MATH& 151 - Calculus I

Credits: 5
Variable Credit Course: No

Lecture Hours: 55
Lab Hours: 0
Worksite/Clinical Hours: 0
Other Hours (LIA/Internships): 0

Course Description: This is the first in a sequence of four calculus courses for students who are planning to major in engineering, mathematics, or the sciences, and introduces the concepts of limits and differentiation. Topics include limits of algebraic, trigonometric, and exponential functions, the derivative of a function and derivative techniques, curve sketching, and an introduction to antiderivatives. Graphing technology required.

Prerequisite: Math& 142 with a grade of C or higher, appropriate placement score, or instructor permission.
Distribution Requirements:

Natural Sciences Distribution Requirement

Meets FQE Requirement: No
Integrative Experience Requirement: No

Student Learning Outcomes

Calculate limits of functions using graphs, numerical data and analytically with limit rules.
Evaluate limits using L’Hospital’s Rule.
Determine the continuity of a function using limits.
Define the derivative as a rate of change and use it in graphical and applied contexts.
Calculate the derivative of polynomial, rational, trigonometric, and other common transcendental functions using the rules of differentiation (power, chain, product, quotient, etc.)
Linearize a function using the derivative.
Construct graphs of functions using calculus, by finding local extremes, inflection points, and asymptotes.
Set up and solve applications, including optimization and related rates.
Compute numerical approximations using appropriate methods.
Compute elementary antiderivatives.

Course Contents

Limits. Evaluate limits. Determine continuity. L’Hospital’s Rule. Indeterminant forms. The precise definition of a limit (optional).
Derivatives. Derivatives as a rate of change. Limit definition of a derivative. Derivatives of polynomials, rational functions, exponential, and logarithm functions. Product Rule, quotient rule, chain rule. Higher order derivatives. Implicit differentiation. Derivatives of hyperbolic functions (optional).
Applications. Growth and decay. Related rates. Optimization. The Mean Value Theorem. The Intermediate Value Theorem (optional). Newton’s Method (optional).
Graphical Analysis. Intercepts. Asymptotes. Symmetry. Intervals of increasing and decreasing. Maximum and minimum values. Concavity and inflection points.
Other Topics. Compute basic anti-derivatives.

Instructional Units: 5