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Course level: Undergraduate
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.
- MTH/290 – Calculus II OR
- equivalent or higher college mathematics course
What you'll learn
Course skills and outcomes
- 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, Polar Coordinates, and Conic Sections
- 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.
- 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.