Math 1A - Lecture 1 - Calculus

InstructorPaul Vojta
LecturesMW 5:00–6:30 PM, Wheeler 150
Course Control Number21760
Office883 Evans
E-Mailvojta@math.berkeley.edu
Office HoursMW 1:30–3
Office hours are drop-in — no appointments are necessary.
PrerequisitesThree and one-half years of high school math, including trigonometry and analytic geometry. Students with high school exam credits (such as AP credit) should consider choosing a course more advanced than 1A.

“As taught in most colleges and universities, calculus presumes fluency in the use of the basic constructs of precalculus from which calculus is built: ratios, algebra, function notation, and especially transcendental functions, with some reference to the nature of limits. Students who are not fluent in the use of these tools will flounder in the fast-paced and demanding environment of university calculus.” From: David Bressoud, “Thoughts on advanced placement precalculus,” Launchings, Teaching & Learning, July 1, 2021.

Syllabus This web page is the syllabus for the course.
A two-page pdf file, containing a summary syllabus and a weekly schedule, is also available at https://math.berkeley.edu/~vojta/1a/syll.pdf.
Required TextStewart, Single-Variable Calculus: Math 1A/1B (without enhanced webassign) 8th edition, You may also get the standard hardcover edition of Stewart, but only if it is the 8th edition and is the Early Transcendentals version. (It'll cost more, though.)

Older editions of Stewart won't work because exercise numbers, page numbers, etc. will be different.

Here is a copy of the table of contents of the textbook.

GradingGrading will be based on:
15%First midtermWednesday, September 28
20%Second midtermWednesday, November 2
25%Component from discussion section
40%Final examFriday, December 16, 3–6 pm

The component from the discussion section is left to the discretion of the section leader, but it is likely to be determined primarily by WeBWorK and weekly quizzes.

I reserve the right to incorporate exam results in the section component of the grade, in case the GSI does not provide useful grades (e.g., gives everybody A's).

HomeworkHomework will consist of weekly assignments. Most of the homework consists of problems asked on a web-based system (WeBWorK). In addition, some supplementary exercises (those not suitable for automation) will need to be done on paper. More details are given below.
CommentsThis is the first semester of the year-long calculus sequence; this particular course is intended primarily for majors in engineering and the physical sciences. This semester's topics will include differentiation, transcendental functions, and integration. This web page contains the official detailed syllabus for the course. A summary syllabus, with a weekly schedule for the course, is available here as a two-page pdf.
Support
  • The Student Learning Center provides support for this class, including study groups, review sessions, and drop-in tutoring.
  • We will use the discussion forum Ed Discussions. To access it, click on the link on the left in bCourses.

Homework

Weekly homework assignments will consist of an online part, plus some supplementary exercises from the book. The online part will use a web-based homework system called WeBWorK. Solutions to the even-numbered supplementary exercises will be posted on bCourses.

Although WeBWorK is very flexible, there are some types of exercises that cannot be done online (e.g., exercises that require any sort of explanation). Because of that, some exercises from the textbook will also be assigned. These are listed on the weekly schedule.

The WeBWorK assignment for week n will be due on Wednesday of week n+1 at 6am (so for practical purposes it's due Tuesday night of week n+1). As an exception, the due dates for WeBWorK assignments 5 and 10 will be different, so that you don't end up finishing a WeBWorK assignment the night before a midterm. There will also be changes for Thanksgiving. Your official due date and time for WeBWorK assignments are always reflected in WeBWorK.

WeBWorK Information

Access to the WeBWorK site is always through bCourses.

Because bCourses handles logging in, bookmarking pages on WeBWorK will not work.

There is no separate "submit assignment" button on WeBWorK. Just make sure that you've pushed "Submit Answers" for each question. (Your score on the overall page for the assignment would show a smaller percent on any problem for which you have not done that.)

After the due date for an assignment has passed, you can see solutions for the problems in that assignment. To do that, navigate to a problem, check the box "Show solutions," and then click "Preview answers."

Additional information on WeBWorK is available on the web at the URL http://webwork.maa.org/wiki/Student_Information. Since bCourses will take care of logging in, you should ignore what it says about logging in and about changing your password.

