Fall 2021: MAT A29 Calculus I for the Life Sciences
From the Course Calendar: “A course in differential calculus for the life sciences. Algebraic and transcendental functions; semi-log and log-log plots; limits of sequences and functions, continuity; extreme value and intermediate value theorems; approximation of discontinuous functions by continuous ones; derivatives; differentials; approximation and local linearity; applications of derivatives; antiderivatives and indefinite integrals.”
Table of contents
- Course Staff
- Your Professor’s Message
- Policy on In-Person and Online Offerings
- Communication Policy
- Access
- Resources
- Grading Scheme
- Campus Resources
- Academic Integrity
- Schedule of Learning Objectives
- Schedule of Tasks
- Exact Dates of Tasks
- Schedule of Material
- Land Acknowledgement
Course Staff
- Instructor: Parker Glynn-Adey (he/him)
- Call Me: “Parker” or “Professor Parker”
- E-Mail : parker dot glynn dot adey at utoronto point ca
- Website: http://pgadey.ca/
- Office: IC 344
- Teaching Assistant:
- E-Mail:
- Tutorials:
- Facilitated Study Group Leader: Varumen Siva
- E-Mail:
- Tutorials:
Your Professor’s Message
Hi! I’m Parker Glynn-Adey, the professor for MAT A29. This is one of my favourite courses at the University of Toronto. The last time I taught it was back in 2016. It was the first course that I ever taught, and I’m glad to be teaching it back teaching it again.
I like it so much because the students in this course are awesome. You want to be doctors, pharmacists, nurses, mental health workers, and all sorts of people in the life sciences. And that’s awesome! I want to help you succeed in that. If I can get you started doing a bit of math, and you can use it on your mission in the life sciences, then I’ll be tremendously happy.
I’ve tried to design this course so that you can succeed. I’m hoping that there are no crazy surprises in the course, and that it does not stress you out too much. If you’re feeling unsure about your ability to succeed, or you need someone to talk to about the course, then please come to me. I’d be glad to help. My goal is to help you succeed, to go on to finish your program in life science, and to support you on your journey.
Policy on In-Person and Online Offerings
As the COVID-19 Pandemic continues to impact the university we need to be ready for a class with mixed in-person and online instruction. An important policy for this course is that: You will be able to complete this course online asynchronously. We have this policy so that people in different time zones will be able to participate in the class, without having to do math at weird times.
We might have to switch to “online only”. If we switch, then there will be optional synchronous online lectures and you can still take the course asynchronously.
COVID Plans
Plan | What it will look like | What might cause it |
---|---|---|
A | Full capacity, in-person lecture and tutorial, videos online | Lifting of all federal and provincial health measures due to COVID-19 |
B (current) | Limited capacity in-person lecture and tutorial, videos online | UTSC Re-Opens |
C | Synchronous online lecture and tutorial, videos online |
|
D | Asynchronous online lecture and tutorial, videos online |
|
Lecture
Lecture will be held in-person and filmed by the WebOption program for distribution. Lecture is a critical moment to ask questions about the material. Many of the students taking MAT A29 this year will not be present in lecture due to travel restrictions, and room capacity limits. As a result, attending lecture in person is a serious commitement. If you attend lecture, please be healthy, alert, and ready to engage. You will be representing all the students who could not attend.
Tutorials
Tutorials will be held in-person and online. You will get to interact with a trained TA who will field your questions from a beginner perspective. All the different tutorials sections will be reviewing the same assigned tutorial problems, so you are free to register for and attend whichever tutorial works for you.
Common Questions:
- Where are the Zoom links? How do I access the online classes? As of September 6th, there are no posted Zoom links yet. We will not have synchronous lecture on Zoom, unless we move to online instruction. However, some tutorial will be online, so links will be posted at the beginning of the second week of classes.
- When do tutorials start? Tutorials start the second week of classes. You do not need to attend tutorials during the first week of the semester.
- Do I have to come to campus? No, you do not need to come to campus. Only come to campus if you are feeling healthy and want to be present in person. All assessments for the course will be conducted online, so you will not need to do any tests or quizzes in person.
