Math 231

I've posted Midterm #2 scores on Blackboard. You can interpret your score as follows:

• 55–78: A- to A
• 44–54: B- to B+
• 34–43: C to C+

Anything lower than that is a D or an F.

Here are the solutions to Wednesday's exam. I haven't graded them yet but I'll post the scores when I do. Have a great break and see when classes resume.

Here are the solutions to the 2019 exam. And here are the extra problems from class today, and here are their solutions.

Here are the solutions to Quiz 4. I'll return these quizzes in class today.

Sorry, the link to the 2019 exam was broken. I've fixed it now.

Some more details about the exam coming up on Wednesday, April 17th:

• The exam will cover everything up to and including Section 4.7.
• You can use any calculator, graphing, scientific, whatever. You cannot use a computer or a phone, even if you have a calculator app on your phone and promise to only use it. No exceptions, sorry. None of the problems will specifically require a calculator, since exact answers are preferred anyhow.
• You may bring to the exam a one-page, two-sided sheet of notes in your own handwriting. I want it to be written in your own handwriting because the process of making a notesheet is helpful for studying, and I don't want people downloading or xeroxing someone else's notesheet. Also I want to avoid weird tiny print, magnifying glass scenarios with typed sheets.
• Please don't use the bathroom, etc., during the exam. This is not an absolute prohibition, since I realize sometimes life compels people to leave the room in some way. I don't like imposing this policy, because I think it's disrespectful to you students, but in recent semesters I've had problems with people exchanging answers in creative ways in bathrooms, and I don't want to have an atmosphere where students do that.

Here is a model exam to help you study for next week's midterm. More information on that coming soon.

I'm on my way to office hours but am late. My apologies, I was dealing with some health issues of my parents'. I will probably not be there until 1:45 or so.

There will be a solar eclipse during class on Monday, peaking at 3:25pm. If you can get yourself safe eclipse-watching glasses (I think many public libraries are distributing them), I encourage you to bring them.

It's been pointed out to me that some of the questions on Section 4.1 mention the error of a linear approximation, something I never talked about. This is just the difference between what the linear approximation predicts it to be at a point, and what it actually is. This is also called the absolute error.

As you'll see on the calendar, we have another quiz coming up on Wednesday. The topic will minima and maxima and monotonicity. There will be a question about finding the minimum and maximum of a function on a closed and bounded interval, and there will be a question about using the first derivative test to find local minima and maxima. The quiz will not cover concavity.

I'm done grading your last quiz and will post the scores this afternoon. Here are the solutions.

Tomorrow's office hours are rescheduled to 1-2pm because I am subbing for another professor's class from 10-12.

As I mentioned in class today, we have a quiz coming up next Monday, March 25. There will be a few problems on taking derivatives, especially with the chain rule. And there will be a related rates problem. My recommendation is that you get started with the Section 3.10 homework as soon as you can, even though it's not due until March 29th.

I've posted your midterm scores on Blackboard. You can interpret your score as follows:

• 55–74: A- to A
• 41–54: B- to B+
• 31–40: C to C+

Anything lower than that is a D or an F.

In the interest of transparency, and also because I hate answering questions about I assign grades, let me explain in as much detail as possible how I assign grades for the class. For each midterm and final, after I grade the test, I make a gradescale as above. I don't set the scale to make a certain number of A's, B's, and C's. Rather, I look at the tests and try to judge what scores match my expectations for what merits an A, B, or C. This means that if everyone in the class does well, I set the gradescale so that there are more A's.

When it comes time to assign final grades for the course, I use the gradescales to convert the midterm and final scores to a numerical scale of 0–100. In more detail, I convert the low end of the A range to 90, the low end of the B range to 80, etc. I set the high end of the A range to something above 100. For scores in the middle of a range, I interpolate linearly to convert them to the numerical scale. As a consequence, even though the gradescale for this exam says that 54 is a B+ and 55 is an A-, there is no big difference in getting a 54 rather than a 55 on this exam. When converted to the numerical scale, you'd just be getting an 89 instead of a 90 or something like that.

For the homework and quiz part of the grade, I also convert your scores to the numerical grade, though I'm a bit more ad hoc about it. Finally, I take all your numerical grades and compute a weighted average according to the weights given in the syllabus and arrive at your final numerical grades. Then, I make the final letter grades based on these. Roughly speaking, I'd convert numerical grades of 90 and above to an A or A-, grades of 80 to 90 to a B+, B, or B-, etc., but I use my judgment when setting the cutoffs (it's not like I'm giving people who got a numerical grade of 89.9 a B+).

