Overview
Differentiation and integration with applications to biology, physics, chemistry, economics, and social sciences; differential equations; multivariable differential calculus.
NOTE: For students intending to pursue a medial or major plan in a subject other than Mathematics or Statistics.
Learning Outcomes
This course will be delivered using a completely online approach using online course materials in onQ and live/synchronous sessions.
Communication tools used in the course
- onQ Forums
- Skype
- Telephone
- WebWork question feedback options
Course Components
- Lectures will introduce the key ideas of the course, and will be used to work through introductory examples
- Assignments, along with solutions, will give you the chance to master the skills of the course
- Tutorials will be where tutors can provide additional examples, as well as the opportunity to get further clarification about the assignment problems.
- Tests are written during your tutorial times, 3 times per term. They will be based on the Test Preparation Problems from the Assignments.
Learning Objectives
After you complete this course you will be able to:
In Single Variable Differential Calculus
- Select a function form or family of functions that have desired graphical and limit properties. (e.g. a function that starts at (0,0), has one peak, and then a horizontal asymptote at y=2)
- Have a toolkit of functions for describing relationships in application problems
- Express (verbally or through calculations or graphs) the meaning of limiting values in application problems.
- Calculate value of finite and infinite limits of continuous and discontinuous functions (with or without l'Hopital's rule), given a function
- Understand the tangent-slope and rate of change meanings of the derivative
- Understand the difference between various possible approximations to a function.
- Construct application models from word problems and use derivatives to investigate properties of the models.
- Use derivatives to locate and classify critical points in optimization problems.
- Use relationships between modeling variables to construct relationships between their rates of change.
- Use relationships between modeling variables to estimate the effects of changes of inputs or outputs
In Single Variable Integral Calculus
- Understand the relationship between integration and area under a curve/rate graph
- Understand the graphical/area interpretation of integration and average value
- Construct application models from word problems and use integrals and/or derivatives to investigate properties of the models.
- Master core integration techniques.
- Understand properties related to the integral - average value, continuous anti-derivatives.
- Understand the issues involved with infinite intervals or asymptotic values in evaluating integrals.
- Construct differential equation models from word problems and use qualitative and algebraic methods to investigate properties of the models.
In Multivariate Differential Calculus
- Demonstrate an understanding between graphical presentation and calculus concepts (1st, 2nd part. derivs, gradient, directional deriv) in multivariate functions.
- Construct application models from word problems involving multivariate functions, and use differential calculus to investigate properties of the model (related rates and optimization)
- Vectors
- Gradient and directional derivative
- Related rates
- Concavity
- Critical points and optimization
- Constrained optimization and Lagrange multipliers
Terms
Evaluation
Please note that the following information is subject to change.
12% - Unit Self-Assessments (best 9 of 12 each half)
3% - Mastery Tests (3 x 1% each)
15% - Live Sessions (best 5 of 6 each half)
20% - In-Term Tests (2 tests each half)
25% - Proctored Mid-Course Exam
25% - Proctored Final Exam
Course Policy
- All tests are mandatory, and can only be missed through pre-arrangement, or due to illness/family emergency. Notification by email is required within 7 days of the missed test in the case of illness/family emergency.
- Missed tests (with appropriate notification) will not be re-taken; the 5% for the test will be added to the exam for the current term. Missed tests without a reason/notification will be given a grade of zero.
- In the tests and exam, no resources can be used, except those provided explicitly in the test.
- First violation on a test: zero on two tests, record with the Faculty.
- Second violation on a test or violation in the exam: zero for the course, communication with the Faculty.
Proctored Exams
Exam Centre Location, Eligibility, and Fees
Students enrolled exclusively in online courses may choose one of two options to write this course’s proctored assessments:
- You may choose to write the assessments online under supervision of Examity proctoring services. A $100 fee will be charged to your SOLUS account. This fee is known as the Off Campus Exam Admin Fee and is applied in SOLUS at the earlier of: term tuition posting date, or the date at which exam writing method is changed to online. The fee is assessed once per ASO course with proctored assessments.
- You may choose to write the assessments in-person on Queen’s campus in Kingston at no additional charge.
Students enrolled in at least one on-campus course are expected to write this course’s proctored assessments on-campus during the scheduled exam time. They will not be permitted to write this course’s proctored assessments online.
Students were prompted to indicate their preferred exam writing method when enrolling in the course in SOLUS. The exam writing method may be changed by contacting the ASO Exams Team at aso.exams@queensu.ca.
Information for students writing online assessments using Examity
Selected assessments in this course will be administered in onQ using online proctoring provided by Examity, a third-party, cloud-based service. This proctoring solution was chosen to support our efforts in maintaining academic integrity when online proctoring is required. Queen’s has conducted an extensive privacy and security review of Examity and has entered into a binding agreement with terms that address the appropriate collection, use and disclosure of personal information in accordance with Ontario’s privacy legislation. To learn more about online proctoring, please see the information provided by the Office of the University Registrar.
If you registered to write online with Examity, all information pertaining to the technical requirements and preparation for writing online will be posted in onQ well in advance of your exam. 
The use of Examity as described is unique to courses offered by the Faculty of Arts and Science Online. Other Faculties use online proctoring solutions in different ways under different regulations. Students should contact the appropriate Faculty examination team if they have questions.
Timing of Final Examinations
The exam period dates for each Term are listed on the Faculty of Arts and Science webpage under "Important Dates". Student exam schedules for the Fall Term are posted to SOLUS immediately prior to the Thanksgiving holiday; for the Winter Term they are posted on the Friday before Reading Week, and for the Summer Term they are individually noted on the Arts and Science Online syllabi. Students should not make any travel plans until after the examination schedule has been posted. Exams will not be moved or deferred to accommodate employment, travel/holiday plans or flight reservations. Students experiencing extenuating circumstances preventing them from writing their exams as scheduled should review the information about the Academic Consideration process.
