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- MAT 240 Calculus & Analytic Geometry III

**Exit Skills**

- Perform the basic operations of vector algebra including the calculation of dot products and projections, cross products, and scalar triple products.
- Write a vector equation, parametric equations, and symmetric equations of a line in space.
- Write an equation of a plane in space using vector form, point-normal form, and general form.
- Differentiate and integrate vector-valued functions.
- Find the arc length of a vector-valued function.
- Analyze the motion of a particle along a curve (position, velocity, speed, and acceleration).
- Calculate the curvature of a curve at a point.
- Find a unit vector that is normal to a surface.
- Graph various quadric surfaces and write the equation of the plane tangent to a surface at a point.
- Convert between rectangular, cylindrical, and spherical coordinates.
- Evaluate the limits and explore the continuity of functions of two or more vari-ables.
- Calculate the first and second partial derivatives of functions of two or more variables, using the multivariable chain rule as necessary.
- Calculate directional derivatives and the gradient of a function.
- Use LaGrange multipliers to maximize or minimize, subject to constraints, a function of two or more variables.
- Use the two-variable Second Partial Derivative Test to find maxima, minima, and saddle points for functions of two variables.
- Evaluate double integrals to calculate the area of a non-rectangular region, or of a region defined by polar curves, and to calculate the area of a surface defined in rectangular or cylindrical coordinates.
- Use triple integrals to find the volume and centroid of a solid, whether defined in rectangular, cylindrical, or spherical coordinates.
- Use the Jacobian for transformations in two- and three- spaces to evaluate multiple integrals by an appropriate change of variables.
- Evaluate line integrals and know when the result is independent of the path.
- Evaluate surface integrals.
- Use and apply the theorems of Green, Gauss, and Stokes.

**Objectives**

- Study vector algebra and introductory vector analysis.
- Find the equations of planes and lines in space.
- Graph surfaces, including quadric surfaces, and find the equation of the tangent plane.
- Study multivariable functions by using partial derivatives to find relative maximum(s)/minimum(s), including those with constraints and using multiple integrals to find volume and surface area.
- Generalize the concepts of functions, derivatives and integrals.

8 a.m.-4:30 p.m. Monday-Friday

Administration Building, Room 1242

636-922-8496

Phyllis Marchand

636-922-8496

phyllis_marchand@stchas.edu

Joseph (Joe) W. Howe

636-922-8318

jhowe@stchas.edu

Joshua (Josh) J. Niemczyk

636-922-8691

jniemczyk@stchas.edu

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