• This web page describes an activity within the Department of Mathematics at Ohio University, but is not an official university web page.
• If you have difficulty accessing these materials due to visual impairment, please email me at mohlenka@ohio.edu; an alternative format may be available.

# MATH 2301-102 (6486), Fall 2018

## Calculus I

### Syllabus

Catalog Description:
First course in calculus and analytic geometry with applications in the sciences and engineering. Includes basic techniques of differentiation and integration with applications including rates of change, optimization problems, and curve sketching; includes exponential, logarithmic and trigonometric functions. No credit for both MATH 2301 and 1350.
Desired Learning Outcomes:
Students can use the tools of differential and integral calculus in a variety of applications.
Requisites:
(A or better in MATH 163A) or (B or better in MATH 1350) or (C or better in MATH 1300 or MATH 1322) or (Math placement level 3).
Instructor:
Martin J. Mohlenkamp, mohlenka@ohio.edu, (740)593-1259, 315-B Morton Hall.
Office hours:
• Monday, Wednesday, and Friday 2:00-2:55pm.
• By appointment. Do not hesitate to ask for an appointment.
Web page:
http://www.ohiouniversityfaculty.com/mohlenka/2191/2301
Class hours/ location:
Monday, Wednesday, Friday 3:05-4:00pm in 115 Morton Hall. Students are also enrolled in one of the recitation sections:
• MATH 2301-109 (6493) Tuesdays 12:00-12:55pm in 126 Morton
• MATH 2301-110 (6494) Tuesdays 3:05-4:00pm in 215 Morton
Both recitations are led by Prabha Shrestha, who also has office hours Tuesdays 1-3pm. On any given day, any given room in Morton Hall can be anywhere between 60 and 95 degrees Fahrenheit, so come prepared.
Text:
Active Calculus (single variable) by Matthew Boelkins, David Austin, and Steven Schlicker; 2018 edition. ISBN 978-1724458322
• website
• html version: Free. Works well on phones, tablets, and computers. Has some interactive content and auto-corrected exercises.
• pdf version: Free. Useful if you want to print portions, make notes in the text on a tablet, or work offline.
• printed version: \$20.95 black and white softcover. (If you already ordered the 2017 version, that will work fine.)
Note: Some sections of MATH 2301 are using a different textbook (by Stewart). You do not need to buy that one.
Text exercises:
Each section of the text has a small number of exercises. These are not collected or graded, but doing them is the foundation for your learning. In the html text, many of them will check your answer and have solutions.
Text Preview Activities:
Each section of the text has a preview activity designed to get you prepared for that day's class. These will be collected at the beginning of the class in which we cover that section. They are graded on a simple scale: 0 means did not turn in the preview activity, 1 means turned in a paper with little or no correct work, 2 means mostly correct, and 3 means fully correct (including being written in complete sentences). In order to account for occasional legitimate absences, your average on Preview Activities will be computed as if each was worth 2 points (instead of 3).
Online Homework/ Practice:
We will use online homework through edfinity. It is free this semester as a pilot project. To use it, first register here using your @ohio.edu email address and name as listed by the university registrar. Edfinity is built on WeBWork, for which there is help on Mathematical notation, available functions, units, interval notation, etc. You have an unlimited number of attempts at each problem. Homework is "due" at the start of class but can be submitted with full credit until 11:59pm that day.
Recitations:
Once a week you will meet in a group of about 30 for recitation. In 10 out of 15 weeks there will be a graded activity during recitation. Your best 8 (out of 10) scores count toward your grade. Typically, you will work in a group of 3-4 students on problems in a handout and submit a group solution at the end of the recitation.
Tests:
There will be a test every third Wednesday. Your best 4 (out of 5) scores count toward your grade. Calculators are not permitted. Bring your student ID to the tests. The tests are cumulative. They can include Pre-Calculus questions.
Why all these tests?
The purpose of the tests is not to assess your mastery in order to assign you a grade; a final exam would be enough for that. Instead, the purpose is to help you learn through what Psychologists have determined to be effective learning techniques.
Practice Testing:
