Fall 2009
Catalog Description: 2210 Calculus III (3) Prerequisite: A grade of C or better in MATH 1220. Fulfills Quantitative Reasoning (Math & Stat/Logic). Vectors in the plane and in 3-space, differential calculus in several variables, integration and its applications in several variables, vector fields and line, surface, and volume integrals. Green's and Stokes' theorems.
This course is the third in a three-semester sequence on the Calculus: Mathematics 1210, 1220, 2210. All courses can be taken online. Exams are taken at testing sites arranged by UOnline/TACC, linked from the course homepage.
Prerequisites: A passing grade in a second semester calculus course e.g., Math 1220 or equivalent, including a passing score (3 or higher) on the AP Calculus BC test.
Instructor: Bob Palais, JWB 104, 585-7664, bp (AT sign) math.utah.edu. Office hours Tu 11:00am-12:30pm, Th 2:00pm-3:30pm
E-mail contact is best way to reach me. I also have office hours on Tuesdays 11:00am-12:30pm and Thursdays from 2:00pm-3:30 pm, or by appointment. I will attempt to answer your emails as quickly as possible, but please allow 24 hours to be safe.
Teaching Assistant: Hankun Ko, JWB 206, 581-7314, kohk@math.utah.edu. Office hours: Monday 12 noon-1:30pm
Contact the TA if you want additional help with the course material, and for basic webwork system issues (e.g., new accounts, login problems, etc.) as well as webwork problem techinical issues (e.g., problems which don't display correctly, etc.)
Text. The text used in this as well all classroom Math 1210-1220-2210 series calculus classes at the University of Utah is Calculus with Differential Equations, Student Edition, by Varberg, Purcell and Rigdon, Prentice-Hall, Ninth edition. ISBN 0-13-230633-6 also listed as ISBN: 9780132306331. Supplementary notes by Prof. Hugo Rossi are also strongly recommended, and available on the Supplementary Materials page.
Grading. There will be three midterm examinations, each counting for 15% of the final grade, and a comprehensive final examination, counting 30%. WebworK assignments make up the remaining 25%. Grades will be based on a fixed scale: 90-100: A, 80-89: B,70-79:C, 65-69:D. Cutoff points for intermediate grades (A-,B+, etc.) will be given in appropriate ranges to be determined.
Dates and Deadlines: The following deadlines apply this semester:
| August 24
| Classes Begin |
September 7
| Labor Day Holiday |
October 12-16
| Fall Break |
November 26-27
| Thanksgiving Break |
December 11
| Classes End |
August 25
| Webwork Assignment 0, Introduction to Webwork, a demo for practicing formats is `due' (This set remains open for latecomers, but complete it ASAP) |
September 1
| Webwork Assignment 1, Cartesian Coordinates, Vectors, the Dot and Cross Product, Vector-Valued Functions, Curvilinear Motion is due (11.1-4) |
September 8
| Webwork Assignment 2, Lines, Curves, Tangents, Velocity, Acceleration and its Components, Curvature (11.5-7) is due |
September 15
| Webwork Assignment 3, Surfaces, Cylindrical and Spherical Coordinates (11.8-9) is due |
September 29
| Webwork Assignment 4, Partial Derivatives, Continuity, and Differentiability (12.1-4) is due |
October 6
| Webwork Assignment 5, Directional Derivatives, The Gradient, Chain Rule, Implicit Differentiation, Tangent Planes and Differentials (12.5-7) is due |
October 20
| Webwork Assignment 6, Maxima, Minima, Lagrange's Method (12.8-9) is due |
November 3
| Webwork Assignment 7, Double Integrals and Applications (13.1-5) is due |
November 17
| Webwork Assignment 8, Surface Area, Triple Integrals (13.6-9) is due |
November 24
| Webwork Assignment 9, Vector Fields and Line Integrals (14.1-14.2) is due |
December 1
| Webwork Assignment 10, Independence of Path, Green's Theorem (14.3-14.4) is due |
December 8
| Webwork Assignment 11, Surface Integrals, Divergence and Stokes' Theorem (14.5-14.7) is due |
September 24, 26 |
Exam 1, Textbook Chapter 11: Vectors, Curves, and Surfaces
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| October 22, 24 | Exam 2, Textbook Chapter 12: Differential Calculus of Several Variables |
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| November 19, 21 | Exam 3, Textbook Chapter 13: Multivariable Integration |
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| December 15 | FINAL EXAMINATION. Cumulative including Chapter 14: Vector integration | ||||||||||||||||||||||||||||||||||||||||||||||||||
Last day to drop: Wednesday, September 2
(You can drop the class by phone or the web with no tuition penalty, and no transcript entry until this date.)
