Homework

Homework comes in two forms. The main form consists of WeBWorK problems, which will generally be due each Saturday at 6:00 AM. WeBWorK problems are done over the web by going to the MTH 162 WeBWorK Page which can be accessed through the MTH 162 Blackboard page. WeBWorK provides instant feedback as to whether you have done a problem correctly or not. You can try each problem as often as you like, with no penalty (before the due date). For more information on WeBWorK, see the Introduction to WeBWorK Page. The second form of homework consists of supplementary problems; see the Supplementary Homework Exercises for a complete list. These problems do not contribute directly to your total grade, but they are part of the course and it is suggested that you work on them; similar problems may very well appear on the exams.

Secondly, you have to read the book. For a rough schedule of reading assignments, see the course schedule. There’s no specific time you should have them read, but you should generally keep pace with the lecture material. It is important to read the book and attend class, and to do both the WeBWorK and supplementary problems.

Each midterm exam will be scored numerically. Do not be alarmed if the score you get is lower than what you are used to from high school! I like to give hard exams and grade them leniently rather than easy exams graded strictly. This is better in the long run because it reduces the effect of minor mistakes on your grade. Your score will be converted to a letter grade by a formula that will be announced when the exam is returned. The formula will give a number between 0 and 4.5. Four means A, three means B, and so on. Your letter grade is often better than what you might expect for your score.

The final exam will consist of two parts: Part A will cover material previously covered on the midterms, while Part B will cover later material. Each of them will be scored numerically and the scores will be converted to letter grades by formulas to be determined later.

Your total Webwork scores (with the lowest individual score dropped) will also be converted to a letter grade at the end of the semester.

Your course grade will be the higher of the two weighted averages as indicated in the table below. The better of the two options will be chosen automatically. You will not have to ask for it.

 Option 1 Option 2 Midterm 1 19% Midterm 1 or 2 24% Midterm 2 19% Final Part A 8% Final Part A 22% Final Part B 23% Final Part B 23% Webwork 23% Webwork 23% Recitation attendance 8% Recitation attendance 8%
• In Option 2, only the better of your two midterm grades will be counted. The lower midterm grade will be dropped, and effectively replaced by your grade on Part A of the final.

• THERE WILL BE NO MAKEUP EXAMS. If you miss a midterm exam due to illness, oversleeping, family emergency, or other personal reasons, Option 2 above will be used. If you miss the final exam or both midterms, you may have to retake the course.

• Late homework will not be accepted.

CALCULATORS, CELL PHONES, iPODS AND OTHER ELECTRONIC DEVICES WILL NOT BE PERMITTED IN EXAMS.

Necessary Background

To take this course, you should have had first semester calculus (MTH 161 or equivalent). That is, you should be familiar with limits and derivatives- both what they mean and how to compute them. You should be comfortable enough with derivatives to compute them fairly quickly. We’ll be using trigonometric functions, as well as exponential and logarithm functions, extensively, so you should know how to work with those. If you’re shaky on some of these details but have had first semester calculus, talk to your instructor to figure out whether this course is right for you.

Course Content

Calculus II covers three main topics: Integration, Parametric Equations, and Sequences and Series.

• In Chapter 6, we’ll see some applications of integration to other problems, including some from physics.

• In Chapter 7, we’ll learn some more advanced techniques for evaluating integrals.

• In Chapter 8, we’ll see some more advanced applications of integration.

• In Chapter 10, we’ll cover some geometric topics, including the length of curves and polar coordinates.

• Next we’ll cover sequences and series in Chapter 11. Two standard problems in this subject are the following: does it make sense to sum up this infinite sum: 1 + 1/2 + 1/4 + 1/8 + …? (Yes; it adds up to 2, as we’ll see.) Does it make sense to sum up this infinite sum: 1 + 1/2 + 1/3 + 1/4 + …? (No; even though the summands keep getting smaller, the sum would add up to infinity.) The main point is that we can write many functions (such as sin(x)) in a very easy to work with form as a polynomial (abeit an infinite polynomial called a power series).