(Rated "high" utility.) Recalling information and practicing skills in a test environment convinces your brain that they are important and should be saved in your long-term memory.
Distributed Practice:
(Rated "high" utility.) Learning/ studying in smaller amounts distributed over time (rather than cramming every few weeks) also convinces your brain to use your long-term memory.
Interleaved Practice:
(Rated "moderate" utility.) Mixing up the problem types (e.g. by having cumulative tests) makes you learn how to distinguish which technique to use and also convinces your brain to use your long-term memory.
(FYI: Elaborative interrogation and self-explanation were rated "moderate" utility. Summarization, highlighting, keyword mnemonics, imagery use for text learning, and rereading were rated "low" utility.)
Final Exam:
The final exam is on Wednesday December 12 at 2:30pm in 226 Morton. This is a combined exam with other sections of MATH 2301. Calculators are not permitted. Bring your student ID to the exam. Note: Please check the final exam schedule for your other classes and notify me as soon as possible if there is a conflict with our exam.
Your final average is composed of 5% for preview activities, 5% for online homework, 20% for your best 8 (out of 10) recitation scores, 45% for your best 4 (out of 5) tests, and 25% for the final exam. An average of 90% guarantees you at least an A-, 80% a B-, 70% a C-, and 60% a D-.
Missed work:
• Preview activities are due at the start of class and may not be turned in early, late, or online. (If you are a few minutes late to class because you are walking across campus, then you can turn it in when you arrive to class.)
• Missed recitations cannot ordinarily be made up since enough are dropped to account for an ordinary amount of absences. It is permitted to occasionally attend the other recitation time instead of your own; if this privilege is abused then it will be revoked. (If you will miss more than the number dropped due to an extraordinary reason such as an extended illness, please consult with me.)
• Tests missed due to university excused absences for illness, death in the immediate family, religious observance, jury duty, or involvement in University-sponsored activities can be made up if pre-approved by me. Otherwise, the first missed test is automatically dropped since only your best 4 out of 5 count in your grade. A second missed test will be replaced by your final exam score. Further missed tests count as 0.
• The online homework is "due" at the start of class but can be submitted with full credit until 11:59pm that day. (I am not sure about the system's capability to give individualized extensions. For now assume there will be no extensions.)
Attendance:
I do not count attendance in your grade, since absences will automatically penalize you through your loss of learning. Note, however, that there is a preview activity due on most class days.
Electronic Devices:
• During class time, your phone must be off and out of sight. (The mere visible presence of you phone decreases your cognitive performance; see the article and research paper.) You may step out into the hall to use your phone. Violators will first receive a warning and then have their preview activity not counted.
• Computers, tablets, and calculators are permitted in class for learning purposes (consulting the online text, producing graphs, etc.). Other uses, especially any that distract your classmates, are prohibited.
Preview Activity:
You can use any help that you can find to do the activity, but you must acknowledge in writing what help you got and from whom or where. (You do not have to acknowledge the book or me.)
Online Homework:
The online homework must be done by you, but you may use any help that you can find. Keep in mind that the purpose of the homework is to develop your ability to do such problems on your own.
Recitation Groupwork:
• You may use your book, Wikipedia, other Calculus books, general websites about Calculus, etc. without special acknowledgment.
• If your group receives any help specifically on the problem you are trying to solve (such as assistance from another group or software that solves the problem), you must acknowledge in writing what help you received and from whom or what source (including internet links). (You do not need to acknowledge your recitation leader.)
A minor, first-time violation will receive a warning and discussion and clarification of the rules.
Tests, final exam:
You may not give or receive any assistance during a test or the exam, including but not limited to using notes, phones, calculators, computers, or another student's solutions. (You may ask me questions.) A minor, first-time violation will result in a zero grade on that test.
Serious or second violations will result in failure in the class and be reported to the Office of Community Standards and Student Responsibility, which may impose additional sanctions. You may appeal any sanctions through the grade appeal process.
Special Needs:
If you have specific physical, psychiatric, or learning disabilities and require accommodations, please let me know as soon as possible so that your learning needs may be appropriately met. You should also register with Student Accessibility Services to obtain written documentation and to learn about the resources they have available.
Responsible Employee Reporting Obligation:
If I learn of any instances of sexual harassment, sexual violence, and/or other forms of prohibited discrimination, I am required to report them. If you wish to share such information in confidence, then use one of the confidential resources listed by the Office of Equity and Civil Rights Compliance.
Historically, about 40% of Calculus I students are unsuccessful, meaning they earn a grade below C or withdraw from the class. Here are some behaviors that contribute to being successful or unsuccessful.
How to be successful at CalculusHow to be unsuccessful at Calculus
Have a growth mindset: believe that through effort you can improve your mathematical skills. Have a fixed mindset: believe that your mathematical skills are set, so effort is either unneccessary or futile.
Show up and do the work.Skip stuff. Start with an occasional class, then a recitation, then some online homework, ...
Figure out the solutions to activities and exercises. Find the solutions to activities and exercises by copying from classmates, looking at posted answers, searching the internet, etc.
Work the online homework problems out on paper (and save this work) before entering them. Do the online homework by pattern-matching with a similar problem or using another website to figure out the answer.
Be active in class: think, write, talk, do, ...Be passive (or distracted) in class, waiting for learning to somehow happen.
Read the book. Carefully. Multiple times. Don't read the book. Make excuses like "It is too confusing.", "I learn better from videos.", or "The instructor should tell me everything I need to know in class."
Do the exercises in the text. Ignore the exercises in the text. Convince yourself that since it is not collected it must not be important.
Strive for mastery. Mastery is when you can solve the problem confidently by yourself. Settle for familiarity rather than mastery. Familiarity is when you recognize a problem and can follow along when someone else, a video, or the book solves it.
Sparingly use videos like Just Math Tutorials or Khan Academy. When you do, pay attention and work along with the video.Use videos a lot and as a replacement for reading. Let them play in the background while you do something else.
Make sure all members of your group (including yourself) understand the recitation groupwork before submitting it.Do the recitation groupwork by splitting up the problems and working on them separately. That way you only have to learn a fourth of it.
Use learning resources:
People:
Ohio University Resources:
Software:
The sage cell lets you do math on the web.
There are some preloaded Calculus cells. There is a "sagemath" app for mobile devices.
Invent and use false rules like
• $$\frac{a+b}{a+c}=\frac{\not a+b}{\not a+c}=\frac{b}{c}$$
• $$\frac{a+b}{a}=\frac{\not a+b}{\not a}=b$$
• $$\frac{a}{ab}=\frac{\not a}{\not a b}=b$$
• $$\frac{a+b}{c+d}=\frac{a}{c}+\frac{b}{d}$$
• $$\frac{\frac{a}{b}}{a}=\frac{\frac{\not a}{b}}{\not a}=b$$
• $$\frac{h^{-1}}{h}=\frac{\not h^{-1}}{\not h}=1^{-1}$$
• $$\frac{1}{x^2}=x^{1/2}$$
• $$\frac{1}{x+h}- \frac{1}{x}=\frac{1}{\not x+h}- \frac{1}{\not x}=\frac{1}{h}$$
• $$\frac{x+h^2}{h} = \frac{x+h^{\not 2}}{\not h} = x+h$$
• $$(x+h)^{-1}-x^{-1}=\frac{1}{(x+h)-x}$$
• $$x+x^{-1}=0$$
• $$\frac{\sin(x^3)}{\sin(x^2)}=\frac{\not\sin(x^3)}{\not\sin(x^2)}=\frac{x^3}{x^2}=x$$
• $$\frac{\sin(7x)}{\sin(3x)}=\sin(4x)$$
• $$\sin(x+y)=\sin(x)+\sin(y)$$
• $$\sqrt{x^2+y^2}=\sqrt{x^2}+\sqrt{y^2}=x+y$$
• $$f(x)=x^{-1}\;\Rightarrow\;f(x+h)=x^{-1}+h$$
• $$f(a+h)-f(a)=f(\not a+h)-f(\not a)=f(h)$$
• $$f(a+h)-f(a)=f(a)+f(h)-f(a)=f(h)$$
• $$\tan(7\theta)=7\tan(\theta)$$
• $$\sin\left(\frac{1}{x}\right)=\frac{\sin(1)}{x}$$
When you are struggling, get help.When you are struggling, hide.