Last day to add without a permission code: Sunday, August 30
(You can add the class by phone or the web through this date.)
Last day to elect CR/NC or audit: Tuesday, September 8
Tuition payment due: Tuesday, September 8
Last day to withdraw: Friday, October 23
Last day to reverse CR/NC: December 4
Final exam period: Monday-Friday, December 14-18
Grades available: Tuesday, December 29
Examinations will be arranged in a flexible manner by the UOnline/TACC office according to the schedule above. You must register online for each exam two weeks before the exams.. However, if you have to miss an exam for a legitimate reason, then let me know, preferably before, but no later than one day after the exam. Only in exceptional circumstances, shall we give a make-up exam. There will be three midterm examinations, each counting for 15% of the final grade, and a comprehensive final examination, counting 30% (WebworK assignments make up the remaining 25%). Practice and Past Examinations linked from the course homepage contain sample problems and actual past examinations for this course, with detailed solutions. The midterm examinations will be held on the dates specified below. You must register for these examinations through U Online, at least two weeks before the exam. If you have any problems with this registration, contact the Uonline office, not the instructor. You may use graphing calculators on the exams, but no notes. Remember that you are graded on the work that you show; just giving the answer is insufficient.
Make ups: There will be no makeups on webwork assignments. They open on the first day of class, and close sequentially. It is essential that they be completed in a timely way.
Calculators. You are encouraged to use calculators in this class. Keep in mind however, that it is possible to do every routine calculus problem by pushing a few buttons. Thus, you should anticipate that at least half the problems on examinations will require some complex thinking, and you will be required to show work on all problems. See the Frequently Asked Questions page for more informations regarding calculators.
Mathematics Center. The Benny Rushing Mathematics Center (RMC) between LCB and JWB on President's Circle offers study and meeting space, a computer lab, and tutoring services, all free of charge. For more information call Angie Gardiner at 585-9478, send her e-mail at gardiner@math.utah.edu, or visit her in the Center.
Guide for doing the work of the course.
1. Do the readings from the Text and Supplementary Notes, Practice Problems and Worked Solutions. The textbook readings cover the topics of the course; illustrative examples and descriptions of methods for solving problems. The schedule link gives an approximate guide to how you should progress through the textbook, at a one section per regular class period rate. Recommended text problems provide an opportunity to test your comprehension. Answers to odd-numbered problems are available in the back of the book. A complete solutions guide is on reserve in the Math library. For each topic to be covered, there are also supplementary notes and practice problems with detailed solutions from Prof. Hugo Rossi who originated these courses. It is strongly recommended to do these problems, checking your work against the answers, before going on to the webwork assignments. It is recommended that you do these problems, for they are typical of the problems in the assignments and in the examinations. Try to do the problem first, and then compare your work with the solution in the "Answers". The practice problem sets loosely correspond to the webwork sets of the same number. The purpose of the practice problem sets is to compensate for the classroom experience; these are written so as to reproduce, as well as possible, the act of watching the instructor work through a problem.
2. Do the Webwork Assignments. These are weekly (or sometimes biweekly in summer) sets, usually of about 10-15 problems each, to be done on the web using a facility called WeBWorK. The Webwork assignments form the core of this course; Assignments must be completed by 10:59 p.m. on the date shown, usually Tuesdays. Do assignment 0 ("Demo", non-credit) first in order to understand the protocols for submitting answers on Webwork. When you submit an answer, you are informed whether or not it is correct. You may redo the problem as often as needed without penalty until the closing date. Webwork keeps track of your scores. Your final total on assignments counts 25% toward your final grade.
