Course Description

This course builds on the concepts of presented in MTH/310 Calculus I and MTH/320 Calculus II. Students examine functions of more than one variable, curves in space, and Newtonian mechanics in three dimensions. Students explore partial derivatives and differentials as well as local and global extrema. In addition, students use differentiation techniques for functions of many variables.

This undergraduate course is 5 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.

Course Objectives

Differential Equations

  • Solve basic differential equations.
  • Approximate first-order equations numerically using slope fields and Euler's method.
  • Model real-life situations using differential equations.
  • Use graphical methods to solve autonomous equations.
  • Use phase-plane analysis to solve systems of differential equations.

Parametric Equations, Polar Coordinates, and Conic Sections

  • Identify key features of the graphs of parametric equations.
  • Calculate geometric values of parametric curves.
  • Use the polar coordinate system.
  • Graph curves using polar coordinates.
  • Compute areas and lengths in polar coordinates.
  • Identify the equations of conic sections.
  • Apply the polar coordinate system to conic sections.

Three-Dimensional Space; Vectors

  • Solve equations in three dimensions.
  • Describe physical properties using vectors.
  • Perform dot products and cross products.
  • Evaluate planes in space.
  • Evaluate quadric surfaces.

Partial Derivatives

  • Evaluate functions of multiple variables.
  • Determine continuity of functions.
  • Determine partial derivatives of functions.
  • Use the Chain Rule for derivatives.
  • Compute gradient vectors from directional derivatives.
  • Find relative and absolute extrema for functions of two variables.

Second-Order Differential Equations

  • Solve basic second order differential equations with initial values or boundary conditions.
  • Use variation of parameters to solve nonhomogeneous equations.
  • Solve applied harmonic oscillation problems with second order differential equations.
  • Find general solutions to Euler equations.
  • Use the power series method to solve second order homogeneous differential equations.


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.

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 888-484-1815.


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. 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.


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Instructor Led
T, M
12:00AM to 11:59AM
Jan 12, 2021 to Feb 15, 2021
Online Campus
Online Non-Degree
Schedule and Location
Contact Hours
  • Online Campus
Course Fee(s)
Undergraduate Tuition credit (3 units) $1,194.00 Click here to get more information
Section Fees
Resource Fee $170.00 Mandatory
3 Credit Hours
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