### Schedule

Subject to change. Some links, such as test solutions, will become active after we pass that date.

Week Date Section/Topic Preview Activity due Online Homework due
1
Mon Aug 27 Introduction
Tues Aug 28Recitation: groupwork
Chapter 1 Understanding the Derivative
Wed Aug 29 1.1 How do we measure velocity? PA 1.1.1 Pre-Calculus
Fri Aug 31 1.2 The notion of limit (sage) PA 1.2.1 1.1
2
Mon Sep 3 Labor day holiday, no class
Tues Sep 4Recitation: Test preparation (test guide)
Wed Sep 5 Test on Pre-Calculus and 1.1 (solutions)
Fri Sep 7 (drop deadline) 1.3 The derivative of a function at a point PA 1.3.1 1.2
3
Mon Sep 10 1.4 The derivative function PA 1.4.1 1.3
Tues Sep 11Recitation: groupwork
Wed Sep 12 1.5 Interpreting, estimating, and using the derivative PA 1.5.1 1.4
Fri Sep 14 1.6 The second derivative PA 1.6.1 1.5
4
Mon Sep 17 1.7 Limits, Continuity, and Differentiability PA 1.7.1 1.6
Tues Sep 18Recitation: groupwork
Wed Sep 19 1.8 The Tangent Line Approximation PA 1.8.1 1.7
Fri Sep 21 Squeeze and Intermediate Value Theorems Supplement PA 1.1.1 and 1.2.1 1.8
5
Chapter 2 Computing Derivatives
Mon Sep 24 2.1 Elementary derivative rules PA 2.1.1 ST-IVT
Tues Sep 25Recitation: Test preparation (test guide)
Wed Sep 26 Test through Squeeze and Intermediate Value Theorems (solutions)
Fri Sep 28 2.2 The sine and cosine functions (sage $$2^x$$, sine) PA 2.2.1 2.1
6
Mon Oct 1 2.3 The product and quotient rules PA 2.3.1 2.2
Tues Oct 2Recitation: groupwork
Wed Oct 3 2.4 Derivatives of other trigonometric functions PA 2.4.1 2.3
Fri Oct 5 Reading Day, no class
7
Mon Oct 8 2.5 The chain rule PA 2.5.1 2.4
Tues Oct 9Recitation: groupwork
Wed Oct 10 2.6 Derivatives of Inverse Functions PA 2.6.1 2.5
Fri Oct 12 2.7 Derivatives of Functions Given Implicitly PA 2.7.1 2.6
8
Mon Oct 15 2.8 Using Derivatives to Evaluate Limits PA 2.8.1 2.7
Tues Oct 16Recitation: Test preparation (test guide)
Wed Oct 17 Test through 2.7 (solutions)
Chapter 3 Using Derivatives
Fri Oct 19 3.1 Using derivatives to identify extreme values PA 3.1.1 2.8
9
Mon Oct 22 3.2 Using derivatives to describe families of functions PA 3.2.1 3.1
Tues Oct 23Recitation: groupwork
Wed Oct 24 Curve Sketching Supplement PA 1.3.1 3.2
Fri Oct 26 3.3 Global Optimization PA 3.3.1 Sketching
10
Mon Oct 29 3.4 Applied Optimization PA 3.4.1 3.3
Tues Oct 30Recitation: groupwork
Wed Oct 31 3.5 Related Rates PA 3.5.1 3.4
Fri Nov 2 (drop deadline with WP/WF) More Applied Optimization and Related Rates 3.5
11
Mon Nov 5 The Mean Value Theorem Supplement PA 1.4.1 More 3.4-3.5
Tues Nov 6Recitation: Test preparation (test guide)
Wed Nov 7 Test through 3.5 (solutions)
Chapter 4 The Definite Integral
Fri Nov 9 4.1 Determining distance traveled from velocity PA 4.1.1 MVT
12
Mon Nov 12 Veterans day (observed) holiday, no class
Tues Nov 13Recitation: groupwork
Wed Nov 14 4.2 Riemann Sums (sage) PA 4.2.1 4.1
Fri Nov 16 4.3 The Definite Integral PA 4.3.1 4.2
13
Mon Nov 19 4.4 The Fundamental Theorem of Calculus PA 4.4.1 4.3
Tues Nov 20Recitation: groupwork
Wed Nov 21 Thanksgiving holiday, no class
Fri Nov 23 Thanksgiving holiday, no class
14
Chapter 5 Evaluating Integrals
Mon Nov 26 5.1 Constructing Accurate Graphs of Antiderivatives PA 5.1.1 4.4
Tues Nov 27Recitation: Test preparation (test guide)
Wed Nov 28 Test through 4.4 (solutions)
Fri Nov 30 5.2 The Second Fundamental Theorem of Calculus PA 5.2.1 5.1
15
Mon Dec 3 5.3 Integration by Substitution PA 5.3.1 5.2
Tues Dec 4Recitation: groupwork
Wed Dec 5 Odds and Ends Supplement PA 1.5.1 5.3
Fri Dec 7 Recap/ Review/ Exam preparation OddsEnds
16
Wed Dec 12 Final Exam 2:30-4:30pm in 226 Morton. (old final exams; how the final exam is made) (results)

Martin J. Mohlenkamp