Do your webwork assignments by first printing out the assignment, then doing the problems on paper, referring to the sources as needed. After the problem is done, submit your answer. If it is correct, proceed to the next problem; if not, try to find your error. It could just as well be arithmetic, a syntactical error in submission, or a conceptual error. In the latter case, reread the appropriate text and try again (there is no penalty for incorrect tries), or finally, send an email to the instructor for assistance for guidance by clicking the Feedback button from that problem - this gives us a link directly to your specific version of the problem, and allows you to describe to us what you have tried and what is or isn't working. You can avoid roundoff errors by entering your answer symbolically rather than numerically and let webwork do the calculations (e.g., sqrt(2) may work where 1.41 may not.) The help button on each problem page hasuseful information for using webwork.
Plan to complete your assignment two days before the closing time. If the system goes before then, you still have time to submit answers. If you wait until the last night, you will not have that time. I will sometimes extend a due date collectively or individually if there are significant technical difficulties or other pressing reasons, but once a set closes, reopening it wipes out your previous work and you would have to repeat your work on different versions of each problem.
3. Examinations. Take the practice exam posted before the exam (and past practice exams) to get the best idea of what will be on the exam, what you are solid on, and what you need to review. When solutions are posted, check that your assessment was correct. If you are comfortable with a practice exam, you should do very well on the actual exam. The exam dates on the schedule are just approximate, indicating when the material for that exam should be covered. The actual dates on Thursdays and Saturdays when UOnline does proctoring are listed above. New practice exams with detailed solutions will be posted (i.e., the are links emailed to you through the webwork system) shortly before the exam dates and are the best guide to what you may expect to be covered on the current actual exams. I recommend doing the practice problems before consulting the solutions to get the best idea of what you feel solid on and what you most need to review. We usually receive the completed exams from UOnline in the middle of the week after they are taken, due to out of area exams and campus mail times. After they are graded, your scores will be mailed and solutions posted through the webwork system around the following weekend.
Getting Started: The webwork accounts are on a different system from the campus information system (CIS) used by UOnline, so your uID and password from that system will not work on it. The first day of the class, you should receive an email from the system giving you your username and initial password. You can change the password after you log in. If you registered late, you may not receive this email. In this case, email me (bp (AT sign) math.utah.edu) to let us know you've registered and be sure to include the course number, your uID, and your @utah.edu email address so we can set up a webwork account, email you a login and password, and catch up up on any other communications we have sent out. If you did not register late, or still do not receive an email with your account information, please let us know and we can check if we have been given the correct email address. Another possibility is that our emails are being prevented from reaching you by a spam filter (a mistake we hope!) You should check this to make sure you receive our correspondence. If you email either of us directly instead of through the webwork feedback button, please make sure to include which class you are referring to. If you just say `I don't understand the solution to #3 on the practice exam', we might have to look through all three class lists to find you, especially near the beginning of the semester when it's hard to know which class ever one of over a hundred names is in. For webwork problems however, the only way to request help is with the feedback button which takes us directly to your version of the problem and allows you to add comments about what you've been trying. It is highly recommended that you bookmark the links to the course homepage
http://www.math.utah.edu/online/2210
so you can reach it if you usually reach it from the Uonline site and that site happens to be down, and to the webwork login page
http://webwork2.math.utah.edu/math2210summer2009-90/ so you can reach this if the course homepage is down.
About Calculus
The central difference between Calculus and Algebra is the notion of instantaneous change instead of simple differences and continuous accumulation rather than simple sums. These concepts involve working with the infinite and the infinitesimal systematically, which makes calculus both challenging and rewarding. In algebra the basic objects we operate on are numbers, while in calculus we operate on functions. The purpose of `the Calculus' is to be able to understand the relationships between the behavior of different functions and their instantaneous and cumulative change.
In order to succeed in Calculus III, you must be proficient in Calculus I and Calculus II. Calculus I emphasizes differential calculus, or instantaneous rates of change, and Calculus II emphasizes integral calculus, or cumulative change. Calculus III emphasizes multivariable calculus: instantaneous and cumulative change of functions with potentially more than one independent variable, more than one dependent variable, or both. The student is urged to look at (or take) the previous Calculus I and Calculus II exams on the Math 1210 and 1220 online pages to check for this proficiency. You should do, with ease, about 80% of the problems.
