Course information for MATH 242: Calculus B

Instructor

Prof. Toby Driscoll
505 Ewing Hall
831-3383 or driscoll(AT)math.udel.edu
Office hours: TBA

Meetings

Lectures	MWF 9:05-9:55 Kirkbride 005	The lectures stay close to the way material is presented in the book, but I like to simplify the presentation and narrow the focus when I can. Only in lectures will you find out exactly what I think is important.
Discussions	1 per week varies by section	A discussion section is a smaller group meeting run by a TA. The idea is for you to get answers about material that wasn't clear when you tried to do the homework.
Labs	1 per week varies by section	You will be learning how to use the Maple computer algebra system, in a format much like a chemistry lab. The idea is for you to spend more time learning the calculus without temporarily having to simplify expressions and apply identities from days gone by. You may also find Maple useful as a tool in other and in future classes.

Required textbook

Stewart, Calculus, 5th ed. You must get the correct edition!

Maple

Maple is a computer package that does symbolic mathematics. In Math 242 and 243 we teach how many of the concepts in the courses can be implemented in Maple. This can help you learn the theoretical material and give you skills to use in other math, science, and engineering courses. You will use Maple in a computer classroom on lab days.

Due dates

Assignments are due at the beginnings of class periods. Work turned in during class will get a 10% grade penalty. No work will be accepted after class ends on the due date. Extensions may be granted if you can demonstrate a genuine emergency.

Academic integrity

To insure the integrity of your degree, the university takes academic honesty very seriously. You are urged to read the Student Guide to University Policies regarding academic integrity. Acceptable practices include discussing homework or lab problems with other students, showing another student how to solve a problem, getting help from a TA, instructor, or tutor. Unacceptable practices include, but are not limited to, copying others' work, handing in someone else's work as your own, duplicating all the steps from a reference, inserting bogus steps that do not logically lead to the shown result, allowing your own work to be copied, posting your work to a public forum. Official policy is to refer all allegations of academic dishonesty to the Office of Judicial Affairs. Any violation may result in grade penalities and other consequences for all individuals involved.

Homework

There will be 13 homework assignments due approximately weekly throughout the semester. You are required to turn in all of the problems, even though only a subset of them will be graded. The homework problems are the only chance you get to test your understanding of the material before exams, so I encourage you to invest a lot of time in them. I expect them to be written neatly and completely; otherwise, grade penalties may apply.

Maple TA

Maple TA is a web-based system for generating and grading mathematical problems. One of its advantages is instant feedback. Some of your homework problems will be assigned and graded through Maple TA. There will also be exam reviews based on the technology.

Exams

There will be three midterm exams on nonoverlapping units of the course, and a comprehensive final. No computing devices will be allowed during the exams.

Grading

Each category below will have an average score based on all the coursework in that category. This score (as a percentage) is multiplied by the maximum points available in the category:

Homework		100 points
Online homework (Maple TA)		100 points
Maple work		100 points
Midterm exams		3 x 150 points
Final exam		250 points

Letter grades: 940-1000 A; 900-939 A-; 870-899 B+; 830-869 B; 800-829 B-; 770-799 C+; 730-769 C; 700-729 C-; 670-699 D+; 630-669 D; 600-629 D-

Synopsis

The first semester of calculus is mostly preoccupied with limits, derivatives, and integrals. In Math 242, functions are the central character. We discuss inverse functions and learn a critical inverse pair, the log and exponential functions, as well as others. We look at some tricks for common difficult integrals, by finding the right functional representations. We show that some functions can be made simpler to understand by changing or even adding a variable. We show how to represent functions by infinite sums, which is tremendously useful in some ways. Finally, we'll end by trying to find functions whose derivatives satisfy certain equations--equations whose existence are why Newton invented calculus in the first place.

Here is an overview of the topics. Book sections are meant as guidelines only. You are responsible for knowing what is covered in class. Note that we will not go in the chapter order.

Sections	Topic
7.1	Inverse functions
7.2*-7.4* (blue pages)	Logs and exponentials
7.5-7.6	Inverse trigs and hyperbolics
7.7	L'Hopital's rule
October 3	Midterm 1
8.1-8.4	Special integration methods
8.8	Improper integrals
11.1-11.2	Parametric representation
11.3-11.4	Polar coordinates
11.5	Conic sections (quadratic equations)
October 31	Midterm 2
12.1-12.2	Sequences and series
12.3-12.7	Convergence tests
12.8-12.9	Power series
12.10, 12.12	Taylor series
November 30	Midterm 3
10.1, 10.4, 10.5	Elementary differential equations
TBA	Comprehensive final

Homework

If I had eight hours to chop down a tree, I'd spend six sharpening my axe. --Abraham Lincoln

There is a lot of homework in this course. Doing the homework is how most learning will happen.

There are two possibilities: either the homework will seem easy, or it will seem hard. If it's easy, then it's just a nuisance--but on the bright side, you should be able to ace the exams. If the homework is hard, then you know it's valuable to you. You will have to pull out all the stops to get it done--find a study group, get a tutor, attend office hours--and above all, spend the time it takes. If you don't understand a topic well enough to do the homework, then you don't understand it, period.

There are certainly shortcuts you can take to get the homework answers submitted without intellectual effort. Not only is such dishonesty (or, as we like to call it, "cheating") lazy and corrupting, it's ultimately pointless, because the homework score is not worth enough to save you from incompetence on the exams.

