Math 220
Catalog Description:
Solid analytic geometry, vector algebra, partial derivatives, line surface and volume integrals, multiple integrals, vector field theory, Green's Theorem, Stoke's Theorem and Gauss' Theorem are topics included in this course.
Note: Mathematics 220 was formerly numbered Mathematics 6A.
Course Objectives:
1)Use vector algebra (addition, scalar multiplication, magnitude, dot-product and cross-product) in a variety of problems.
2)Determine equations of lines (parametric, symmetric and vector), planes and quadrics.
3)Find tangent, normal and binormal vectors, curvature, velocity and acceleration.
4)Convert between rectangular, cylindrical and spherical coordinates.
5)Determine limits and the continuity of functions of several variables, and prove the existence or non-existence of limits.
6)Calculate partial derivatives, and use the chain rule to find partial or total derivatives of functions of several variables.
7)Find tangent planes and differentials and use in applications.
8)Calculate directional derivatives and gradients and use in applications.
9)Determine extrema of functions of several variables with and without Lagrange multipliers and use in applications.
10)Find potential functions of conservative vector fields.
11)Evaluate multiple integrals directly and by converting to cylindrical or spherical coordinates.
12)Use multiple integrals to find plane areas, surface areas and volumes.
13)Evaluate line integrals, surface integrals and find flux.
14)Calculate the curl and divergence of vector fields and use these to solve problems.
15)Use Green's Theorem, Stoke's Theorem and Gauss' Theorem to solve a variety of problems.
SLO Statements
1)Students will find the equations of lines and planes in 3-dimensional space.
2)Students will locate points in space using rectangular, cylindrical and spherical coordinates.
3)Students will calculate the curvature of a space curve.
4)Students will calculate partial derivatives of functions of several variables.
5)Students willcalculate directional derivatives of functions of several variables.
6)Students willsolve optimization problems using Lagrange multipliers.
7)Students will calculate double and triple integrals.
8)Students will calculate line integrals.
9)Students will calculate the curl and divergence of vector fields.
10)Students will demonstrate an understanding of Stokes’ Theorem and the Divergence Theorem.
11)Students will be able to find the unit vector tangent to a given space curve at a given point.
12)Students will be able to find the standard form of the plane tangent to a given surface at a given point.