This is considered a first course in calculus, primarily for students intending to continue to
advanced courses in calculus, and mathematics in general. Students conduct a detailed study of
differential calculus and its applications, and are introduced to antiderivatives.
Upon the completion of this course, the student will be able to:
- Know what a function is and know the four ways to represent a function.
- Appreciate how functions can be used to model situations such as population growth, tides,
vibrating springs, and gas emissions.
- Make new functions from old by transforming, combining, and composing.
- Know when a function has an inverse and how to find the inverse.
- Know and sketch the members of the catalogue of essential functions.
- Understand the concepts of a limit and one-sided limits, continuity, and
- Determine limits numerically, algebraically, and from a graph.
- Determine limits of indeterminate forms, using l'Hospital's Rule.
- Understand the concepts of continuity and differentiability and the relationship between
- Know the differentiation formulas for polynomial, rational, trigonometric, inverse
trigono¬metric, exponential, and logarithmic functions.
- Apply the rules and techniques of differentiation to any combination of functions.
- Apply the derivative to solve a variety of problems (related rates problems, optimization
problems, curve sketching).
- Use the derivative to find the linear approximation of a function.
- Use Newton's method to find the roots of a function.
- Understand the concept of the antiderivative, and find antiderivatives.
Unit 1: Function and Models
Unit 2: Limits and Derivatives
Unit 3: Differentiation Rules
Unit 4: Applications of Differentiation I
Unit 5: Applications of Differnentiaion II
Required text and materials
Stewart, J. (2016). Single Variable Calculus: Early Transcendentals (8th
ed.). Boston, MA: Cengage Learning.
Type: Textbook: ISBN: 978-1-305-27033-6
Anders, D., Cole, J.A., & Drucker, D. (2016). Student Solutions Manual for Stewart’s
Single Variable Calculus: Early Transcendentals (8th ed.). Boston, MA: Cengage
Type: Textbook: ISBN: 978-1-305-27242-2
A good-quality scientific calculator is required.
Please be aware that should your course have a final exam, students are responsible for the fee to the online proctoring service, ProctorU, or to the in person approved Testing Centre. Please contact firstname.lastname@example.org with any questions about this.
To successfully complete this course, students must achieve a passing grade of 50% or higher on
the overall course and 50% or higher on the mandatory Final Exam.
|Final Examination *
Open Learning Faculty Member Information
An Open Learning Faculty Member is available to assist students. Students will receive the necessary contact information at the start of the course.