Basic course information
Time: MTWF 12:00–12:50 p.m.
Place: 105 Peterson.
Textbook: OpenSTAX Calculus Volume I.
Office hours: TBD in person, TBD on Zoom. Subject to change.
Final exam: Per the university Final Exam Schedule
Midterm exams:
April 30 and May 16. Subject to change if necessary.
There is also WebWork homework and a Canvas webpage for tracking grades.
Prerequisites
Math 112Z (with a C- or better) or satisfactory placement exam score.
Description and goals
Calculus, the quantitative study of change, is one of the basic mathematical tools in physical and social sciences and mathematics. Math 251-253 is an introduction to calculus, aimed primarily at students in mathematics and the physical sciences. This quarter focuses on differential calculus---defining and computing the rate of change of a quantity, and how the rate of change is useful. (Math 252 focuses on integral calculus---going from the rate of change to the original quantity.)
Specific “learning outcomes” include:
- Understanding the intuition behind limits and continuity and being able to compute limits and test for continuity in simple situations.
- Understanding the meaning of the derivative and being able to compute the derivatives of elementary functions. ("Elementary functions" is a technical term.)
- Be able to relate features of graphs to first and second derivatives.
- Be able to use derivatives to solve optimization, related rates, and other modelling problems.
A course is more than its “learning outcomes”: the goal is understanding, not the ability to perform specific manipulations.
Policies
Grading
| Online homework | 20% |
| Quizzes | 15% |
| Midterm 1 | 17% |
| Midterm 2 | 18% |
| Final | 30% |
Scores will be curved before averaging the different components, in case some component is unexpectedly hard, but a combined raw score of 90% will receive at least an A-, a combined raw score of 80% will receive at least a B-, and so on.
Homework
Online homework, via WebWorks, is due at the end of the day on Mondays, except as noted. (Due dates may change.) There will also be suggested problems from the textbook each week; quiz problems are adapted from these. There will be homework assignments due during “dead week”. Well-prepared students should expect to spend 8-12 hours per week (2 to 3 hours per hour of class) outside of class on homework and review.
Homework will be accepted up to two days late, but at a 50% penalty. Homework more than two days late will not be accepted, but the lowest two online homework score will be dropped to accommodate illnesses and other unforeseen events.
The WebWork homework site, for online homework: https://uowebwork.uoregon.edu/webwork2/Math251-33066/.
Suggested textbook problems are posted below.
Quizzes and Exams
All quizzes and exams will be given in class. Quizzes are typically on Wednesdays. Exam dates are as indicated in the schedule.
All quizzes and exams are closed-note, closed-book, and without electronic assistance (including calculators and cell phones). Using any notes or electronic device or communicating with anyone except me during an exam constitutes cheating.
With limited exceptions, the university now requires that students who miss an exam be treated the same, independent of the reason. That is, students who miss the exam because of being hospitalized for illnesses must be treated the same as students who skip an exam because they decide they want more time to study. So:
- The lowest 2 quiz scores will be dropped, to accommodate illnesses, family emergencies, and so on. There will not be makeup quizzes.
- If you have a conflict with a midterm exam and you alert me at least 10 days in advance, you will have the opportunity to take a version the exam a few days early, without penalty. In particular, this is the mechanism for accommodating the exceptions to the UO Attendance and Engagement policy.
- If you miss one midterm exam, I will compute your midterm exam score by taking a weighted average of your score on the other midterm exam and the final (after normalizing using the class means and standard deviations).
- If you miss both midterm exams, you will have the opportunity to take a makeup midterm 2 within two weeks of midterm 2, at a 15% linear penalty. That is, whatever score you get on the makeup exam will be multiplied by 0.85. If you do not take the exam within two weeks, your midterm exam score will be computed as zero.
- If you miss the final exam and are otherwise passing the class, you will receive an incomplete in the class and have the option to take a makeup exam in the first two weeks of the summer quarter or the first two weeks of the fall quarter, with a 5% linear penalty. If you do not take the exam in that time, I will compute your grade as if you received a zero on the final exam.
- If you miss the final exam but were otherwise failing the class, you will not have an opportunity to re-take the exam, and will receive and F in the class.
(I agree that spelling this out as a quasi-legal agreement, instead of treating you fairly on an individual basis, is dehumanizing.)
Students with disabilities
I, and the University of Oregon in general, are committed to an inclusive learning environment. If you have a disability which may impact your performance on exams, please contact the Accessible Education Center to discuss appropriate accommodations. If there are other disability-related barriers to your participation in the course, please either discuss them with me directly or consult with the Accessible Education Center.
Suggested Textbook Problem
Quiz problems are adapted from these.
