# 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:

1. Stewart, J. (2021). Single Variable Calculus: Early Transcendentals + Student Solutions Manual (9th ed.). Belmont, CA: Thomson Brooks/Cole.
Type: Textbook Bundle. ISBN: 9780357717127

Note: The previous 8th edition textbook + SSM is acceptable

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.

Note: 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.

Search To Top