Exams

Policies for exams are as follows.

The two midterms will be given during the normal class hours (5–6:30 pm), and will be in our normal classroom (Wheeler 150) unless additional rooms are announced.

Generally, about a week before each exam, a sample exam will be posted on bCourses. This will usually be an exam from an earlier Math 1a class taught by the instructor. Sample exams should be used to get a general idea of the likely length of an exam and the general nature of questions to be asked (e.g., the balance between computational and more theoretical questions). However, one should not (for example) notice that a sample exam contains questions on material from Sections 1.5, 2.1, 2.7, 3.1, 3.4, etc., and expect to see questions from those sections on the actual exam.

Solutions to the practice exams will also be posted on bCourses, usually a couple of days before the actual midterm.

Exams are cumulative, so the second midterm may have questions from material prior to the first midterm. Of course, the final exam will cover the whole course, but will have increased emphasis on the material not covered on the midterms.

Exams will not be given remotely unless required by the campus.

This course is in exam group 19: Friday, December 16, 3–6 pm. Do not enroll in this course if you cannot take the final exam at that date and time, whether because of a conflict, too many exams on that day, or any other reason. (For your other courses, check their respective syllabi, or see the Registrar's page https://registrar.berkeley.edu/scheduling/academic-scheduling/academic-scheduling-final-exam-guide-and-schedules/.)

Here is a link "How to lose marks on math exams" (by a former GSI Andrew Critch).

Previous Exams

Sample exams will be posted on bCourses shortly before each exam.

The Math Department maintains an archive of old exams (usually without answers). Here is the link for Math 1a.

First Midterm

The first midterm was given on Wednesday, September 28, at the normal class time (5:10–6:30 PM), in our normal classroom (Wheeler 150). It covered all material in the lectures and textbook, up to and including Section 2.8 (The Derivative as a Function). It also covered WeBWorK assignments 1–5, and the corresponding Supplementary Exercises.

A sample exam, solutions to the sample exam, and solutions to the actual midterm, are available in the Files area of bCourses, in the folder “LEC 001 exam-related.”.

The rough curve for the midterm is as follows:

A56–75
B44–55
C26–43
D13–25

The median on the exam was 43, the mean was 40.6, and the standard deviation was 16.8.

Keep in mind that these letter grades are estimates only -- only the numbers are used to compute the final grade. While it is tempting to try to predict the course grade by assigning points to letter grades and forming a weighted average (similar to a GPA), this method tends to predict grades that are more moderate (closer to a B or C) than the actual course grade ends up being.

Second Midterm

The second midterm was given on Wednesday, November 2, at the normal class time (5:10–6:30 PM), in our normal classroom (Wheeler 150). It covered all material in:

Note that we skipped Section 3.11 (Hyperbolic functions), so that section was not covered. Also, we didn't spend much time on Section 3.7 (Rates of change in the natural and social sciences), so that section also was deemphasized.

Material from the first midterm (Sections 2.8 and earlier) was not directly addressed on this midterm, but material in those sections was still be relied on (this is unavoidable in mathematics).

Here are the rules for the second midterm (they were printed on the first page of the exam booklet):

  1. Check that you have all 8 pages of this exam booklet.
  2. Be sure to show all your steps. In particular, a “yes” or “no” or numerical answer by itself is never sufficient. When in doubt, over-explain rather than under-explain.
  3. Calculators are not allowed.
  4. Check your work as time allows.
  5. You may not use anything that has not been covered in the course or its prerequisites.
(These are the same rules as appeared on the first page of the first midterm, except that the last rule no longer prohibits use of l'Hospital's rule. In fact, parts of the exam can't be solved without use of l'Hospital's rule.)

This exam is worth 100 points.

A sample exam, solutions to the sample exam, and solutions to the actual midterm, are available in the Files area of bCourses, in the folder “LEC 001 exam-related.”.

The rough curve for the midterm is as follows:

A72–100
B62–71
C37–61
D18–36

The median on the exam was 62, the mean was 56.6, and the standard deviation was 21.4.

As with the first midterm, the above letter grades are only approximate.

Also, in the above table, “A” means A-, A, or A+; “B” means B-, B, or B+; etc. This applies also to the corresponding tables for the first midterm and (when published) the final exam.