- Why are there two simultaneous sections, such as LEC 01 (in person) and LEC 60 (online synchronous)? The two sections exist for scheduling purposes. You may enroll in either one. If we need to switch to online only delivery, then we will use those synchronous slots. Please note that the course can be complete asynchronously. All materials will be posted online.
- Why are we holding in-person lectures and tutorials? We are holding in-person lectures and tutorials so that there is an opportunity for you to ask questions, and to be around your peers. We want you to have the usual undergraduate experience of lecture or tutorial.
- Will we switch to online only? It might happen. We don’t know how severe the fourth wave of the pandemic will be, and so we cannot make any guarantees. If Parker feels it is unsafe to continue lecture and tutorial in-person, then we will switch to online only.
Communication Policy
There are two ways to contact us:
- Anonymous Feedback
E-Mail must be from an official University of Toronto account. You must include [MAT A29] in the subject line, or your e-mail might get lost. Please include your name and student number in every e-mail that you send. Be sure to include the precise question, and the problem or difficulty. If you’re not able to write out the question, take a photo or attach a PDF.
To: parker.glynn.adey@utoronto.ca
From: leonhard.euler@utoronto.ca
Subject: [MAT A29] Help request!
Hi! I am Leonhard Euler (12932188) from MAT A29.
I need help with this question: Find the derivative of f(x)=x^2.
My problem is this: I don’t know what the word "derivative" means.
Thanks!
Above all, don’t worry about e-mailing me or any of the course staff. We are not evil trolls. We won’t get angry if you e-mail us. Answering student e-mails is a part of our job.
However, e-mail is only part of our job. We might not respond to your e-mail on the same day that you send it. Generally, give us at least two business days to respond. Parker has limited access to his computer on Tuesdays, Thursdays, and weekends.
Anonymous
Anonymous Feedback is welcome in this course. You can submit anonymous feedback here: http://pgadey.ca/feedback.html. You may use the form to comment on lecture, ask questions about the course, or give me tips. You do not need to enter your name or email address unless you want a private response from Parker. Note that your anonymous feedback may be discussed (and answered) in lecture, or on the Quercus.
Access
Students with all learning needs and accomodations are welcome in this course. If you have any reason to believe that you may require accommodations contact Parker and/or the AccessAbility Services as soon as possible. We can discuss the particulars of your situation and, if needed, get your registered with AccessAbility Services.
The AccessAbility Services staff (located in AA142) are available by appointment to: assess specific needs, interact with professors, provide referrals to medical professionals, and arrange appropriate accommoda- tions. You can reach AccessAbility at: ability@utsc.utoronto.ca. Their website is here: https://www.utsc.utoronto.ca/ability/welcome-accessability-services
Specific to this course: If you want access to the LaTeX code for any of the assignment, for your own use, then please contact me. All of our assignments and tests are open source.
Also, if you need additional time for term tests or the final exam, please let Parker know as soon as possible, and he will setup Crowdmark to allow additional time for your submissions.
Resources
- OpenStax Calculus 1. The textbook for the course.
- (extra) Differential Calculus for the Life Sciences by Dr. Leah Keshet of UBC. Lots of life science applications.
- (extra) 3Blue1Brown: The Essence of Calculus. A beautiful visual tour of calculus.
The only resource that you need to pay attention to is the textbook for the course. The other two resources are extra rescources that you can choose to read or watch if you want to.
Grading Scheme
Task | Weight |
---|---|
Exam | 40% |
Term Tests | (3-1)x20% |
Practice Tests | 3x1% |
Assignments | (5-1)x3% |
Assignment Reflections | 5x1% |
Missed Work
You are able to miss one term test and one assignment, during the course. If you’re unable to write a term test or an assignment, then you are free to drop the grade from the course. You do not need to request this, or apologize for missing the work, as it will happen automatically. We are all living through difficult times. Take a break.
There will be three term tests, but only two of them will count towards your final grade. There will be five assignments, but one four of them will count towards your final grade. We hope that this makes things less stressful.
