MATH 1131 Syllabus

Subject Code

MATH

Course Number

1131

Course Title

Calculus I

Prerequisites

MATH 1113 with a grade of C or higher or placement by diagnostic testing

Corequisites

Terms Offered

Offered every semester

Credit Hours

(3-1-4)

Course Description

This course includes the study of limits and continuity, derivatives, and integrals of functions of one variable. Applications are incorporated from a variety of disciplines. Students will study algebraic, trigonometric, exponential, and logarithmic functions.

Course Outcomes

Derivatives and Applications

• Calculate limits of functions.
• Understand the definition of continuity.
• Differentiate algebraic, trigonometric, exponential, and logarithmic functions.
• Apply the Chain Rule.
• Perform implicit differentiation.
• Calculate higher derivatives.
• Solve related rate problems.
• Understand the Mean Value Theorem.
• Apply the Mean Value Theorem.
• Apply the First Derivative Test.
• Apply the Second Derivative Test.
• Determine the critical numbers and points of inflection.
• Solve optimization problems.

Introduction to Integration and Applications

• Find the most general antiderivative of a function.
• Understand and use sigma notation.
• Calculate area using the limiting value of approximating polygons.
• Understand the definition of definite integral.
• Apply the properties of definite integrals.
• Apply both parts of the Fundamental Theorem of Calculus.
• Apply the Substitution Rule for integrals.
• Calculate the area between two given curves in a plane.
• Calculate volumes using the disk method and method of cylindrical shells.