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Second Order Differential Equations
- Find general solutions to Euler equations.
- Use the power series method to solve second order homogeneous 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.
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.
- Determine partial derivatives of functions.
- 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.
- 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.
- 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.
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