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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.
-
Second Order Differential Equations
- Use the power series method to solve second order homogeneous differential equations.
- Find general solutions to Euler equations.
- Solve applied harmonic oscillation problems with second order differential equations.
- Use variation of parameters to solve nonhomogeneous equations.
- Solve basic second order differential equations with initial values or boundary conditions.
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Partial Derivatives
- Find relative and absolute extrema for functions of two variables.
- Compute gradient vectors from directional derivatives.
- Use the Chain Rule for derivatives.
- Determine partial derivatives of functions.
- Determine continuity of functions.
- Evaluate functions of multiple variables.
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Three-Dimensional Space; Vectors
- Evaluate quadric surfaces.
- Evaluate planes in space.
- Perform dot products and cross products.
- Describe physical properties using vectors.
- Solve equations in three dimensions.
-
Parametric Equations
- Apply the polar coordinate system to conic sections.
- Identify the equations of conic sections.
- Compute areas and lengths in polar coordinates.
- Graph curves using polar coordinates.
- Use the polar coordinate system.
- Calculate geometric values of parametric curves.
Identify key features of the graphs of parametric equations.
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Differential Equations
- Use phase-plane analysis to solve systems of differential equations.
- Use graphical methods to solve autonomous equations.
- Model real-life situations using differential equations.
- Approximate first-order equations numerically using slope fields and Euler's method.
- Solve basic 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.
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