Given proficiency in Calculus I and II (as well as the geometry, algebra and trigonometry that it uses), and a willingness to think in terms of multidimensional images representing changing and accumulating quantities, you should do well in Calculus III. To succeed in an online course, you must also be strongly self-motivated and prepared to work on your own until the topics are mastered. Such independent study, particularly when you must begin by thinking in a way different from the way of Algebra, is a challenge. It can be argued that a regular class with live instruction is much richer and more complete. Online, it is you who must provide the motivation, search for the subtleties, and notice the pitfalls; they will not be presented to you. Having said this, I welcome you to this challenge, will provide as much assistance as possible in this context, and wish you well!
General Comments about Online Mathematics Courses
In-class versus on-line. You may still be wondering if you should take this class on-line or in-class. The two versions cover the same material. The same deadlines apply to both versions. The main advantages of the in-class sections include: regular personal contact with the instructor and fellow students, a regular opportunity to ask questions, and regular presentation of the material by an actual person. The main advantage of the on-line course is that you can work on it on your own schedule, and wherever it is convenient (literally anywhere on the planet). The main requirements for taking the on-line version are Availability of an internet browser such as Netscape or Internet Explorer. Your ability and willingness to use e-mail almost daily. Your ability to view/print postscript of pdf files.
University versus High School Classes. Some mathematics (essentially Intermediate Algebra through Calculus, and some basic statistics) are taught at High Schools as well as at a University like this one. There are two main differences between classes on the same subject taught at a University or a High School. The University class is faster paced, and at a University there is no supervision of your learning by the teacher. I will frequently make suggestions about how you should go about it, but you are in charge of your learning. This is a difference in philosophy, not a matter of not caring. I measure my success by seeing how much students in this class learn, but I assume you are fully responsible and capable to make the best of what this class has to offer. I'd be pleased to talk with you about ways of maximizing your success. Don't hesitate to contact me if I can be of assistance.
About Studying and Learning Mathematics
Taking any math class is a serious enterprise that requires your commitment, time, and energy. Obviously, we are all busy, and there are many competing claims to our attention, all of which are legitimate. So it's not a moral problem if you don't have enough time to dedicate to this class. But it is a fact of life that understanding new mathematics takes a great deal of time and effort, and if you are not prepared to spend that time and effort you will not understand the mathematics. As a guide-line you should count on spending a total of about 12 hours per week on this class, approximately and on average. Moreover, you should be able to spend that time in good sized chunks without distractions.
Many people feel they are intrinsically unable to learn mathematics. This feeling is usually sincere, but it's also irrational, a poor excuse, and unnecessarily self-limiting. Anybody who has the mathematical prerequisites can study mathematics successfully. Here are some hints for success:
Do your work regularly and don't fall behind. If you have difficulty with a particular concept, don't set it aside for later; confront it and conquer it. Seek help, from me, from the study center, or from your peers.
Work with friends or study partners. Soon after the class starts I will distribute a list of participants, including e-mail addresses, phone numbers, and suitable study times. Then it will be up to you to contact your classmates and arrange times to get together. It's OK if you and your partner or partners have different levels of experience or ability. One of you will benefit from explaining something and the other from having something explained again in a different way.
Focus on understanding the subject rather than memorizing recipes for doing simple things. You understand a piece of mathematics if you can explain it in terms of simpler mathematics, you can make multiple logical connections between different facts and concepts, and you can figure out how to apply the mathematics to solve new problems. Too much teaching of mathematics is directed towards memorizing and rehearsing the application of simple recipes to narrow classes of problems. Focusing on the underlying connections and learning how to figure things out is vastly more efficient and empowering than trying to memorize countless formulas.
You can learn mathematics only by doing mathematics. Mathematics at this level is about connections, not about isolated truths or techniques. You can only make those connections by doing complex problems. Always Have Expectations: Take the time with each problem to fully understand it and to think about what kind of answer to expect. There is only one way to prepare for an exam: make sure you understand the material. Rather than worrying about what specific problems might or might not be on the test, just make sure the mathematics covered by the test make sense to you, following the suggestions above. Cramming does not work. Go over the practice exam, check on points which seem fuzzy to you, and then relax with confidence. Confidence level- even if by hypnotic suggestion - is a better predictor of success on exams than late hour cram sessions with the ensuing tensions.