MAT 201 Calculus 1 - Utica Science Academy
Undergraduate course, Mathematics Department, Utica University, 2023
Welcome to the home page of Dr. Xiao Xiao’s Calculus 1 course at Utica University. You can find all the information for this course on this page. Note that this is the course home page for the Utica Academy of Science bridge program. If you are a student of Utica University registered for Calculus 1, please check out the other Calculus 1 home page.
Important Links
Important Dates
- UAS Winter break: 02/20/23 - 02/24/23
- UU Spring break: 03/13/23 - 03/17/23
- UAS Spring break: 04/10/23 - 04/14/23
- SOOT: 04/24/23 - 05/01/23
- Final exam: 05/01/23 - 05/05/23
Instructor Information
- Instructor: Prof. Xiao Xiao
- Email: [email protected]
- Office: White Hall 255
- Office hour: Via zoom by appointment.
Homework
- Apr. 28, 2023
- Complete WileyPLUS Assignment 13.
- Don’t forget to fill out SOOT.
- Apr. 27, 2023
- Please start working on WileyPLUS Assignment 13.
- Apr. 24, 2023
- Complete Actvity 3.1.2.
- Check out this video for a review of global/local max/min, this video for first derivative test, and this video for second derivative test.
- Fill out the student survey by Friday this week. You will need your university log in.
- Apr. 19, 2023
- Complete Activity 3.5.5.
- Keep working on WileyPLUS Assignment 12.
- Apr. 18, 2023
- Complete Activity 3.5.3.
- Keep working on WileyPLUS Assignment 12.
- Apr. 17, 2023
- Try to complete Activity 3.5.4.
- Start working on WileyPLUS Assignment 12.
- Apr. 5, 2023
- Complet Preview Activity 3.5.1.
- Use Spring break to complete all WileyPLUS until Assignment 11.
- Apr. 4, 2023
- Complete Part (c) of Activity 2.7.4.
- Keep working on Week 11 Assignment in WileyPLUS.
- Apr. 3, 2023
- Complete Activity 2.7.4 and let me know if you wawnt to present.
- Start Week 11 Assignment in WileyPLUS.
- Mar. 24, 2023
- Complete Week 10 Assignment in WileyPLUS.
- Complete Preview Activity 2.7.1 before our next meeting.
- Mar. 23, 2023
- Complete Activity 2.6.4.
- Complete Week 10 Assignment in WileyPLUS.
- Mar. 22, 2023
- Complete Activity 2.6.4 part b and part e.
- Keep working on Week 10 Assignment in WileyPLUS.
- Mar. 21, 2023
- Complete Activity 2.6.2. Let me know if you want to present.
- Start working on Week 10 Assignment in WileyPLUS.
- Mar. 20, 2023
- Complete Activity 2.5.3, especially part (e). Complete Activity 2.5.4 Part (d).
- Complete Week 9 Assignment in WileyPLUS.
- Mar. 16, 2023
- If you need extra practice for goals 8 and 9, check out the special assignment in WileyPLUS.
- Complete Activity 2.5.3.
- Mar. 15, 2023
- Complete Activity 2.4.4 (if you have not already done so) and Activity 2.5.2. Let me know if you want to present (and please be prepared if you volunteer). We will do some presentations on Thursday.
- Start working on Week 9 Assignment in WileyPLUS.
- Mar. 9, 2023
- Complete Activity 2.4.4 and let me know if you want to present.
- Complete Week 8 Assignment in WileyPLUS.
- Mar. 8, 2023
- Keep working Week 8 Assignment in WileyPLUS.
- Mar. 7, 2023
- Complete Activity 2.3.3 and 2.3.4. Let me know if you want to present.
- Work on Week 8 Assignment in WileyPLUS.
- Goal for Friday’s quiz, 8, 9, 10, 11, 12, 13
- Mar. 6, 2023
- Complete Activity 2.2.4 Part (c) and (e), 2.3.2 Part (c) and (d), 2.3.3 Part (a) and (b) and let me know if you want to present.
