# 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. This course is available to take individually or as part of a degree or certificate program. To enroll, speak with an Enrollment Representative.

### 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.
• Solve basic differential equations.

### Parametric Equations

• Use the polar coordinate system.
• Identify key features of the graphs of parametric equations.

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

### Three-Dimensional Space; Vectors

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

### Partial Derivatives

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

### 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.

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