This course is an introduction to differential calculus. Students explore limits and continuity. They examine the basic concept of differentiation and practice differentiation techniques. Students develop competence applying differentiation to solve problems. Students also examine simple antiderivatives.
This undergraduate course is 7 weeks.
This course has a prerequisite. Please see details in the Prerequisite section below.
Attendance and participation are mandatory in all university courses, and specific requirements may differ by course. If attendance requirements are not met, a student may be removed from the course. Please review the Course Attendance Policy, Tuition Refund Policy and all University Policies in the Catalog for more information.
Topics and Objectives
Functions and Rates of Change
- Graph various functions.
- Create new functions performing scaling and shift operations.
- Calculate slopes of tangent lines to a curve at given points.
Limits and Continuity
- Determine limits of functions.
- Assess the continuity of functions at given points.
- Compute the derivatives of linear, quadratic, polynomial, and trigonometric functions.
- Apply differentiation rules for powers, multiples, sums, differences, products, and quotients.
- Recognize derivatives as rates of change.
Chain Rule and Related Rates
- Find the derivative of the composition of two functions, using the chain rule.
- Calculate the derivative of multivariable expressions, implicit differentiation.
- Derive rates of change from related known rates of change.
- Approximate derivatives using linearization.
Graphing and Applications
- Determine extrema, concavity, and critical points of functions using derivatives.
- Evaluate a continuous function using the Mean Value Theorem to find the derivative.
More Applications of Derivatives
- Solve applied optimization problems.
- Approximate a solution to an equation using Newton’s method.
- Recover the antiderivative of simple polynomial and trigonometric functions.
Calculus I Concept Review
- Apply the concepts presented in this course.
A prerequisite is required for this course. The purpose of a prerequisite is to ensure students have the knowledge and/or skills needed to be successful in the course. Students are required to provide proof of prerequisite during the enrollment/registration process. To meet to a course prerequisite requirement, a student must have successfully completed the prerequisite course at University of Phoenix, provide proof via transcript of completing a comparable course (at least 75% match) or higher level course with at least a grade of C at another institution or have a University of Phoenix approved Student Appeal on file with the University.
This course requires the prerequisite below. Click on the prerequisite course to review the course topics and objectives.
- MTH/225 – Pre-Calculus OR
- equivalent or higher college mathematics course
During the checkout process you will be prompted to provide proof of the requirement(s). If you completed the prerequisite at another institution be prepared to upload an official/unofficial transcript. If you have questions about meeting the prerequisite requirements for this course please contact an enrollment representative at 866-354-1800.
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While widely available, not all programs are available in all locations or in both online and on-campus formats. More information about eligibility requirements, policies, and procedures can be found in the catalog.
Transferability of credit is at the discretion of the receiving institution. It is the student’s responsibility to confirm whether or not credits earned at University of Phoenix will be accepted by another institution of the student’s choice.