- Watch this video to review the quotient rule.
- Complete Week 7 Assignment in WileyPLUS and start working on Week 8 Assignment.
- Mar. 2, 2023
- Keep working on Week 7 Assignment in WileyPLUS.
- If you want to present Activity 2.2.4 Part (c) or (e), please let me know.
- Watch this video to learn about product rule.
- Mar. 1, 2023
- Complete Actvity 2.2.4 and let me know if you want to present.
- Keep working on Week 7 Assignment in WileyPLUS.
- Review the unit circle if you are rusty.
- Friday quiz goal: 5,6,7,8,9,10.
- Watch this video to review differentiation of sine and cosine.
- Feb. 28, 2023
- Complete Activity 2.1.3 and let me know if you want to present.
- Start work on Week 7 Assignment in WileyPLUS.
- Watch three videos to review basic differentiation principles. Video 1 on differentiate power functions, Video 2 on differentiate expoential functions, Video 3 on basic differentiation rules.
- Feb. 27, 2023
- Complete Activity 2.1.2 and let me know if you want to present. Each presenter must present at three parts, one constant function, one power function, and one exponential function.
- You should be able to complete Week 6 Assignment in WileyPLUS now.
- Feb. 16, 2023
- Keep working on Week 6 Assignment in WileyPLUS.
- Watch this video to see an example of how to use linear approximation in practical problems.
- If you have previous assignments in WileyPLUS that you were not able to complete on time, the winter break is a great opportunity to catch up. I will still be teaching next week at the university. If you want to meet and discuss math problems with me, just email me and we can make an appointment.
- Feb. 15, 2023
- Watch this video to review how to use tangent line approximation.
- Continue to work on Activity 1.8.3. We will discuss this on Thursday.
- Start working on Week 6 Assignmment in WileyPLUS.
- Feb. 14, 2023
- Complete Week 5 Assignment in WileyPLUS.
- The goals for Friday’s quiz are 4,5,6,7,8,9.
- Feb. 13, 2023
- Complete Activity 1.7.3. Let me know if you want to present.
- Keep working on Week 5 Assignment.
- Feb. 9, 2023
- Feb. 8, 2023
- Complete Week 4 Assignment in WileyPLUS.
- Complete Preview Activity 1.7.1 (Just Part (a) and Part (b)).
- Feb. 7, 2023
- Feb. 6, 2023
- Complete the question that was left at the end of the class.
- Start to work on Week 4 Assignment in WileyPLUS.
- Feb. 2, 2023
- Finish the handout on sketching graphs of derivatives. They will help you prepare Quiz 3.
- Watch video to review graph sketching of derivatives.
- Complete Week 3 Assignmment and start working on Week 4 Assignment in WileyPLUS.
- Keep working on Activity 1.4.3 part f. You need to use an algebraic trick that helped us to solve Activity 1.2.2(c).
- Feb. 1, 2023
- Complete Activity 1.4.3 and the handout sheet. Please let me know if you want to present.
- Keep working on Week 3 Assignment in WileyPLUS.
- Jan. 31, 2023
- Complete Activity 1.4.3. If you get stuck for Parts (e) and (f), you can skip those two parts for now.
- Continue to work on Week 3 Asssignment in WileyPLUS. You should expect to complete that assignment before Friday’s quiz.
- Watch this video on derivative of a function as a review.
- You will get 4 questions on Quiz 3 on Friday, addressing Goal 1, 2, 3, 4. We will discuss the materials for Goal 4 on Wednesday and Thursday.
- Jan. 30, 2023
- Complete Activity 1.3.3 and Preview Activity 1.4.1.
- Start to work on Week 3 Assignment in WileyPLUS.
- Jan. 23 - Jan. 29, 2023
- Complete Activity 1.3.3.
- Complete Week 2 Assignment in WileyPLUS if you have not done so. If you need extra attempts, please let me know. If you there are questions that you got stuck, please reach out to me.