Common Questions:
- Why does it say (3-1)x20% for term tests? This is a short way of writing that there are three term tests, but one of them will be dropped. It’s a saying that there are 3-1 = 2 term tests that count for 20% each.
Term Tests
Goal: these written tests give you the opportunity to demonstrate your understanding of core concepts and topics in a written format. You will gain experience of communicating mathematical ideas in a logical manner. We write tests in a limited amount of time to assess your fluency with the material.
Procedure: we will be using Crowdmark to grade assignment/test submissions. You will get a personalized submission link sent to your UToronto email address. Do NOT share this link with other students.
Submission Guidelines: Tests need to be submitted online through Crowdmark. Each test lasts twenty-four hours. We expect that it should take about an hour to complete the test.
Evaluation Criteria: In general, you need to present your solutions in a logical and clear manner. Detailed solutions will be made available shortly after the deadline of submission.
Please pay attention to the following when writing tests:
- Format: solutions are neatly and correctly assembled with professional look.
- Completeness: all steps are clearly and accurately explained.
- Content: the written solutions demonstrate mastery and fluency with the content of the course.
Common Questions:
- Will the tests be hard or easy? This depends on your level of fluency with the material. Some student will find the tests hard, and other students will find the tests easy. We have designed the tests to accurately assess the learning objectives, and believe that they are a fair reflection of the course.
- What should I do to prepare for the test? Practice. Practice. Practice! You can practice via the Suggested Questions from the Reading Guide, the Practice Tests, and attending and participating in Tutorials.
- Will both sections of the course write the same test? Yes. Both sections of the course will write the same test, so that everyone gets a fair and equal grade. Both sections of the course will cover the same material.
- Will the real test be similar to the practice test? Yes. They will be similar because we want your experience with the practice test to improve your score on the real test.
Practice Tests
Goal: These written practice tests give you the opportunity to see what the upcoming tests will look like. We have them so that you can get ready and practice for the real tests.
Procedure: We will use Crowdmark to upload the practice tests submissions. You will get a personalized submission link sent to your UToronto email address. Do NOT share this link with other students.
Submission Guidelines: Tests need to be submitted online through Crowdmark. Each test lasts twenty-four hours. We expect that it should take about an hour to complete the practice test. The practice tests will be available the Thursday through Friday before the real tests.
Evaluation Criteria: The practice tests will NOT be graded. Solutions will be posted online for your reference. If you submit a paper, and it is clear that you attempted all the problems, then you will get full marks. The practice tests are graded for completion only.
Common Questions:
- Can I make-up a missed practice test? No. There is no policy for missing or making up a missed practice test. We are freely offering the opportunity to practice before the real test, and if you do not take that opportunity, then there will be no opportunity to submit a practice test.
Assignments
Goal: these assignments give you the opportunity to deepen your understanding of topics covered in this course, and to practice. We use these assignments to determine if you can solve problems slowly, without time constraints.
Procedure: we will be using Crowdmark to grade assignment submissions. You will get a personalized submission link sent to your UToronto email address. Do NOT share this link with other students.
Submission Guidelines: Assignments need to be submitted online through Crowdmark. You will have a week to write the assignment.
Evaluation Criteria: present your solutions in a logical and clear manner. Detailed solutions will be made available shortly after the deadline of submission.
Assignment Reflections
Goal: The reflection assignments give you the opportunity to reflect on what you learned from each assignment. Your responses to the assignment reflections will help us determine how much you learned from the assignments.
Procedure: We will be using Crowdmark to grade assignment submissions. You will get a personalized submission link sent to your UToronto email address. Do NOT share this link with other students.
Submission Guidelines: Assignment reflections need to be submitted online through Crowdmark. You will have a two days to complete the assignment reflection. Assignmnent reflections will be available once the graded assignments are returned to students via Crowdmark.
Evaluation Criteria: The assignment reflections will NOT be graded. If you submit a paper, and it is clear that you considered your graded assignment, then you will get full marks. The assignment reflections are graded for completion only.