RRR Week

Lectures will be held in the usual time and place on December 5 and 7 (Monday and Wednesday of RRR week). During that time we will review the course. Participation will be optional, but is recommended.

On Sunday, December 4, a sample final exam and a sheet of review exercises will be posted on bCourses. Solutions to both will be posted on Friday or Saturday of RRR week.

Office hours will continue as usual during RRR week (MW 1:30–3:00) in the usual location (883 Evans) and on Zoom (use the link on bCourses).

Final Exam

The final exam was given on Friday, December 16, 3–6 PM.

It covered all material in the course. Roughly half of the exam was on material covered in earlier midterms, and half was on new material. For a list of which sections of the book were covered, see the summary syllabus.

The exam is worth 200 points.

This final exam was still be an in-person exam, but the questions were shorter and there will be more of them. These questions were designed to be easier to grade. For example, there were multiple-choice and True-False questions, and some questions asked you to compute something and place the answer in a box on the page.

The rules for this exam will be similar to those in past midterms: No calculators and no other electonic devices (smartphones, laptops, etc.) were allowed, and no “cheat-sheets” were permitted.

Some questions were graded with partial credit, and some were not. This is at least a little better than an exam on webwork would have been, but you should expect that partial credit is not possible.

A sample exam, solutions to the sample exam, and solutions to the actual final exam, are available in the Files area of bCourses.

The rough curve for the final is as follows:

A160–200
B124–159
C80–123
D40–79

The median on the exam was 136, the mean was 129.1, and the standard deviation was 42.5.

Incomplete Grades

University Policies: Please, consult the University policies regarding incomplete grades.

Reasons for an Incomplete: An Incomplete "I" grade is rarely given. The only justifications for an "I" grade are:

Conditions for giving an Incomplete: When requesting an Incomplete, the student must:

For more information on Incomplete grades and the conditions on making them up, see the L & S Advising web page on Incomplete grades.

Frequently Asked Questions

What are the GSIs' office hours?

The GSIs' office hours are available on this spreadsheet.

You may attend someone's office hour even if they are not your GSI.

How do I access homework assignments on webwork?

Do the following steps:
  1. Log in to bCourses.
  2. Click on the Assignments tab.
  3. Click on the relevant homework assignment.
  4. Click on the link “Load [name] in a new window” (where [name] is the name of the assignment).

This should take you to the assignment in webwork.

You only need to do this once per assignment. After that, you can go to the assignment by clicking on “Webwork” in the left navigation bar in bCourses, and then clicking on the assignment.

This step is necessary in order to set up the connection for passing the score on the homework set back to bCourses. It is not necessary for GSIs, because their scores are not passed back to bCourses.

Why am I no longer able to view my overall grade on bCourses [either it shows a lock icon where it normally gave a percentage, or it says, “Calculation of course totals has been disabled”]?

The percentage previously shown in bCourses was not an accurate reflection of how well you were doing in the class, so I have turned it off permanently.

The problem is that bCourses just adds up the total of all (turned-in) assignments and divides by total possible. This is wrong because

  1. it doesn't take into account dropping the lowest two quizzes, the lowest webwork score, and the lowest midterm (if appropriate), and
  2. it doesn't take into account that a point on a webwork score carries much less weight than a point on a quiz in your discussion section, which in turn carries less weight than a point on a midterm or final exam.

How will the course grade be determined?

The first midterm will be out of 75 points, the second midterm will be out of 100 points, and the final exam will be out of 200 points. Notice that these numbers are proportional to the weighting of each exam in the course grade. (See below for information on dropping the lowest midterm score.)

Likewise, the section scores will be out of 125 points, corresponding to a hypothetical exam worth 125 points.

These numbers will be added, and the total will determine the course grade, according to cutoffs that will be decided, mostly by a curve, when all of the scores are available.

What if I miss a midterm, or do poorly on one?

The lowest midterm score will be dropped, if lower than scores on subsequent exams. This will be done as follows.

Before adding up the total scores on exams and discussion component, one (and only one) of the following will be done.

