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Differential & Integral Calculus

MATH 121/6.0

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 in Elluminate Virtual Classroom.

Communication tools used in the course

  • Email
  • 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

  1. 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
  2. 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
  3. Understand the tangent-slope and rate of change meanings of the derivative
    • Understand the difference between various possible approximations to a function.
  4. 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

  1. Understand the relationship between integration and area under a curve/rate graph
    • Understand the graphical/area interpretation of integration and average value
  2. 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.
  3. Construct differential equation models from word problems and use qualitative and algebraic methods to investigate properties of the models.

In Multivariate Differential Calculus

  1. Demonstrate an understanding between graphical presentation and calculus concepts (1st, 2nd part. derivs, gradient, directional deriv) in multivariate functions.
  2. 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


This online calculus course covers 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.

NOTE: This course is for students who have received a transfer credit for MATH 123/3.0. Students wishing to register in MATH 124/3.0 must obtain permission from Professor A. Ableson. Students who register in MATH 124/3.0 will join the MATH 121 class in week 7, June 13 2016.


Fall-Winter 2018-19
Course Dates: 
Sept 6, 2018 - Apr 5, 2019
Exam Dates: 
Proctored Midterm: Dec 5 - 20, 2018; Proctored Final: Apr 11 - 27, 2019


Please note that the following information is subject to change.

  • Weekly Concept Check-Ins: 5%, based on completion
  • Unit Self-Assessments (Best 10 out of 12 each term): 7%
  • Mastery Tests (3 x 1% each): 3%
  • Live Sessions (6 x 1% each) (Best 5 out of 6): 5%
  • In-Term Tests (Best 2 out of 3 each term): 20% 
  • Proctored Mid-Course Exam: 30%
  • Proctored Final Exam: 30%
  • 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.

Final and Midterm Examination

Midterm exam: The date and time will be scheduled during the Fall term final examination period. You will write your midterm exam at the same exam centre location as the final proctored exam. 

The final exam will be held during the Winter term final examination period. The exam schedule will be determined approximately eight weeks before the start of the exam period.

Students must write their exam on the day and time scheduled by the University. The start time may vary slightly depending on the off-campus exam centre. Do not schedule vacations, appointments, etc., during the exam period.


Professor Alan Ableson (ableson@mast.queensu.ca)

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 total) on the course.

Course Resources


SOLUS is Queen’s Student On-Line University System. You’ll have access to a SOLUS account once you become a Queen’s student. You’ll use SOLUS to register for courses, add and drop courses, update your contact information, view financial and academic information, and pay your tuition.

About OnQ

onQ is Queen's online learning platform. You'll log into onQ to access your course. All materials related to your course—notes, readings, videos, recordings, discussion forums, assignments, quizzes, groupwork, tutorials, and help—will be on the onQ site.

About Credit Units

Queen’s courses are weighted in credit units. A typical one-term course is worth 3.0 units, and a typical two-term course is worth 6.0 units. You combine these units to create your degree. A general (three-year) BA or BSc requires a total of 90 credit units.

Computer Requirements

To take an online course, you’ll need a high speed internet connection as well as a microphone and speakers to be able to watch videos, hear sounds, and participate in interactive online activities. A webcam is recommended but not necessary.

System Requirements:

  • Laptop or Desktop computer purchased within the last 5 years. (mobile devices are not supported)
  • Windows Vista SP2/Mac OSX 10.9 or higher
  • Up to date versions of Firefox, Internet Explorer or Safari. Please note that Google Chrome is not recommended for use in our courses.
  • Most recent version of Adobe Reader and Adobe Flash

 See also Getting Started.


The deadlines for new applications to Queen’s Arts and Science Online courses are in our Upcoming Application Dates section.

Tuition Fees

Tuition fees vary depending when you start, your year, faculty, and program. Fees for Summer Term 2018 first-year Distance Career Arts & Science Domestic students are as follows: for a 3.0-unit course, $685.90; for a 6.0-unit course, $1371.80 See also Tuition and Fees.

Grading Scheme

The information below is intended for undergraduate students in the Faculty of Arts and Science. Academic Regulations in other Faculties may differ.

Letter Grade Grade Point

GPA Calculators
Have your SOLUS grade report handy and then follow the link to the Arts and Science GPA calculators.

How does this affect my academics?
See the GPA and Academic Standing page.

Follow the link above for an explanation of how the GPA system affects such things as the Dean’s Honour List, requirements to graduate, and academic progression.

Frequently Asked Questions on the Grading Scheme
Please follow this link to the FAQ's

Campus Bookstore

All textbooks can be purchased at Queen’s Campus Bookstore.

Non-Queen’s Students

All Queen’s Arts and Science Online courses are open to students at other universities. Before applying as a visiting student, request a Letter of Permission from your home university that states that you have permission to take the course and apply it to your degree. See also Apply.

Academic Integrity

Please see Queen’s policy statement on academic integrity for information on how to complete an online course honestly.