Common Questions:
- Can I make-up a missed assigment reflection? No. There is no policy for missing or making up a missed assignment reflection. We are freely offering the opportunity to reflect on what you learned, and if you do not take that opportunity, then there will be no opportunity to submit an assignment reflection.
- Why don’t the assignment reflections have due dates listed? We are going to distribute the assignment reflections on the day that assignements are returned to students. We do not yet know how fast or slow grading will be, and so we cannot list dates for the assignment reflections.
Campus Resources
Facilitated Study Groups
Facilitated Study Groups (FSGs) are weekly drop-in collaborative learning sessions for students who want to improve their understanding of challenging content in selected courses at UTSC. FSG sessions give you a chance to discuss the lecture material and important concepts, develop study strategies and fresh approaches, and work through problems as a group to prepare for your assignments and tests. FSGs in MATA29, will be led by Varumen Siva, who excelled in this course previously. He will attend lectures with you and will prepare activities and questions to ensure that each session is productive.
Research shows that students who regularly attend FSGs gain a deeper understanding of the material and, on average, achieve better grades. It’s also a great way to meet classmates and study in a relaxed, judgment-free space.
Center for Teaching and Learning Academic Learning Support
The Centre for Teaching and Learning provides academic learning support to students through online tutoring, workshops, and peer supports to drive student success. To find out more about all their offerings, see this website:
uoft.me/AcademicLearningSupport
Math and Stats Support
The Center for Teaching and Learning’s Math & Statistics Support provides free seminars, workshops, virtual tutoring, individual appointments, and small-group consultations to improve students’ proficiency in various subjects of mathematics and statistics. Their main goal is to create a friendly, vibrant environment in which all students can come to learn and succeed.
For their online help offerings see: https://uoft.me/MathStats
Academic Integrity
The instructional team wants to make sure that everyone has a fair chance to succeed in this course. We believe that academic integrity is important in guaranteeing that everyone has a fair chance to succeed. Therefore, we define an academic integrity violation to be accessing or communicating with any person or resource that gives a unique advantage to some students. For example: participating in private group chats, posting questions and reading solutions on websites, hiring or requesting external help. All of these would give some students advantages that would not be available to other students.
Common Questions:
- What rescources can I use during tests and assignments? You can use your notes, the textbooks, online references such as videos and Wikipedia, and any online calculators that are freely available. You can also contact Parker and the TAs. If you’re unsure whether you’re allowed to use a particular resource: Ask!
- What calculator do you recommend for this course? When designing the course, and checking the assignments, I used WolframAlpha and Desmos.
- What recources are forbidden durings tests and assignments? Anything that is private or specific to you. You cannot post questions online, participate in group chats, ask for help from online communities.
- How does the instructional team monitor academic integrity? We grade the assignments and tests. If we spot suspicious answers, we enter them in to a spreadsheet. We also look at popular study help websites to see if our the material from our course is being posted online. At the end of the course, we compile all the academic integrity material and send it to the Office of Academic Integrity.
- What should I do if someone is pressuring me in to cheating? Contact Parker. Send any screenshots / photos / text messages that are relevant. You have the right to succeed in this course without other people trapping you in an academic integrity violation case.
References on Academic Integrity
Schedule of Learning Objectives
- Limits and Differentiation (Week 1-4)
- Investigate quantitative relationships using graphs, their domains, and ranges.
- Evaluate limits numerically, visually, and algebraically.
- Apply the rules of differentiation to algebraic and transcendental functions.
- Application of Differentiation (Weeks 5-8)
- Use derivatives to determine properties, such as shape and the highest/lowest points, of graphs.
- Investigate and explain quantitative relationships between variables.
- Use differentiation to approximate general functions by linear functions.
- Integration (Weeks 9-12)
- Explain and apply the relationship between derivation and integration.
- Use integeration techniques to solve problems involving areas of bounded by graphs and volumes of solids.
- Integrate algebraic and transcendental functions.
