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MATH 1141: Calculus I

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.

Learning outcomes

  • 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 differentiability.
  • 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 them.
  • 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.

Course topics

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

The following materials are required for this course:

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 Learning.
Type: Textbook: ISBN: 978-1-305-27242-2

Additional requirements

A good-quality scientific calculator is required.

Assessments

Please be aware that should your course have a final exam, you are responsible for the fee to the online proctoring service, ProctorU, or to the in-person approved Testing Centre. Please contact exams@tru.ca 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.

The final exam for this course is only available as a paper exam and must be taken in person at an approved Testing Centre. Please email exams@tru.ca with any questions.

Assignment 1 10%
Assignment 2 10%
Assignment 3 10%
Assignment 4 10%
Assignment 5 10%
Final Exam (mandatory) * 50%
Total 100%

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.

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