MAT 240 Calculus & Analytic Geometry III

Exit Skills

1. Graph spheres and cylindrical surfaces in 3-space.
2. Perform vector algebra including dot product and projections, cross product and triple scalar product.
3. Find vector equation and parametric equation of a line in space.
4. Find vector equation, point-normal form and general form of equation of plane.
5. Graph quadric surfaces.
6. Convert between rectangular, cylindrical and spherical coordinates.
7. Find limit of, differentiate, and integrate vector-valued functions. Find arc length for vector-valued functions and determine motion-velocity, speed and acceleration-along a curve.
8. Find unit tangent and normal vectors to surfaces. Calculate curvature.
9. Determine limit and continuity of functions of two or more variables.
10. Calculate first and second partial derivatives of function of two or more variables.
11. Demonstrate differentiability and chain rules for functions of two or more variables; calculate directional derivatives and gradients. Generalize chain rule for functions of n-variables.
12. Use second partials test for find maxima and/or minima and/or saddle points for functions of two variables.
13. Use Lagrange Multipliers to maximize/minimize, subject to constraints, a function of two or more variables.
14. Integrate double integrals to find area over nonrectangular region or in polar coordinates and surface area.
15. Use triple integrals to find volume of solids, centroids and centers of gravity and in spherical and cylindrical coordinates.
16. Calculate Jacobian for two and three-spaces. Evaluate multiple integrals by change of variables.
17. Evaluate a line integral and relation to independence of path.
18. Evaluate surface integrals including vector-valued functions.
19. Apply Green’s Theorem, the Divergence Theorem and Stokes’ Theorem.

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.