Schedule of Tasks
Week | Tasks and Learning Objectives |
---|---|
1 | |
2 | Assignment 1 (LO: 1a) |
3 | |
4 | Assignment 2 (LO: 1b, 1c) + Term Test 1 (LO: 1a, 1b, 1c) |
5 | |
6 | Assignment 3 (LO: 1c) |
Reading Week! | |
7 | Term Test 2 (LO: 1c, 2a, 2b, 3a) |
8 | Assignment 4 (LO: 2a) |
9 | |
10 | Assignment 5 (LO: 2c, 3a, 3b) |
11 | Term Test 3 (LO: 3b, 3c) |
12 |
Exact Dates of Tasks
Task | Dates and Times |
---|---|
Assignment 1 | Friday September 10 @ 1:00pm to Friday September 17 @ 1:00pm |
Assignment 2 | Friday September 24 @ 1:00pm to Friday October 1 @ 1:00pm |
Assignment 3 | Friday October 15 @ 1:00pm to Friday October 22 @ 1:00pm |
Assignment 4 | Friday October 29 @ 1:00pm to Friday November 5 @ 1:00pm |
Assignment 5 | Friday November 12 @ 1:00pm to Friday November 19 @ 1:00pm |
Practice Term Test 1 | Thursday September 23 @ 3:00pm to Friday September 24 @ 3:00pm |
Term Test 1 | Monday September 27 @ 4:00pm to Tuesday September 28 @ 4:00pm |
Practice Term Test 2 | Thursday October 21 @ 3:00pm to Friday October 22 @ 3:00pm |
Term Test 2 | Monday October 25 @ 4:00pm to Tuesday October 26 @ 4:00pm |
Practice Term Test 3 | Thursday November 18 @ 3:00pm to Friday November 19 @ 3:00pm |
Term Test 3 | Monday November 22 @ 4:00pm to Tuesday November 22 @ 4:00pm |
The complete table of due dates is available as a Google Calendar.
Common Questions:
- Why don’t the assignment reflections have due dates listed? We are going to distribute the assignment reflections on the day that assignements are returned to students. They will be available for fourty eight hours. We do not yet know how fast or slow grading will be, and so we cannot list dates for the assignment reflections.
Schedule of Material
- Week 0: Pre-Course
- OpenStax 2.1 A Preview of Calculus
- Week 1: Functions
- OpenStax 1.1 Review of Functions
- 14, 15, 17, 19, 46, 47, 53, 55
- OpenStax 1.2 Basic Classes of Function
- 59, 61, 69, 73, 83, 85, 87, 91, 93, 95, 97
- OpenStax 1.1 Review of Functions
- Week 2: Limits
- OpenStax 2.2 The Limit of a Function
- 35, 36, 37, 46, 47, 48, 59, 60, 61, 62, 63, 64
- OpenStax 2.3 The Limit Laws
- 83, 85, 93, 95, 111, 113
- OpenStax 2.2 The Limit of a Function
- Week 3: Differentiation
- OpenStax 3.1 Defining the Derivative
- 11, 13, 19, 25, 27, 39
- OpenStax 3.2 The Derivative as a Function (differentials!)