Tips for Webwork

The best feature of Webwork is that when you enter an answer to a homework problem, the system immediately tells you whether the answer is correct. On top of that, you can try again as many times as you like. Once you get it right, that fact is immediately recorded (provided it is before the due date), and any wrong answers are not counted in your grade. So

• Get started early on Webwork each week, and enter some answers at least a couple days before the due date. That way, you will have time to seek help on the harder problems (and the ones that looked easy at first but turned out to be trickier) before the set is due.

• Avoid the last-minute rush. The system often becomes overloaded and slow in the last couple hours before a set is due, since everyone is trying to enter their answers at the same time. Try to be done before that.

• Webwork usually requires very precise answers. For instance, if the correct answer is 1.60045 and you enter 1.6, the system will say that’s incorrect. So if you’re entering a decimal answer, give at least five digits of accuracy. On most problems, you can enter answers like  cos(9.81sqrt(340))  instead of a messy decimal, and Webwork will do the calculation for you.

• Some Webwork problems require formulaic answers, like x^(2/3), which means x raised to the power of 2/3 (two-thirds). However, if you enter x^2/3, the system will say that’s wrong, since Webwork interprets that as one third of x squared. So be careful, and check your syntax. (Webwork Set 0, which is recommended but not counted in your grade, will help you learn about entering formulaic answers.)

• Webwork has an automatic previewing feature which allows you to see how a complicated formula you just entered is actually interpreted by Webwork. The previewer should help you track down syntax errors as well as ensure that your answer is being interpreted the way you want without having to add extra unnecessary parentheses.

Getting Extra Help

If you get stuck on a homework problem, or you don’t understand some concept as well as you’d like, or you feel lost and confused, please know that there are lots of places you can go for help. Besides lecture and recitation (please speak up and ask questions in both), here are some more informal avenues for assistance:

• Office Hours. All instructors and TAs hold office hours, for you to drop in with whatever random questions you may have. Office hours are a good thing; you should take advantage of them in all your classes.

• Math Study Hall. At certain times Monday to Thursday, math grad students will be availableon Zoom for the math study hall, where calculus students can drop in for homework help and questions.

• Webwork Feedback. All Webwork problems have a button on the page for “Email Web TA”. When you click this button, a form comes up that allows you to write a message which will be emailed to the instructors and TAs. Someone will get back to you within a day or so (and maybe sooner). You don’t have to copy out the problem (the system automatically tells us which problem was on the screen when you clicked the “Email Web TA” button), but it does help us to help you if you give some idea of your thought process so far. In particular, if you’ve gotten an answer that Webwork won’t accept, then say what that answer is and how you came up with it. Be aware that emails sent the night that a set is due will almost certainly not get a reply before the set closes.

Dropping Down to MTH 142

Hopefully the following information will concern very few students. If you are having difficulty with the MTH 162 material, one option to consider is dropping down to MTH 142. The sequence MTH 141-3 covers exactly the same material as MTH 161–2, but at a slower pace. MTH 142 covers the last third of MTH 161 and the first third of MTH 162. Changing to Math 142 may improve your grade, but it often means taking an extra semater of caluls to meet the requirement sof your major. If you are in this situation, you should consult with your MTH 162 instructor. The deadline for changing courses is TBA.

What to Expect

College calculus is generally much more intensive than high-school calculus. Theory and concepts will probably be emphasized more than you are used to, if you’re coming from a standard AP course. Furthermore, Calc II is usually harder than Calc I (even if you’re a sophomore coming from MTH 161). The main reason is that in Calc I, most of the problems have a set method used to solve them. (For instance, taking a derivative becomes a rote process once you get used to it.) However, many of the problems in Calc II require several attempts with different strategies before you find one that works; and that’s even if you know the subject inside and out. In its glory, math is not about formulas and set methods and algorithms (in spite of what it appears to be before calculus). It’s about messing around, trying things, trying again, and trying again. If you never find it frustrating, then you’re probably not trying hard enough. But if you stick with it, it will make sense. Trust me. Some of the things we’ll get to see by wading through the muck are truly beautiful and elegant. Is calculus (and math in general) a tool? Yes, partly; but it also has a wonderful grace of its own. Hopefully, you’ll be able to appreciate some of that grace before the course is over.