Course Overview:

This introductory calculus course develops students’ ability in understanding functions, limits, derivatives, and their applications in analyzing change. Students will learn key concepts in differential calculus, including rates of change, continuity, approximation, and optimization, and will then apply those skills across a variety of contexts involving polynomial, rational, exponential, logarithmic, and trigonometric functions. This course will also introduce multivariable functions and partial derivatives. Emphasis is placed on logical reasoning, mathematical modeling, and problem-solving using analytical and numerical techniques. This course prepares students for further study in calculus and quantitative disciplines and is suitable for students pursuing science, economics, business, computer science and social sciences.

Prerequisite:

  • The students must have completed grade 12 or equivalent education, or mature student status (19 years or older).
  • All applicants must meet one of the following Language Proficiency Requirements (LPR):
    • Completion of 2 years of secondary education (including English 10 and 11 with grade of ‘C’ or higher) from a country where English is one of the principal languages, or
    • Completion of 2 years of full-time post-secondary education at an accredited institution where English is the language of instruction, or
    • Students from non-English speaking countries must have completed grade 12 or equivalent education and provide verified results for one of the English Language Proficiency tests with minimum scores listed below:
      • IELTS 6.0, TOEFL 50, CAEL 45, CELPIP 6.5, DET 105, PTE 47, PCE 175, CAMBRIDGE B2 Level, LANGUAGECERT B2 Level, MET B2 Level, ITEP 3.8, EIKEN Grade Pre-1. or
    • Provide proof of achieving at least 65% in Grade 12 English (or equivalent) from a recognized institution.
  • Mature Student Applicants
    • Applicants who are 19 years of age or older at the start of the program, are Canadian citizens or permanent residents, and are unable to provide official secondary or post-secondary education records may demonstrate English proficiency by:
      • Submitting a signed attestation confirming they have completed at least three years of full-time education in English in a country where English is one of the primary languages and
      • Completing the Accuplacer English Assessment (Next Generation: Reading, Writing, and WritePlacer) with the following minimum scores:
        • Reading: 235
        • Writing: 235
        • WritePlacer: 4

Learning Outcomes:

Upon successful completion of this course, the students will be able to:

  • Analyze polynomial, rational, exponential, logarithmic, and trigonometric functions and graph their behaviours using transformations and limits.
  • Interpret formal and informal definitions of limits, continuity, and function behaviour near asymptotes and at infinity.
  • Compute derivatives using first principles and apply them to determine instantaneous rates of change and slopes of tangent lines.
  • Apply differentiation techniques, including the product, quotient, and chain rules, as well as implicit and logarithmic differentiation, to solve complex derivative problems.
  • Implement Newton’s Method, linear approximations, and differentials to estimate values and numerically solve equations.
  • Solve simple differential equations and use Euler’s Method and phase diagrams to model dynamic systems.
  • Develop logical reasoning and apply mathematical modeling strategies to represent and solve real-world problems in quantitative fields.

Course Content & Topics:

Class 1: Introduction to Functions and Graphs
Class 2: Limits and Continuity
Class 3: Derivatives and Rates of Change
Class 4: Differentiation Rules I
Class 5: Differentiation Rules II
Class 6: Applications of Derivatives I
Class 7: Applications of Derivatives II
Class 8: Linear Approximations and Differentials
Class 9: The Derivative in Physics and Engineering
Class 10: Introduction to Integration
Class 11: Multivariable Functions
Class 12: Applied Modelling and Real-World Problems
Class 13: Review and Cumulative Practice
Class 14: Final Assessment and Project Presentations

Credit Information:

  • Credits: 3

Duration:

  • 14 Weeks: 3 hrs/week

Course & Related Fees:

  • Domestic & International: $700 (Seven hundred dollars)

For a detailed breakdown, please refer to Policy #S-005 Programs & Course Fee Schedule

Non-Refundable Fees:

  • Application Fee: $50.00/course (payable online and non-refundable)