- 57, 59, 61, 65, 71, 73, 93
- OpenStax 3.1 Defining the Derivative
- Week 4: Differentiation
- OpenStax 3.3 Differentiation Rules
- 107, 111, 117, 123, 125, 127, 131
- OpenStax 3.5 Derivatives of Trigonometric Functions
- 175, 181, 183, 191, 193, 209
- OpenStax 3.3 Differentiation Rules
- Week 5: Related Rates
- OpenStax 3.6 The Chain Rule
- 215, 217, 221, 223, 235
- OpenStax 3.8 Implicit Differentiation
- 301, 303, 307
- OpenStax 4.1 Related Rates
- 1, 3, 5, 9, 17
- OpenStax 3.6 The Chain Rule
- Week 6: Optimization
- OpenStax 4.3 Maxima and Minima
- 91, 93, 95, 105, 107, 109, 117, 119, 123, 125, 129, 145
- OpenStax 4.7 Applied Optimization Problems
- 311, 317, 319, 321, 353
- OpenStax 4.3 Maxima and Minima
- Week 7: Curve Sketching
- OpenStax 4.5 Derivatives and the Shape of a Graph
- 201, 205, 207, 217, 219, 225, 227, 229, 241, 243
- Additional Resource: log-log and semi-log graphs
- OpenStax 4.5 Derivatives and the Shape of a Graph
- Week 8: Approximation
- OpenStax 4.2 Linear Approximations and Differentials
- 51, 53, 33, 69, 73, 77, 83, 85
- OpenStax 4.2 Linear Approximations and Differentials
- Week 9: Antiderivatives and The Fundamental Theorem
- OpenStax 4.10 Antiderivatives
- 465, 467, 471, 473, 475, 477, 483, 489, 491
- OpenStax 5.3 The Fundamental Theorem of Calculus
- 151, 153, 157, 161, 171, 173, 175, 177, 183
- OpenStax 4.10 Antiderivatives
- Week 10: Integration Techniques
- OpenStax 5.4 Integration Formulas and the Net Change Theorem
- 207, 209, 211, 213, 221, 231
- OpenStax 5.5 Substitution
- 257, 259, 261, 263, 265, 269, 271, 273, 275, 279, 313
- OpenStax 5.4 Integration Formulas and the Net Change Theorem
- Week 11: Area and Volume
- OpenStax 6.1 Areas between Curves
- 1, 3, 5, 7, 13, 15, 17, 21, 23, 27, 29
- OpenStax 6.2 Determining Volume by Slicing
- 63, 67, 69, 71, 75, 77, 79, 83, 85, 89
- OpenStax 6.1 Areas between Curves
- Week 12: Summary and Exam Prep
Land Acknowledgement
As the instructor of this course, I wish to acknowledge the land on which the University of Toronto operates. For thousands of years it has been the traditional land of the Huron-Wendat, the Seneca, and the Mississaugas of the Credit. Today, this meeting place is still the home to many Indigenous people from across Turtle Island and we are grateful to have the opportunity to work on this land.
If you want to get in contact with the people of this place, Parker encourages you to check out: The Native Canadian Center of Toronto. They are very welcoming people. Their a weekly drum circle and meal on Thursdays is the most inclusive and open event that Parker has ever attended.
One last thing, appreciate the land while you’re here as a student. There is a beautiful hike on the south side of campus called the Valley Land Trail. If you go south from Humanities Wing, then you can see a wonderful stream and relax a little.
Old Schedule
This is the old schedule from when I taught the course back in 2016. The following weekly schedule uses section titles adapted from: Bittinger, Marvin L., Neal E. Brand, and John Quintanilla. Calculus for the life sciences. 2006.
- Functions and graphs
- Slope and Linear Functions
- Polynomial Functions
- Rational and Radical Functions
- Functions and graphs
- Trigonometric Functions
- Trigonometric Functions and the Unit Circle
- Differentiation
- Limits and Continuity: Visually and Numerically
- Limits and Continuity: Algebraically
- Differentiation as a Limit
- Differentiation
- Differentiation Techniques
- Instantaneous Rates of Change
- Product and Quotient Rules
- The Chain Rule
- Higher-Order Derivatives
- Applications of Differentiation
- Using the First Derivative to Find Max and Min
- Using the First Derivative to Sketch Graphs
- Using the Second Derivative to Find Max and Min
- Using the Second Derivative to Sketch Graphs
- Reading Week!
- Applications of Differentiation
- Graph Sketching: Asymptotes and Rational Functions
- Using Derivatives to Find Absolute Max and Min Values
- Maximum-Minimum Problems
- Applications of Differentiation
- Approximation Techniques
- Implicit Differentiation and Related Rates
- Explonential and Logarithmic Functions
- (!) Log-Log and Semi-Log Plots
- Exponential Functions
- Logarithmic Functions
- The Uninhibited Growth Model $\displaystyle \frac{dP}{dt} = kP$
- Explonential and Logarithmic Functions
- Decay
- The Derivatives of $a^x$ and $\log_a(x)$
- Integration
- Integration
- Area and Accumulation
- The Fundamental Theorem of Calculus
- Integration
- The Properties of Definite Integrals
- Substitution
- Integration
- Integration by Parts
- Tables and Technology
- Volume