Exams

The will to win is important, but the will to prepare is vital. --Joe Paterno

Most of your evaluation in the course comes down to how you perform during a few hours of exams. While that may seem unfair, it's what we expect of athletes and performers, and in any case I don't have a better system for a class on this scale.

I avoid covering new ground on an exam. For the most part, the problems will be almost exactly like those that were assigned for homework. Some problems will combine elements of homework problems in a new way, or try to disguise the same old stuff a little. But if you can do all of the homework, you can do the exams.

Here is how not to study: Sit down with the book, a friend, and an iPod and try to 'work through' the homework problems one by one.

Athletes use regular-season games to prepare for the playoffs, and performers have dress rehearsals before they go on stage. These preparations are as close to the real things as possible. Consider how an exam is different from the standard buddy-study scenario:

• You work alone.
• You have a time limit.
• You have no textbook, notes or distractions.
• You haven't seen the problems before.
• The problems don't come with handy section numbers to tell you what they're about.
• Someone else gets to decide how well you did.

I suggest the following plan. You and a friend separately copy 5-6 problems like those that you did for the homework, using problems sequentially close to those assigned or from the end-of-chapter problems. Exchange problems with your friend, put everything away, go to a quiet place alone, and give yourself 50 minutes to do the best you can. Meet back with your friend and grade each other's papers as honestly as possible. (You may feel uncomfortable or corny doing this step. However, it's vital. You can learn a lot about how to 'game' an exam just from grading one. Besides, wouldn't you rather get bad news from a friend than a professor?) Now that you both know where you really stand, study separately or together. Concentrate on your weaknesses, since that is the best strategy to add a lot of points to your score.

Maple

The website has tutorial pages that introduce the Maple commands you will be responsible for. Early in the semester we start with basic mathematical skills, later adding the kinds of things being done in class. Before each lab meeting you will be told which page(s) are relevant to the next lab. You should read these before going to lab. The TA may or may not choose to review them at the start of the lab period.

Most weeks you will go to the lab classroom and work on a prepared worksheet. The worksheet introduces some new mathematical techniques and applies new Maple commands to them. (You will not be examined later on the mathematical content.) You may work with any resources, including the web tutorials, the TA, and nearby classmates, but you must complete the lab with your own work, not copied from anyone. Good use of Maple formatting (sections, text comments) is expected. You will turn in your completed lab at the end of the period, or on a later date if more time is needed.

For three designated lab periods you will have a Maple quiz instead of lab. In these you will be given a list of routine tasks to perform--for example, differentiate a given function, plot a graph of y=f(x), or find the volume of a solid of rotation. These tasks will have been covered in the web tutorials, but perhaps not in the labs. You will again be allowed use the web resources for the quiz, but you will not be allowed to discuss it with anyone.

Illness and emergency

Stuff happens. Going to college doesn't shield you from that. Illness and emergencies--accidents, family issues, etc.--will interfere for everyone at some point. Please note that while a heavy workload may cause a crisis, it is not an emergency, and you will have to deal with it. If you must miss a regular class or recitation, no special notice or action is required. But if you miss four or more consecutive days, contact me--it's too easy to fall behind for good at that point.

If you have an illness or issue that causes you to fall behind on a homework assignment, typically you will get an extension upon request, without a formal excuse, unless you have already had extensions granted.

If you miss a lab, quiz, or exam, you will need some form of documentation for your emergency, or explicit permission from me. Missed exams due to illness require a note from the health center or a doctor, or you will get a zero. Contact me as soon as possible about your absence, in advance if feasible. Normally I don't give make-ups for midterm exams/practica. If you are excused from an exam, your exam score will be based on the midterms that you do take.

What I will expect

Be courteous. Don't distract everyone else, and me, by coming in late, having a light chat, or playing with your electronic toys. If you don't want to be in class, then fine--don't come. But respect those of us who want to be here.

Stay informed. Even when you miss a class, it's your responsibility to stay current. Use a classmate for this, as I don't give private encores.

Also, every student is given a udel.edu email account. This account is automatically enrolled in a mailing list for each course you take. You are responsible for all announcements and materials sent to your udel.edu email account. If you want to use another account as your primary email, you can enable mail forwarding--see www.udel.edu/help.

Don't waste time. I am happy to spend time helping you in this course. But I want it to be time well spent. For example, if you come to office hours, bring specific questions and all the work you've tried.

Work hard and smart.A few students do fine just from natural ability, but most successful students have to work hard, consistently, to keep up. Also, use your resources--classmates, your TA, me, the web site that goes with the textbook. I'm always amazed at how few students take advantage of all the help that is available to them. Your education is expensive, so get your money's worth!

What you should expect

Professionalism. I strive to treat everyone equally and with respect. You can express your opinions to me without fear of retribution.

Fairness. I view grading as an unpleasant but very serious responsibility. I intend to stick to the guidelines in the syllabus. If you feel I have made an error or misjudgment, ask me about it.

Transparency. The grading scheme should be clear enough, and work should be returned reasonably promptly, such that you should always have a good understanding of how you are faring in the course. If not, request a meeting.

Responsiveness. If I stop making any sense during lecture, interrupt and tell me to slow down or backtrack. Sometimes, it's not you, it's me. If I can't answer a question right away, I will try to answer later. If I don't, I have probably forgotten. Please remind me.