Xiao Xiao

Xiao Xiao

A mathematician, a classical music lover, a number theorist, a skier, a stamp collector, a Manchester United fan, ...

MAT 201 Calculus 1 - Utica University

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 Calculus 1 at Utica University. If you are a student of Utica Academy of Science registered for the bridge program, please check out the other Calculus 1 home page.

Important Dates

  • Add/Drop deadline: 01/20/23
  • Spring break: 03/13/23 - 03/17/23
  • Withdraw deadline: 03/27/22
  • SOOT: 04/24/23 - 05/01/23
  • Final exam: 05/02/23 - 05/06/23

Instructor Information

  • Instructor: Prof. Xiao Xiao
  • Email: [email protected]
  • Office: White Hall 255
  • Office hour: Tuesdays, Thursdays 1-2 pm, Wednesday 10-11 am

Homework

  • Apr. 27, 2023
    • Complete WileyPLUS Week 14 Assignment.
    • Final exam will be on Tuesday May 2 8am at Hubbard 210.
  • Apr. 25, 2023
    • Complete Activity 3.4.2. Let me know if you want to present.
    • Start working on Week 14 Assignment in WileyPLUS.
    • Goal for this week’s quiz: 8,9,17,18,19,20.
    • Please don’t forget to fill out the SOOT.
  • Apr. 20, 2023
    • Finish Week 13 Assignment in WileyPLUS.
  • Apr. 18, 2023
    • Complete Activity 3.3.3 Part (a) to (c), Activity 3.1.2 and 3.1.3. Let me know if you want to present.
    • Start working on Week 13 Assignment in WileyPLUS.
  • Apr. 13, 2023
    • Complete the rest of Activity 3.5.4. If you want further practice on related rates, you should also do Activity 3.5.2. Feel free to do stop by my office if you want me to check your work.
    • Complete Week 12 Assignment in WileyPLUS.
    • Complete Preview Activity 3.1.1.
  • Apr. 11, 2023
    • Complete Activity 3.5.3.
    • Goal for this week’s quiz, 5,6,7,15,16,19.
    • Start working on Week 12 Assignment in WileyPLUS.
  • Apr. 6, 2023
    • Complete Week 11 Assgnment in WileyPLUS.
  • Apr. 4, 2023
    • Complete Activity 2.7.4.
    • Start working on Week 11 Assignment in WileyPLUS.
  • Mar. 30, 2023
    • Complete Preview Activity 2.7.1.
    • Complete Week 10 Assignment in WileyPLUS.
  • Mar. 28, 2023
    • Complete Activity 2.6.2 and 2.6.4 (especially the problem you are assigned to). Be prepared to present on Thursday.
    • Work on Week 10 Assignent in WileyPLUS.
    • Goal for this week’s quiz, 1, 10, 11, 12, 13, 14, 15.
  • Mar. 23, 2023
    • Complete Activity 2.6.2 and let me know if you want to present.
    • Complete Week 9 Assignment in WileyPLUS.
  • Mar. 21, 2023
    • Complete Activity 2.5.3 and let me know if you want to present.
    • Start working on Week 9 Assignment in WileyPLUS.
  • Mar. 9, 2023
    • I apoglize for the wrong homework annoucement on Mar. 8. If you saw that, please ignore it. That was a mistake.
    • Keep working on Week 8 Assignment. You should be able to complete all the questions except for the questions that involve derivatives of tangent, cotangent, secant, and cosecant. We will discuss these after the spring break.
  • Mar. 7, 2023
    • Complete Activity 2.3.2 and 2.3.3. Let me know if you would like to present.
    • Complete Week 7 Assignment in WileyPLUS and start working on Week 8 Assignment.
    • Goals for Thursday, 7, 8, 9, 10, 11, 12.
  • Mar. 2, 2023
    • Work on Week 7 Assignment in WileyPLUS although you won’t be able to fully complete it yet.
    • Watch this video to learn how to differentiate sine and cosine functions.
    • Complete Activity 2.1.3 if you have not already done so.
  • Feb. 28, 2023
    • Watch three videos to learn basic differentiation principles. Video 1 on differentiate power functions, Video 2 on differentiate expoential functions, Video 3 on basic differentiation rules.
    • Work on Week 7 Assignment in WileyPLUS.
    • There will be no quiz this Thursday. The next quiz will be next Thursday Mar. 9.
  • Feb. 23, 2023
    • Complete most of Week 6 Assignment in WileyPLUS except for the problems on calculating derivatives. We will cover that next week.
  • Feb. 21, 2023
    • Complete Activity 1.8.3 and let me know if you want to present.
    • Work on Week 6 Assignment in WileyPLUS.
    • Watch this video for an example of using linear approximation application.
    • Goals for this week’s quiz: 4, 5, 6, 7, 8, 9.
  • Feb. 16, 2023
    • Complete Week 5 Assignment in WileyPLUS.
    • Complete Preview Activity 1.8.1.
  • Feb. 14, 2023
    • Complete Activity 1.7.2. Let me know if you want to present.
    • Work on Week 5 Assignment in WileyPLUS.
    • Watch this video to review interpretation of first derivative, and this video to review interpretation of second derivative.
  • Feb. 9, 2023
    • Complete Activity 1.6.2. Let me know if you want to present.
    • Complete Week 4 Assignment in WileyPLUS.
  • Feb. 7, 2023
    • Complete Activity 1.4.3.
    • Work on Week 4 Assignment in WileyPLUS.
  • Feb. 2, 2023
    • Complete Week 3 Assignment in WileyPLUS.
    • Watch video to review graph sketching of derivatives.
  • Jan. 31, 2023
    • Complete Activity 1.3.3. Let me know if you want to present.
    • Complete the hand out sheet on sketching graph of the derivative.
    • Start working on Week 3 Assignment in WileyPLUS.
    • Watch this video on derivative of a function as a review.
    • There are three questions on Quiz 2, addressing Goal 1, 2, and 3.
  • Jan. 26, 2023
    • Try to work on Activity 1.3.2.
    • Complete Week 2 Assignment in WileyPLUS.
    • Watch this video on the definition of derivative at a point (as a review).
  • Jan. 24, 2023
    • Complete Activity 1.2.2 if you have not completed it during the class. Let me know if you would like to present.
    • Start working on Week 2 Assignment in WileyPLUS. Aim to complete at least half of the assignment before Thursday.
  • Jan. 19, 2023
    • Complete Activity 1.1.4. Let me know if you would like to present.
    • Complete Preview Activity 1.2.1.
    • Watch this video on computing instantaneous velocity as a review.
    • Complete Week 1 Assignment in WileyPLUS.
    • No quiz for this week. Quiz 1 is scheduled next week.
  • Jan. 17, 2023
    • 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.
    • Sign up at WileyPLUS (if you have not done so). 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.
    • Print learning goal sheet (if you have not done so), carry this with you to class.