- Jan. 18, 2023
- Complete Activity 1.3.2. Let me know if you would like to present.
- Complete Week 2 Assignment in WileyPLUS.
- Watch this video on how to compute derivative at a point.
- Jan. 17, 2023
- You should complete week 2 assignment in WileyPLUS before the quiz on Friday.
- Watch this video about the definition of derivative at a point.
- Read the course materials in Section 1.3.1, including the Example 1.3.8. You do not have to start working on Activity 1.3.2.
- Jan. 11, 2023
- Goal 1 and 3 will be on Quiz 1.
- You should complete week 1 assignment in WileyPLUS before the quiz on Thursday. Each homework assignment is worth 1 point, and in order to earn 1 point, you need to get above 90% for that assignment.
- Complete Activity 1.2.2. Part (c) of this activity is a little bit tricker than Part (a) and (b). You will need to use a trick call rationalizing the numerator. If you don’t remember this trick, here is a quick video for review.
- Complete Activity 1.2.3. This activity is very similar to Activity 1.1.4 except that you need to use the limit notation now.
- You should start working on week 2 assignment in WileyPLUS.
- Jan. 10, 2023
- Jan. 9, 2023
- Watch this video on computing instantaneous velocity as a review.
- Complete Activity 1.1.4. If you got stuck, refer to the example we did today in class.
- Complete Preview Activity 1.2.1.
- Work on Week 1 Assignment in WileyPLUS. You are expect to complete this assignment by Wednesday this week.
- First quiz is on Thursday this week.
- Jan. 5, 2023
- Complete Activity 1.1.3. For part (b), you have two different methods to estimate the instantaneous velocity. Take t=1.5 as an example. You can 1) either zoom in repeatedly at t=1.5 until you see a straight line and then estimate the slope of the line or 2) compute the average velocity of small intervals near t=1.5 such as from 1.4999 to 1.5 or from 1.5 to 1.50001 and guess what the instantaneous velocity will be.
- You should start working on the problems in the Week 1 assignment in WileyPLUS. You are expected to complete the Week 1 assignment before Quiz 1 (see the next bullet point).
- Since you will have async on Friday Jan. 13, we will have in-person lessons next week on Monday, Tuesday, and Wednesday. Quiz 1 is scheduled on Thursday Jan. 12 (not the usual Friday).
- Jan. 4, 2023
- Try your best to complete Activity 1.1.2. Here is a Desmos template that will be helpful for this activity. A hint for Part (b): to sketch the required line, you need to first figure out the line equation. A review question: given two points, how do you get the equation of the line that goes through those two points?
- Presentations will be a big part of this course so we need to start to get comfortable talking in front of others. If you feel like you can present your solution (does not matter if it is not completely correct) for Activity 1.1.2 (or any part of activity, e.g., just one part), please let me know either by email or at the beginning of the next class. I hope to see many volunteers.
- A video on average velocity. Good for review.
- You should start trying problems in Week 1 assignment in WileyPLUS. Note that you have 10 attempts for each problem so don’t be afriad to try if you think you know how to do a problem. In the meantime, if you don’t know how to start a problem, we probably have not discussed the topic yet so wait until we have covered the materials.
- Jan. 3, 2023
- Complete Preview Activity 1.1.1, you can use Desmos to construct the graph in part (a).
- Sign up at WileyPLUS (if you have not done so).
- Print learning goal sheet (if you have not done so), carry this with you to class.
- Complete the placement exam (if you have not done so).
- Complete the introduction survey (if you have not done so).
An Important Course Policy
I pride myself on having a good environment for working and learning. It is very important to me that we all treat each other with care and respect, in equal measure. I know that I ask students to take risks in class almost every day, and this can be challenging for many. I ask that you help me keep our classroom a supportive place for each of the people in it. Each of us deserves the space to bring our full, authentic selves to class and be comfortable. (Adapted from T.J. Hitchman.)