Textbook and Materials
ASO reserves the right to make changes to the required material list as received by the instructor before the course starts. Please refer to the Campus Bookstore website at to obtain the most up-to-date list of required materials for this course before purchasing them.
Technology and Equipment Requirements
- Computer access with internet
- Firefox Internet Browser
- Adobe Acrobat
- Adobe Flash Player
- QuickTime Player
- Calculator - Casio 991
- Digital Camera or Scanner (used to electronically submit hand-written work)
Recommended Textbook
- Single and Multivariable Calculus, Seventh Edition or earlier – Hughes-Hallett
Time Commitment
To complete the readings, assignments, and course activities, students can expect to spend, on average, about 10-11 hours per week (262 hours in total) on the course.
Evaluation
Please note that the following information is subject to change.
12% - Unit Self-Assessments (best 9 of 12 each half)
3% - Mastery Tests (3 x 1% each)
15% - Live Sessions (best 5 of 6 each half)
20% - In-Term Tests (2 tests each half)
25% - Proctored Mid-Course Exam
25% - Proctored Final Exam
- If the exam mark in a term is higher than any written term test, the test mark will be replaced with the exam mark (applies to all tests with grades lower than the exam grade, not just the lowest).
- If a student misses a test without a valid reason, the mark for the test will remain a zero, regardless of exam performance. See Course Policy below.
Course Policy
- All tests are mandatory, and can only be missed through pre-arrangement, or due to illness/family emergency. Notification by email is required within 7 days of the missed test in the case of illness/family emergency.
- Missed tests (with appropriate notification) will not be re-taken; the 5% for the test will be added to the exam for the current term. Missed tests without a reason/notification will be given a grade of zero.
- In the tests and exam, no resources can be used, except those provided explicitly in the test.
- First violation on a test: zero on two tests, record with the Faculty.
- Second violation on a test or violation in the exam: zero for the course, communication with the Faculty.
Proctored Exams
Exam Centre Location, Eligibility, and Fees
Students enrolled exclusively in online courses may choose one of two options to write this course’s proctored assessments:
- You may choose to write the assessments online under supervision of Examity proctoring services. A $100 fee will be charged to your SOLUS account. This fee is known as the Off Campus Exam Admin Fee and is applied in SOLUS at the earlier of: term tuition posting date, or the date at which exam writing method is changed to online. The fee is assessed once per ASO course with proctored assessments.
- You may choose to write the assessments in-person on Queen’s campus in Kingston at no additional charge.
Students enrolled in at least one on-campus course are expected to write this course’s proctored assessments on-campus during the scheduled exam time. They will not be permitted to write this course’s proctored assessments online.
Students were prompted to indicate their preferred exam writing method when enrolling in the course in SOLUS. The exam writing method may be changed by contacting the ASO Exams Team at aso.exams@queensu.ca.
Information for students writing online assessments using Examity
Selected assessments in this course will be administered in onQ using online proctoring provided by Examity, a third-party, cloud-based service. This proctoring solution was chosen to support our efforts in maintaining academic integrity when online proctoring is required. Queen’s has conducted an extensive privacy and security review of Examity and has entered into a binding agreement with terms that address the appropriate collection, use and disclosure of personal information in accordance with Ontario’s privacy legislation. To learn more about online proctoring, please see the information provided by the Office of the University Registrar.
If you registered to write online with Examity, all information pertaining to the technical requirements and preparation for writing online will be posted in onQ well in advance of your exam. 
The use of Examity as described is unique to courses offered by the Faculty of Arts and Science Online. Other Faculties use online proctoring solutions in different ways under different regulations. Students should contact the appropriate Faculty examination team if they have questions.
Timing of Final Examinations
The exam period dates for each Term are listed on the Faculty of Arts and Science webpage under "Important Dates". Student exam schedules for the Fall Term are posted to SOLUS immediately prior to the Thanksgiving holiday; for the Winter Term they are posted on the Friday before Reading Week, and for the Summer Term they are individually noted on the Arts and Science Online syllabi. Students should not make any travel plans until after the examination schedule has been posted. Exams will not be moved or deferred to accommodate employment, travel/holiday plans or flight reservations. Students experiencing extenuating circumstances preventing them from writing their exams as scheduled should review the information about the Academic Consideration process.
Textbook and Materials
ASO reserves the right to make changes to the required material list as received by the instructor before the course starts. Please refer to the Campus Bookstore website at to obtain the most up-to-date list of required materials for this course before purchasing them.
Technology and Equipment Requirements
- Computer access with internet
- Firefox Internet Browser
- Adobe Acrobat
- Adobe Flash Player
- QuickTime Player
- Calculator - Casio 991
- Digital Camera or Scanner (used to electronically submit hand-written work)
Recommended Textbook
- Single and Multivariable Calculus, Seventh Edition or earlier – Hughes-Hallett
Time Commitment
To complete the readings, assignments, and course activities, students can expect to spend, on average, about 20-22 hours per week (262 hours total) on the course.
Testimonials
"I really liked having the Webwork due a week after the content was covered. That gave me time to use my weekend previous for the practice questions and be more successful on the webwork quiz. The in-term tests were a fair evaluation of each unit and I really liked the organization/set-up of how they were to be completed (me choosing an hour on my own time rather than having to stress/cram a set time in). I am very happy with my decision to take it online rather than concurrently with other courses during the school year."
- Course evaluation, MATH 121: Differential and Integral Calculus (2014)