Calculus III –

mth380

(3 credits)

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-level course is 5 weeks. To enroll, speak with an Enrollment Advisor.

Topics and 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
- 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.

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 III –

mth380

Differential Equations

Parametric Equations

Three-Dimensional Space; Vectors

Partial Derivatives

Second Order Differential Equations

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