General Course Information and Policies
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Course name: MAT 201 Calculus 1
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Course credit hours: 3 credit
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Course Prerequisite: MAT 151, or satisfactory performance in the math placement test administered by the math department.
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Class time and location: M-F 8:49 am-9:31 am at UAS. On Mondays, Tuesdays, and Thursdays, lessons will be taught by Prof. Xiao. On Wednesdays, students should spend the time in groups completing classroom activities. On Fridays (except for the first Friday), students will spend the entire time on weekly quizzes.
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Textbook: Please see the course material link above.
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Online homework system: We will use the WileyPLUS online homework system designed for Hughes-Hallett’s Calculus textbook. You do not need to purchase the hard copy of Hughes-Hallett’s Calculus textbook. If you want to have that textbook as a reference, you will have the access to an electronic version of it after you have signed up the WileyPLUS access. All of you should be automatically enrolled in the university’s book bundle program so you should have access to WileyPLUS as soon as you sign up for it. Keep in mind that you need to use your official Utica University email address when signing up at WileyPLUS. Do not use nickname or your private email address. The class key you need to self-enroll in WileyPLUS is “B81178”.
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Calculator: We will be using a free graphing calculator app called Desmos. You can use Desmos directly by going to their website at www.desmos.com. You are strongly encouraged to use Desmos on a computer or on a tablet. You can download Desmos at Apple or Android.
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Course description: We will discuss the concepts of limits and derivatives, how to compute them, and how to apply them to solve real world problems.
- Course learning objectives (mathematics program): Upon successful completion of this course, students will be able to:
- formulate and solve mathematical problems using the differential calculus of Newton and Leibniz.
- understand necessary differential calculus content for license for teachers in the State of New York.
- communicate mathematics orally and in written form.
- Course learning objectives (general education program): Upon successful completion of this course, students will be able to:
- interpret and communicate quantitative information, and mathematical or statistical concepts, using language appropriate to the context and intended audience.
- make sense of problems and develop strategies to determine solutions using quantitative data and mathematical reasoning.
- reason, model, and draw conclusions or make decisions with mathematical and quantitative information, including estimating and checking answers to determine reasonableness, identifying alternatives, and selecting optimal results.
- critique and evaluate quantitative arguments that utilize mathematical, statistical, and quantitative information.
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Class organization: This course will likely be different from any other math course you have taken before. As an instructor, I will not be lecturing most of the time although I love lecturing very much. Scientific research shows that most people do not learn mathematics by listening, instead, they learn by doing it! I am sure you have said to yourself before “It looked so easy when the professor was doing it, but now I am confused when I have to do it by myself.” Why? Because the knowledge belongs to your professor and does not belong to you. You do not learn the knowledge simply by hearing it once or twice from somebody else. In order for you to have a more thorough understanding of the knowledge, we will use a pedagocial practice called inquiry-based learning. Most of the time during the class, students will be working in groups and presenting solutions that they have produced by themselves and not by other people or textbooks.
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Attendance is mandatory. Attending class meetings will have a direct impact on your learning as well as your grade. If you miss class for any reason, you are responsible for getting the information from a classmate, and checking the course web page for any handouts and assignments. You will not be able to make up the quiz for the day if you were not in class unless you have met the makeup policy below.
- Makeup policy: You can only make up a quiz or an exam if all three conditions are met:
- You have a legitimate reason (as determined by me) with documented proof. Visit of emergency rooms due to urgent health conditions is an example of legitimate reason. Attending non-academic events, such as someone’s wedding is an example of non-legitimate reason.
- You have informed me well in advanced.
- You can only make up the quiz or the exam after the scheduled date.
Your Role and My Role
- Professor Xiao’s role: I want you to succeed and I am here to help you succeed, but I cannot succeed for you! I have designed the structure of the course to help you learn. The class format will challenge you but it will be exhilarating and even fun at times. I will do what I think is the best to help you understand the material in the course.
- Student’s Role:
- You are responsible for making sense of the concepts and processes in this course. Success in mathematics is less about “ability” and more about willingness to think and to work hard to make sense of things.