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

  • Course name: MAT 201 Calculus 1

  • Course credit hours: 3 credit

  • Course Prerequisite: MAT 151, or satisfactory performance in the math placement test administered by the math department.

  • Class time and location: Tuesdays and Thursdays 10:00-11:15 am at Hubbard 210

  • Textbook: Please see the course material link above.

  • 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. The ISBN for the WileyPLUS standalone access card is 9781119777847. If you have enrolled in the book bundle program, then you will automatically have access to it. Otherwise, you can purchase the access directly from the publisher. Note that it is very unlikely that any used Calculus textbook will come with the WileyPLUS access. The class key you need to self-enroll in WileyPLUS is “B71652”. Please use your Utica College official name and email address to register. Do not use nickname or your private email address.

  • 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.

  • 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.

  • 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.

  • 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

  1. I can compute instantaneous rate of change by using average rates of change.
  2. I can evaluate limits of basic functions algebraically.
  3. I can evaluate limits of basic functions geometrically.
  4. I can sketch the derivative given the graph of a function.
  5. I can use first derivative to describe the monotonicity of a function.
  6. I can use second derivative to describe the concavity of a function.
  7. 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.
  8. I can find the algebraic equation of the tangent line to a differentiable function at any give point in context.
  9. I can use the tangent line of a function to approximate function values in context.
  10. I can compute derivatives of polynomials, exponential functions, and logarithmic functions.
  11. I can compute derivatives of trigonometric and anti-trigonometric functions.
  12. I can compute derivatives using the product rule.
  13. I can compute derivatives using the quotient rule.
  14. I can compute derivatives using the chain rule.
  15. I can find derivatives of inverse functions.
  16. I can find derivatives using implicit differentiation.
  17. I can use derivatives to find local extreme values.
  18. I can use derivatives to find global extreme values.
  19. I can solve related rates problems.
  20. 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.

  • 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.

  • 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 Thursday 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.