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.
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
An Open Learning Faculty Member is available to assist students. Primary communication is
through the Learning Environment's "Mail" tool or by phone. Students will receive the necessary
contact information at the start of the course.