MATH 1141

Calculus I

3.0 Credits

Description

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.

Delivery Methods

Online, self-paced.

Prerequisites

Test MA 12, Pre-Calculus 12, or MATH 0633 or equivalent skills as established by the math placement test found at: http://www.tru.ca/__shared/assets/Math_Assessment_March_20123802.pdf, is strongly recommended.

Exclusions

MATH 1130, MATH 1150, MATH 1140, MATH 1157, MATH 1170, MATH 1171

Objectives

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 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 Outline

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

Course Duration

30 weeks.

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

Additional Requirements

A good-quality scientific calculator is required.

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.

Assessments

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.

Assignment 1 8%
Assignment 2 8%
Assignment 3 8%
Assignment 4 8%
Assignment 5 8%
Final Examination * 60%
Total 100%

* Mandatory