One very special grading policy that I have: If you ask me whether I grade on a curve, I will ask you questions about what you mean by grading on a curve, probably until you give up asking your question. (If you can explain to me what you mean by grading on a curve, I am happy to answer the question, but it is not very common that anyone has a clear sense of what it means to grade on a curve.) I do hope that my explanation here is enough that you'll understand how the grading works.

Here are solutions to Monday's midterm, version A and version B. I'm still not done grading them, though. I'll return your exam on Monday.

Here is another old midterm of mine. And here are its solutions, as well as the solutions to the 2019 midterm.

Here are the solutions to Monday's quiz.

Here is some more information about the exam coming up on Monday, March 4th:

• The exam will cover everything up to and including Section 3.3.
• You can use any calculator, graphing, scientific, whatever. You cannot use a computer or a phone, even if you have a calculator app on your phone and promise to only use it. No exceptions, sorry. None of the problems will specifically require a calculator, since exact answers are preferred anyhow.
• You may bring to the exam a one-page, two-sided sheet of notes in your own handwriting. I want it to be written in your own handwriting because the process of making a notesheet is helpful for studying, and I don't want people downloading or xeroxing someone else's notesheet. Also I want to avoid weird tiny print, magnifying glass scenarios with typed sheets.
• Please don't use the bathroom, etc., during the exam. This is not an absolute prohibition, since I realize sometimes life compels people to leave the room in some way. I don't like imposing this policy, because I think it's disrespectful to you students, but in recent semesters I've had problems with people exchanging answers in creative ways in bathrooms, and I don't want to have an atmosphere where students do that.

Here is a midterm from 2019. More information about the exam will be forthcoming, but I wanted to post this sample exam right away. The best and most important thing you can do to get ready for the midterm is to try to solve the problems on the sample exam, and then to learn how to solve any problems you can't solve at first. I'll post the solutions soon and we'll discuss these and other practice problems in class on Wednesday.

Update: I should add that calculators will not be allowed (or needed) on Monday's quiz.

We will have a quiz on Monday, February 26. The main topic is limits. There will be a problem that shows you a graph and asks about limits (like in HW 2.1, #5, say). There will be a problem where you have to do algebraic manipulations to work out a limit, as in the Section 2.5 homework. And I might throw in a bit more algebra practice, to reinforce what I talked about last week, which was that there are two main types of algebra tasks we carry out, solving equations and simplifying/expanding expressions. When we're solving equations, the goal is to write down one equation after another, each one obtained from the last by doing the same thing to both sides of the equation. (You don't need to write down what you did to both sides unless you want to, since it will be clear from the two equations.) For example, if the first equation is \( \frac{x}{1+x}=3x^2 \), the next might be \(x = 3(1+x)x^2 \), obtained by multiplying both sides by \(1+x \).

When simplifying/expanding expressions, the goal is to repeatedly rewrite an expression in some different form. The goal here is to write down a chain of equalities. For example, if you're expanding \(3(1+x)x^2\), you might write down \( 3(1+x)x^2 = 3(x^2+x^3)=3x^2+3x^3 \).

It's not like it's absolutely necessary in life to write things this way when you're doing algebra, and it's not that I want to give you more rules to follow. But it is much harder to make mistakes if you do algebra in this style, and it's much easier both for me and for yourself to follow what you've done.

I'll be late to my office hours today. I've got a sick child at home and need to stick around at home with her in the morning. I'll arrive on campus sometime between 1 and 2, depending on how long the bus takes.

Here are the solutions to today's quiz.

A few people have asked me about the calculator policy for the class. Originally, I wrote in the syllabus that you could use a scientific calculator but not a graphing calculator. But actually, I've decided I don't care and whatever calculator you want is fine. I've edited the syllabus to reflect this.

Quizzes may or may not allow calculators, depending on the topic covered. For next week's quiz, it will be no calculators.

As listed on the calendar, there will be a quiz next week on Wednesday, February 7th. The topic will be basic algbra. It won't be anything complicated and it will only be for 15 minutes at the end of class. I'll ask you to find the equation for a line through two points and to solve a quadratic equation, and probably a few more things. No calculators on this quiz, but you won't need them.

Here is the algebra worksheet from yesterday's class and its solutions.

Welcome to Math 231, Calculus I. We meet on Mondays and Wednesdays in room 1S-218 from 2:30 to 4:10. The textbook for the class is Calculus: Early Transcendentals by Rogawski. A used copy is as good as new. Another good source is OpenStax Calculus. More or less all calculus textbooks are the same; on the calendar page, there's a list of the topics covered in each section, so you can go back and forth between different books.

The class will include online homework through WebWork, which is free. Here is the syllabus for the class. There is also an official departmental syllabus available for the class, which we'll basically follow, though our schedule won't match up exactly. You can see on the calendar when things will be, including quizzes and exams. See you all on the first day of class on the 29th!