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

CATALOG 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.
DESCRIPTION: The third of a three-semester sequence, this course is intended for students in mathematics, engineering and the physical sciences. It is essentially a traditional course, though it incorporates the use of electronic technology as a body of tools for learning and for calculation. Additionally, faculty members often incorporate some of the tools and methods that have grown out of nationwide efforts to reform Calculus education.
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.
OBJECTIVES: Students in Math 214 develop enough of the basic tools of Multivariate Calculus to solve a wide variety of problems involving vector valued functions, functions of several variables, and vector fields. They also learn how to construct their own solutions to such problems and how to verify their solutions. As they acquire the multivariate point of view, they deepen their understanding of Calculus and of mathematical modeling. Furthermore, they ready themselves for abstraction of mathematical concepts and for a variety of educational experiences in many disciplines.

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.