# MAT 240 Calculus & Analytic Geometry III

Exit Skills

1. Perform the basic operations of vector algebra including the calculation of dot products and projections, cross products, and scalar triple products.
2. Write a vector equation, parametric equations, and symmetric equations of a line in space.
3. Write an equation of a plane in space using vector form, point-normal form, and general form.
4. Differentiate and integrate vector-valued functions.
5. Find the arc length of a vector-valued function.
6. Analyze the motion of a particle along a curve (position, velocity, speed, and acceleration).
7. Calculate the curvature of a curve at a point.
8. Find a unit vector that is normal to a surface.
9. Graph various quadric surfaces and write the equation of the plane tangent to a surface at a point.
10. Convert between rectangular, cylindrical, and spherical coordinates.
11. Evaluate the limits and explore the continuity of functions of two or more vari-ables.
12. Calculate the first and second partial derivatives of functions of two or more variables, using the multivariable chain rule as necessary.
13. Calculate directional derivatives and the gradient of a function.
14. Use LaGrange multipliers to maximize or minimize, subject to constraints, a function of two or more variables.
15. Use the two-variable Second Partial Derivative Test to find maxima, minima, and saddle points for functions of two variables.
16. 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.
17. Use triple integrals to find the volume and centroid of a solid, whether defined in rectangular, cylindrical, or spherical coordinates.
18. Use the Jacobian for transformations in two- and three- spaces to evaluate multiple integrals by an appropriate change of variables.
19. Evaluate line integrals and know when the result is independent of the path.
20. Evaluate surface integrals.
21. Use and apply the theorems of Green, Gauss, and Stokes.

Objectives

1. Study vector algebra and introductory vector analysis.
2. Find the equations of planes and lines in space.
3. Graph surfaces, including quadric surfaces, and find the equation of the tangent plane.
4. 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.
5. Generalize the concepts of functions, derivatives and integrals.

#### Office Hours

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