- Attend every class meeting, participate, present whenever you can and work on the assignments outside of class.
- Please respect the ideas and opinions of others.
- If you are having trouble, please make an appointment to visit me.
- Cell phones should be off or set to vibrate. Do not place a call or send a text during class, and do not answer a phone call without first leaving the room.
Intellectual Property
- My lectures and course materials, including powerpoint presentations, tests, outlines, and similar materials, are protected by U.S. copyright law and by Utica University policy. I am the exclusive owner of the copyright in those materials I create. You may take notes and make copies of course materials for your own use. You may also share those materials with another student who is registered and enrolled in this course.
- You may not reproduce, distribute or display (post/upload) lecture notes or recordings or course materials in any other way — whether or not a fee is charged — without my express written consent. You also may not allow others to do so. If you do so, you may be subject to student conduct proceedings under the Utica University Student Code of Conduct
- Similarly, you own the copyright in your original work. If I am interested in posting your solution on the course web site, I will ask for your written permission.
Course Learning Goals
- I can compute instantaneous rate of change by using average rates of change.
- I can evaluate limits of basic functions algebraically.
- I can evaluate limits of basic functions geometrically.
- I can sketch the derivative given the graph of a function.
- I can use first derivative to describe the monotonicity of a function.
- I can use second derivative to describe the concavity of a function.
- I can determine whether a function has a limit at a point, whether a function is continuous at a point, and whether a function is differentiable at a point.
- I can find the algebraic equation of the tangent line to a differentiable function at any give point in context.
- I can use the tangent line of a function to approximate function values in context.
- I can compute derivatives of polynomials, exponential functions, and logarithmic functions.
- I can compute derivatives of trigonometric and anti-trigonometric functions.
- I can compute derivatives using the product rule.
- I can compute derivatives using the quotient rule.
- I can compute derivatives using the chain rule.
- I can find derivatives of inverse functions.
- I can find derivatives using implicit differentiation.
- I can use derivatives to find local extreme values.
- I can use derivatives to find global extreme values.
- I can solve related rates problems.
- I can solve optimization problems.
You are strongly encouraged to download and print a copy of the learning goals to record your grade.
Homework
Homework assignments come in two different formats.
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The first kind is online homework assignment at WileyPLUS (Please get the access as soon as you can). There will be one WileyPLUS homework each week and they are due Saturday at noon. To earn credit, you must earn more than 90% on each assignment. You have 10 attempts for each question and that should be plenty before you can answer the question correctly. Each assignment is worth 1 point.
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The second kind is completing tasks in the course materials assigned every week. You will be working on these assignments during the class time and discuss them with your peers. You will be asked to present your work during the class as part of the evaluations.
Presentations
- You will spend most of the time in class solving tasks in the course materials in groups of three or four. Each group can choose their own presenter when asked. If there are more than one group member that wants to present, the one with fewest presentations achieved at that time has the first dibs. The instructor reserves the right to choose any member from a group that he deemed necessary.
- You will earn credit for a presentation if you are able to correctly explain your solution. It is not enough to have a correct answer.
- The purpose of presentations is not to prove to me that the presenter or their group has done the problem. It is to make the ideas of the solution clear to the other students.
- Confusions and mistakes are very common when learning new mathematics and they should be handled positively to stimulate your thinking. The audience should feel free to ask questions in the discussion forum but please respect the ideas and opinions of others. For example, instead of using the phrase “You should change XYZ.”, start your sentence like “Do we want to change … ?”
- Though the atmosphere in this class should be informal and friendly, what we do in the class is serious business. In particular, the presentations made by students are to be taken very seriously since they spearhead the work of the class.
- Fellow students and the instructor are allowed to ask questions at any point and it is the responsibility of the presenter to answer those questions to the best of his or her ability. The group members of the presenter may also help answering the questions.
