MATHEMATICS 1220 Calculus II Syllabus and Course Information

Summer 2011 - Under Construction - Dates will be updated shortly

Catalog Description: 1220 Calculus II (4) Prerequisite: A grade of C or better in MATH 1210. Fulfills Quantitative Reasoning (Math & Stat/Logic). Geometric applications of the integral, logarithmic, and exponential functions, techniques of integration, conic sections, improper integrals, numerical approximation techniques, infinite series and power series expansions, differential equations (continued).

This course is the second 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 first semester calculus course e.g., Math 1210 or equivalent, including a passing score (3 or higher) on the AP Calculus AB test.

Instructor: Aldo Bernasconi, Ph.D., email: bernasco@math.utah.edu

Office hours TBA, or by appointment

E-mailing me using the Webwork `Email Instructor' button is best way to reach me 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:

Last day to drop: Wednesday, May 25
(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, May 22
Last day to add, elect CR/NC or audit: Tuesday, May 31
Tuition payment due: Tuesday, May 31
Last day to withdraw: Friday, June 24
Last day to reverse CR/NC: Friday, July 29
Final exam period: Thursday-Friday, August 4-5
Grades available: Tuesday, August 17

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.

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 II, you must be proficient in Calculus I. Calculus I emphasizes differential calculus, or instantaneous rates of change, and Calculus II emphasizes integral calculus, or cumulative change. Where Calculus I leaves off, the relationship between these two aspects is first noted, and now it will be explored fully. The student is urged to look at (or take) the previous Calculus I exams on the Math 1210 online pages to check for this proficiency. You should do, with ease, about 80% of the problems.

Given proficiency in Calculus I (as well as the geometry, algebra and trigonometry that it uses), and a willingness to think in terms of changing and accumulating quantities rather than static images, you should do well in Calculus II. 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.