# 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.