Multivariate Calculus
GENERAL EDUCATION: This course fulfills a General Education - Math requirement.

DESCRIPTION: Vectors, vector geometry, quadric surfaces, alternative coordinate systems, vector-valued functions, partial derivatives, gradient, optimization, multiple integration, vector fields, integral theorems of vector calculus, and applications. Math 214 and Math 215 cannot both be taken for credit.
TAUGHT: Winter, Summer, Fall
CONTENT AND TOPICS: Review of vectors and vector geometry. Vector valued functions, limits, continuity, derivatives and integrals of the same. Tangential and normal components of acceleration. Arc length as a parameter and curvature. Projectile motion. Functions of several variables, limits, continuity, and partial derivatives of the same. The total differential and error estimation. Tangents planes, normal lines, the gradient and directional derivatives. Free optimization, absolute extrema and LaGrange multipliers. Multiple and iterated integration, including Fubiniís Theorem. Applications of integration such as volume, surface area, the average value of a function, centers of mass and moments of inertia. Parameterized surfaces and integration in cylindrical and spherical coordinates. The change-of-variables problem and the Jacobian. Vector fields, div, grad, curl and their interpretation. Equivalent conditions for conservative vector fields. Greenís Theorem, Stokesí Theorem and the Divergence Theorem.
GOALS AND OBJECTIVES: 1. Calculate the results of vector addition, subtraction, scalar multiplication, dot product and cross product.
2. Perform calculations for geometry in space.
3. Convert between cylindrical, spherical, and rectangular coordinates.
4. Explain the application of differentiation of vector-valued functions to velocity and acceleration.
5. Find arc length and curvature of a given curve.
6. Evaluate partial derivatives and explain their meaning geometrically.
7. Use local linear approximation applications.
8. Produce a directional derivative for any given direction.
9. Locate and classify extrema for functions of two variables.
10. Apply 2- and 3- dimensional integration to geometric and physical problems.
11. Verify and use four major theorems of vector calculus.
REQUIREMENTS: All students must have their own text (currently Larson, Hostetler & Edwards, Calculus, 7th. edition). If a graphing calculator is to be used, each student must supply his or her own. Homework assignments and exams are required by all faculty. Students must attend classes and may be required to participate in computer labs, projects or other forms of learning and assessment, as determined by their instructor.
PREREQUISITES: Math 113 or the equivalent.
OTHER: (1) The faculty members who teach Calculus I use technology to varying degrees, from the occasional use of graphing calculators to requiring the use of Scientific Notebook, which includes basic features of the Maple computer algebra system. To facilitate the use of these technologies, the Department holds Calculus I classes in a multimedia classroom. A computer lab in the same building is available for the students to use.
(2) Math 214 meets four hours per week, for three semester credits. The fourth hour, traditionally a recitation hour, is used nowadays in the same manner as the other three.