Schedule
This schedule is tentative, and may change during the quarter.
| Week | Date | Topic | Sections |
| 1 | 3/31 | Introduction to the class. Introduction to limits. | §2.1, 2.2 |
| 4/1 | Working with limits, continuity. | §2.3, 2.4 | |
| 4/2 | Continuity, precise definition of limit and continuity, error analysis. Quiz 1. | §2.4, 2.5 | |
| 4/4 | Review. April 5 is last day to drop the class without a W. |
||
| 2 | 4/7 | Definition of the derivative. WebWorks 1 Due. | §3.1 |
| 4/8 | The derivative as a function. | §3.2 | |
| 4/9 | Power rule, product rule. Quiz 2. | §3.3 | |
| 4/11 | Review. | ||
| 3 | 4/14 | Quotient rule. WebWorks 2 Due. | §3.3 |
| 4/15 | Linear approximation, velocity, marginal cost. | §3.4, 4.2 | |
| 4/16 | Derivatives of trig functions. Quiz 3. | §3.5 | |
| 4/18 | Review. | ||
| 4 | 4/21 | The chain rule. WebWorks 3 Due. | §3.6 |
| 4/22 | More chain rule: derivatives of inverse functions. | §3.7 | |
| 4/23 | More chain rule: implicit differentiation. Quiz 4. | §3.8 | |
| 4/25 | Derivatives of exponentials and logs. | §3.9 | |
| 5 | 4/28 | Review. WebWorks 4 Due. | |
| 4/29 | Review. | ||
| 4/30 | Midterm 1 | ||
| 5/2 | Maxima and minima | §4.3 | |
| 6 | 5/5 | Mean Value Theorem. | §4.4 |
| 5/6 | Derivatives and graphs | §4.5 | |
| 5/7 | Optimization. | §4.7 | |
| 5/9 | Review. | ||
| 7 | 5/12 | Limits at infinity and asymptotes. WebWorks 5 Due. | §4.6 |
| 5/13 | More optimization. | §4.7 | |
| 5/14 | Review. WebWorks 6 (short) Due. Quiz 5. | ||
| 5/16 | Midterm 2 The last day to withdraw from the class or change grading option is May 18. |
||
| 8 | 5/19 | Related rates. WebWorks 7 Due. | §4.1 |
| 5/20 | More related rates. | §4.1 | |
| 5/21 | L'Hôpital's Rule. | §4.8 | |
| 5/23 | Review. | ||
| 9 | 5/26 | Memorial day holiday (no class). | |
| 5/27 | Anti-derivatives. WebWorks 8 Due. | §4.10 | |
| 5/28 | Exponential growth. Quiz 6 | §6.8 | |
| 5/30 | Review. | ||
| 10 | 6/2 | Newton's method. WebWorks 9 Due. | §4.9 |
| 6/3 | The fundamental theorem of calculus, logs and exponential redux. | §5.3, 6.7 | |
| 6/4 | Review. Quiz 7. | ||
| 6/6 | Review. WebWorks 11 (short) due |
Handouts
Handouts will be posted here, in case you lost the physical copy.
WebWork Advice
Mathematics is best done (and practiced) with pencil and paper. Avoid solving WebWorks problems at your computer: it leads to guessing, which doesn't help you learn. Instead, write down or print out the WebWorks problems and then step away from your computer. Solve them with pencil and paper (and eraser), keeping track of the steps involved. Once you have the solution, type it in and have WebWorks check your answer. If WebWorks tells you your answer is wrong, step away from your computer again and check your work. Try to find the mistake. If you can't find the mistake, try office hours, a classmate, or the math library.
General Advice
Reading mathematics. You are expected to read the sections in the textbook before coming to class. It's usually only a few pages, so read it carefully. Note down the questions you have; I would expect you to have at least one per page. Read the section again after class. See which questions you now understand. Think about the remaining questions off and on for a day. See which you now understand. Ask someone (e.g., me) about the questions you still have left.
Getting help. If you're having trouble, get help immediately. Everyone who works seriously on mathematics struggles, but if you don't get help promptly you will soon be completely lost. The first places to look for help are my office hours. You can also try the drop-in help at the Math Library. The Tutoring and Academic Engagement Center also facilitates individual and small-group tutoring.
Teaching to learn. The best way to learn mathematics is to explain it to someone. You'll find that, particularly in office hours, I'll try to get you to explain the ideas. You should also try explaining the material to each other. The person doing the explaining will generally learn more than the explainee. Another thing to try is writing explanations to yourself, in plain English or as close as you can manage, of what's going on in the course. File them somewhere, and then look back at them a few days later, to see if your understanding has changed.