Calculus I –

mth310

(4 credits)

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-level course is 7 weeks. To enroll, speak with an Enrollment Advisor.

Topics and Objectives

Functions and Rates of Change
- Recognize mathematical functions from graphs.
- Determine the effects of operations on a graph.
- Graph trigonometric functions.
- Calculate slopes of tangent lines at given points.
- Use limit laws to find limits of functions.
Limits and Continuity
- Calculate limits of functions.
- Calculate one-sided limits.
- Determine the continuity of functions at given points.
- Identify asymptotes of graphs.
Basic Derivatives
- Compute the derivatives of linear, quadratic, and polynomial functions.
- Find the derivative of the sum and difference of two functions.
- Find the derivative of the ratio and the product of two functions.
- Recognize derivatives as rates of change.
- Compute the derivative of trigonometric functions.
Chain Rule and Related Rates
- Find the derivative of the composition of two functions.
- 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
- Use derivatives to find extreme values of functions.
- Use the Mean Value Theorem to find the derivative of a continuous function.
- Find local extrema using the first derivative of a monotonic function.
- Determine critical points and points of inflection of functions with derivatives.
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.

The University of Phoenix reserves the right to modify courses.
While widely available, not all programs are available in all locations or in both online and on-campus formats. Please check with a University Enrollment Advisor.
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.

Calculus I –

mth310

Functions and Rates of Change

Limits and Continuity

Basic Derivatives

Chain Rule and Related Rates

Graphing and Applications

More Applications of Derivatives

Calculus I Concept Review

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