  1. Replace your score on Midterm 1 with a score computed based on the sum of your scores on Midterm 2 and the final exam. In this case, the second midterm would be 25% of your grade and the final would be 50%. The first midterm would be 0% of your grade.
  2. Replace your score on Midterm 2 with a score computed based on your final exam score. In this case, the final exam would be worth 60% of your grade, and the second midterm would be 0% of your grade.
  3. Make no changes.

You do not need to make a choice between the three options. The software will automatically choose for you at the end of the semester, based on what gives you the most total points.

In particular, no midterm score will be reduced, and if both midterm scores would be increased by replacing with scores based on subsequent exams, the score with the most to be gained will be replaced.

This will be done automatically for all students.

This policy is intended to cover all absences or low scores, including those beyond the student's control.

Note that, if you are afraid of doing poorly on a midterm, there is nothing to be gained by staying home. On the other hand, if you miss the first midterm, then missing the second midterm (or doing poorly on it) will definitely hurt your grade.

Of course, if you are ill, then you should stay home unless you are confident that you do not have any communicable diseases.

Will there be a chance to take a make-up midterm?

No. If you miss a midterm exam, then you will get 0 points on the exam, but the exam score will almost certainly be replaced by a score based on subsequent exams (unless you also miss the other midterm). The only exception to this policy is for circumstances related to a student's disability, if supported by the Disabled Students Program (DSP).

What are “Clob 1” and “Clob 2” in the bCourses gradebook?

As noted in the answer to an earlier question, your Midterm 1 score may be replaced by a score based on the sum of your scores on Midterm 2 and the final exam. Let's call this the the replacement score for Midterm 1.

If your replacement score for Midterm 1 is less than your actual Midterm 1 score, then your score on Midterm 1 will not be changed by the policy on replacing grades. Therefore, in this case, “Clob 1” will be left blank (and treated as zero for subsequent calculations).

Otherwise, “Clob 1” will be the difference between your replacement score and your actual score on Midterm 1.

“Clob 2” is the similar thing for Midterm 2.

So, your scores in Midterm 1 and Midterm 2 as shown on bCourses are the scores that you got on the actual exam (and not the replacement scores). Instead, when computing grades, the scores for Midterm 1, Midterm 2, the Final Exam, the Discussion score, and the larger of Clob 1 or Clob 2 are added, and that sum is used to determine your letter grade in the course.

If I do well on the final, will that make up for lower scores on both midterms (“resurrection final”)?

No. There is no policy that “all is forgiven” if one does well on the final exam. I feel that such policies foster cramming, which is not good pedagogy. Material learned by cramming is not retained as well as material learned over the course of the semester.

Will we have class on November 21?

Yes. We will also have (or also had) class on September 12, October 3, October 26, November 7, September 7, October 12, September 21, October 31, August 24, October 19, August 29, November 16, November 30, November 28, November 14, September 26, October 24, September 14, December 7, December 5, November 9, October 10, October 17, September 19, October 5, and August 31 (and also midterms on September 28 and November 2).

Note that this list includes RRR week. We will review for the final exam during RRR week.

I joined the class late. What do I need to do in order to catch up?

To catch up on the class, you should:

Welcome to the course!

I just signed up for the class [or am still on the waitlist]. Can I get access to bCourses?

When you sign up for a class, you are automatically enrolled in bCourses, even if you are only on the waitlist. However, you usually have to wait overnight before this can happen.

I just signed up for the class (after classes started). Can I get an extension on the due dates for webwork assignments, so I can get caught up?

Yes. Webwork does this automatically. Note that the extended due dates will show up on webwork but not on bCourses.

Webwork and bCourses are showing different due dates for the same assignment. Which one should I believe?

The due dates on Webwork are the official ones.

How do I “submit” an assignment on Webwork?

You don't. You submit answers to each question (and pay attention to the score). Each time you click on “Submit Answers”, your score on that problem is updated (but only if it is higher than the score so far), the total of the scores for all of the problems on that homework assignment is sent back to bCourses. When the deadline passes, your most recent score becomes your final score for that assignment.

I may have COVID, may have been exposed to it, or have symptoms. What should I do?

For matters regarding COVID, please follow campus guidance, on the following web pages:

Last updated 31 December 2022