Group Participation
During the class, you will be actively working in a small group with your peer classmates. Here are a few tips on how to be a productive group member:
- Be helpful when your peer has a question. Also don’t hesitate to ask if you have a question. The best way to learn something is to teach it.
- It is common that the class time is not enough for you to complete all the activities, so it would be a good idea to get together with your group members between classes to work on them.
- Respect others’ idea. Give everyone a chance to share their opinion. Do not dominate a conversation.
Quizzes and Examinations
There will be a quiz every week on Friday except for the first week. There will be one cumulative final exam.
Evaluation
In this class, we will use a system known as standards-based grading. You will have multiple opportunities to demonstrate that you have met a goal. A goal is met if a student has successfully demonstrated it twice in either (a) quizzes, or (b) on one quiz and one other (final exam or a presentation). There is no partial credit. Once you have score a goal from a quiz or a presentation, you should put a note in one of the boxes before the relevant goal on this print out. You should use clear labeling to indicate when you score that goal, for example, Q2 stands for Quiz 2, or 3/2(P) stands for presentation on March 2. If you are unsuccessful on a quiz problem, prepare yourself to do better on the next quiz. Feel free to stop by my office and ask for practice problems. Quizzes are scheduled on Thursdays. The goals that will be tested on a quiz will be posted at this page on Wednesday evenings. Presenting problems and participating discussion in class, doing homework and exercises are all ways to help you prepare for the next quiz. All of goals appear on multiple quizzes so you have multiple chance to demonstrate that you have met the goals. Your final letter grade will be determined in two steps. For Step 1, you will be assigned a base letter grade based on the following criteria.
| Letter Grade | Criteria |
|---|---|
| A | at least 19 goals, and at least 13 homework points |
| B | at least 16 goals, and at least 12 homework points |
| C | at least 13 goals, and at least 10 homework points |
| D | at least 10 goals, and at least 8 homework points |
| F | less than 10 goals, or less than 8 homework points |
For Step 2, your final letter grade will be determined based on your base letter grade from Step 1 and possible adjustment based on your presentation grade.
| Final Letter Grade | Presentation |
|---|---|
| + | more than 3 |
| No change | 2-3 |
| - | 0-1 |
For example, if you score 16 goals, 12 homework points, and 4 presentations. Use the first table to determine that you letter grade is B. Then because presentation grade is 4, your final letter grade is B+.
Tentative Schedule
| Chapter 1 | Week 1-5 |
| Chapter 2 | Week 6-10 |
| Chapter 3 | Week 11-14 |
Tutoring Services
There are two kinds of (free) tutoring services offered by the university.
- The first kind is at the learning commons at the Utica University Library.
- The second kind is Smarthinking, which is a 24/7 online tutoring service.
Academic Integrity
I have zero tolerance on dishonesty. Any forms of dishonesty such as copying homework or cheating on quizzes and examinations, will result in zero credit for that particular assignment, and will be reported to the Academic Standards Committee. The highest penalty a student can receive is “F for cheating” for the course. There might be additional sanctions by the Academic Standards Committee such as dismissal from the university. See Utica University official page for Academic Honesty for more details.
Special Accommodation
The stuff just below is the University approved language, and is a bit… “legalese’’. The point is, if you need accommodations to succeed in this course, talk to me and we can make sure you get what you need. And the social environment of this course is important to me, too. Let’s work together to make a welcoming and affirming space for everyone.
Any student who has need of special accommodations in this class due to a documented disability should speak with me as soon as possible, preferably within the first two weeks of class. You should also contact Judy Borner, Director of Learning Services in the Academic Support Services Center (315-792-3032 or [email protected] ) in order to determine eligibility for services and to receive an accommodation letter. We will work with you to help you in your efforts to master the course content in an effective and appropriate way. See Utica University official page for Office of Learning Services.
Disclaimer
It is the students’ responsibility to keep informed of all announcements, syllabus adjustments, or policy changes during the semester via this web page or via school emails. The author of this syllabus reserves the right to change it with notice at any time during the semester.