Engineering Mathematics I

CATALOG DESCRIPTION: Polar Coordinates, parametric curves, vectors, vector geometry, vector-valued functions, partial derivatives, gradient, optimization, multiple integration, vector fields, integral theorems of vector calculus. Emphasis on methods and applications. Math 215 and Math 113 cannot both be taken for credit. Similarly Math 215 and Math 214 cannot both be taken for credit.
TOPICS: (Note: As many as possible of the following topics are accompanied by applications.) Calculus in the contexts of conic sections, polar coordinates and parametric curves. Vectors in R^2 and R^3. The dot and cross products. Distance, angles, lines and planes. Quadric surfaces. Cylindrical and spherical coordinates. 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 Fubini's Theorem. Applications of multiple 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-veriables problem and the Jacobian. Vector field, div, grad, curl and their interpretation. Equivalent conditions for conservative vector fields. Green's Theorem, Stokes' Theorem and the Divergence Theorem.
OBJECTIVES: Math 215 introduces students to the tools of multivariable calculus and to science and engineering problems that it can solve. Students will develop a heuristic understanding of how and why the tools work, as well as how to decide which tools to use in solving a given problem.
PREREQUISITES: Math 112 or the equivalent.
EFFECTIVE DATE: January 2003