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

Undergraduate course, Mathematics Department, Utica University, 2024

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. Please check this page frequently for announcements and assignments.

Important Dates

  • Add/Drop deadline: 8/30/24
  • Fall break: 10/14/24 - 10/15/24
  • Withdraw deadline: 11/04/24
  • Thanksgiving break: 11/27/24 - 11/29/24
  • SOOT: 11/29/24 - 12/06/24
  • Final exam: 8am Tuesday 12/10/24

Instructor Information

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

Homework

  • Dec. 3
    • Complete all WileyPLUS homework.
  • Nov. 26
    • Start working on Week 14 Assignment in WileyPLUS.
    • Quiz 13 will cover Goal 17, 18, 19, 20.
  • Nov. 21
    • Complete Week 13 Assignment in WileyPLUS.
    • No quiz next week.
  • Nov. 19
    • Complete Activity 3.3.3 (a)-(c) and Activity 3.1.2
    • Start Week 13 Assignment in WileyPLUS.
    • Quiz 12 will cover Goal 16, 17, 18, 19.
  • Nov. 14
    • Complete Preview Activity 3.1.1.
  • Nov. 12
    • Complete Week 12 Assignment in WileyPLUS.
    • Complete Activity 3.5.5.
    • Quiz 11 will cover Goal 8, 9, 10, 11, 12, 13, 14, 15, 16, 19.
  • Nov. 7
    • Complete Week 11 Assignment in WileyPLUS.
    • Try Activity 3.5.3.
  • Nov. 5
    • Start working on Week 11 Asssignment in WileyPLUS.
    • Quiz 10 will cover Goal 5, 6, 7, 11, 14, 15, 16.
  • Oct. 31
    • Complete Week 10 Assignment in WileyPLUS.
    • Complete Activity 2.6.4.
  • Oct. 29
    • Complete Activity 2.5.4 and 2.6.2.
    • Starting working on Week 10 Assignment in WileyPLUS.
    • Quiz 9 will cover Goal 1, 2, 3, 4, 11, 12, 13, 14, 15.
  • Oct. 24
    • Complete Activity 2.5.3.
    • Complete Week 9 Assignment in WileyPLUS.
  • Oct. 22
    • Complete Activity 2.4.4 and 2.5.2.
    • Complete Week 8 Assignment in WileyPLUS.
    • Quiz 8 will cover Goal 8, 9, 10, 11, 12, 13, 14.
  • Oct. 17
    • Complete Activity 2.3.2 and 2.3.3.
  • Oct. 16
    • Quiz 7 will cover Goal 8, 9, 10, 11, 12.
  • Oct. 10
    • Complete Activity 2.2.4 and Activity 2.3.2.
    • Complete Week 7 Assignment in WileyPLUS.
  • Oct. 8
    • Complete Activity 2.1.4.
    • Start working on Week 7 Assignment in WileyPLUS.
    • Quiz 6 will cover Goal 2, 6, 7, 8, 9, 10.
  • Oct. 3
    • Complete Activity 2.1.2.
    • Complete Week 6 Assignment in WileyPLUS.
  • Oct. 1
    • Complete Activity 1.8.3.
    • Start working on week 6 assignment in WileyPLUS.
    • Quiz 5 will cover Goal 4, 5, 6, 7, 8, 9.
  • Sep. 26
    • Complete Week 5 assignment in WilyPLUS.
  • Sep. 24
    • Complete Activity 1.7.2.
    • Start working on week 5 assignment in WileyPLUS.
    • Quiz 4 will cover Goal 2, 3, 4, 5, 6.
  • Sep. 19
    • Complete Activity 1.6.2.
    • Complete week 4 homework in WileyPLUS.
  • Sep. 17
    • Complete Preview Activity 1.6.1.
    • Start working on week 4 homework in WileyPLUS.
    • Quiz 3 will cover Goal 1, 2, 3, 4.
  • Sep. 12
    • Complete Activity 1.4.3 and let me know if you want to present.
    • Complete week 3 homework in WileyPLUS.
  • Sep. 10
    • Complete Activity 1.3.3 and Preview Activity 1.4.1. Let me know if you would like to present.
    • Start working on week 3 homework in WileyPLUS.
    • Quiz 2 will cover Goal 1, 2, 3.
  • Sep. 5
    • Complete Activity 1.2.3 and let me know if you want to present.
    • Complete week 2 homework in WileyPLUS.
  • Sep. 3
    • Try Activity 1.2.2. You should be able to find the limits by consturcting the graph, and by using values that are close to the point. If you are stuck on how to find the limits using algebra, don’t worry, we will spend more time on Thursday for that.
    • Complete weekly homework 1 in WileyPLUS.
    • Quiz 1 will cover Goal 1.
  • Aug. 29
    • Complete Activity 1.1.3 before Tuesday. We will have presentations.
    • You should start working on Weekly Homework 1 in WileyPLUS. If your WileyPLUS still does not work, please email me with a screenshot.
    • The first quiz will be on Thursday Sep. 5.
  • Aug. 27
    • Complete Preview Activity 1.1.1. We will have student presentation on Thursday Aug. 29.
    • Print the learning goal sheet
    • Complete the course survey if you have not done so.
    • The bookstore is still working on the WileyPLUS access. You should sign up using your university email account and the class key “B32285”.

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 10:00-11:15am 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 “B32285”. Please use your Utica University 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 pedagogical 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. 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 the tutoring service at the learning commons of library. Please visit the learning commons for detail schedules.

  • The second kind is an online tutoring service provided by the university called ThinkingStorm. You can access the service here with your university username and password.

There is a third (also free) option gaining popularity among students: using generative artificial intelligence, such as ChatGPT. Here are some examples (by no means exhaustive) of how AI can enhance your learning experience:

  • Ask ChatGPT to create a practice problem for you. Be very specific about the types of problems you’re looking for.

  • Ask ChatGPT for a hint if you’re stuck on a problem or to provide a complete step-by-step solution.

  • Ask ChatGPT to evaluate your work and check if you’ve answered correctly.

However, there are ways in which using AI can be harmful and even detrimental to your learning:

  • Asking ChatGPT to do your homework for you (your future employer might just hire ChatGPT instead of you).

  • Using ChatGPT to get answers without truly understanding the material, which will hinder your critical thinking and problem-solving skills.

  • While ChatGPT can provide quick responses, there is no guarantee of the quality of the information. Accepting everything ChatGPT gives you without critical reflection is like taking advice from a stranger on the street.

If you have ideas on how ChatGPT or other generative AI can help you learn, please don’t hesitate to reach out. I’m happy to discuss it with you.

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 us 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.