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.
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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