notes: Plus/minus grades will be assigned for the final grade in this course. 4

5 All your grades will be posted on Quest (not on Blackboard!). 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. Grading on a curve will not be practised in this course. 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. 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. However, the scale may be more lenient than that, at my discretion. These are lower bounds for your grade! 6 Further information and policies 6.1 Optional Materials Calculators and Wolfram Alpha may be used to check the accuracy of your homework. However, neither will be available in exams or quizzes. 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. 6.2 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 about these special needs. 6.3 Disabilities Students with disabilities may request appropriate academic accommodations from the Division of Diversity and Community Engagement, Services for Students with Disabilities (SSD), 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. 6.4 Deadlines for Dropping a Course If you drop a class on or before January 30, the class will not show up on your transcript. If you drop a class after that date, the course will show up on the 5

6 transcript with a Q grade. After April 1, it is not possible to drop a course except for extenuating (usually non-academic) circumstances. 6.5 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 class and during exams. 6.6 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. 6.7 Resources The following resources may help you with this course: 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. See 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. 6

7 6.8 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): A link to information regarding emergency evacuation routes and emergency procedures can be found at 7

8 Date Topic Section Warm-up Jan 15 Review of differentiation and integration. Note: discussion session will review l Hospital s rule Jan 17 Improper integrals 7.8 Sequences and series 11 Jan 22 Sequences Jan 24 Series. Idea of estimating sums Jan 29 The integral test. Estimates of sums Jan 31 Comparison tests. Alternating series Feb 5 Absolute convergence. Ratio and root tests Feb 7 Strategy for testing series. Power series Feb 12 Representing functions as power series Feb 14 Taylor series. Applications of Taylor polynomials Parametric equations and polar coordinates 10 Feb 19 Curves defined by parametric equations. Tangents and arc-length Feb 21 First midterm test Feb 26 Polar coordinates. Areas and lengths Vectors and the geometry of space 12 Feb 28 3D coordinate systems. Vectors Mar 5 The dot product Mar 7 The cross product 12.4 Mar 12, 14 Spring break Mar 19 Lines and planes Mar 21 Cylinders and quadrics Vector functions 13 Mar 26 Vector functions and space curves. Their derivatives and integrals Partial derivatives 14 Mar 28 Functions of several variables. Limits and continuity Apr 2 Partial differentiation. Examples of PDE Apr 4 Second midterm test. Apr 9 Tangent planes and linear approximations Apr 11 The chain rules Apr 16 Directional derivatives, gradients Apr 18 Maxima and minima Apr 23 Lagrange multipliers Double integrals 15 Apr 25 Double and iterated integrals Apr 30 Double integrals over general regions. Applications May 2 Applications of double integrals