## MAT 2290 Calculus & Analytic Geometry III

Vectors in the plane and space, dot and cross product of two vectors. Lines, planes and surfaces in space, vector-valued functions, arc length and curvature. Functions of several variables, partial derivatives with applications, multiple integrals with applications, line integrals, surface integrals, vector fields, Green’s Theorem, the Divergence Theorem and Stokes’ Theorem.

Division: Science, Mathematics and Engineering
Department: Mathematics
Repeatable Credit: No
Offered Online: No

Prereqs: MAT 2280

#### Outcomes

• Evaluate multiple integrals using rectangular, polar, cylindrical, and spherical coordinates. Calculate surface area using double integrals. Determine mass, center of mass, and moments of inertia of planar and solid regions with continuous density functions. Apply multiple integrals to solve applied problems.
• Demonstrate the ability to perform operations involving vectors in the plane and in space. Calculate the divergence and curl of a vector field and the flux of a field through a surface. Evaluate line and surface integrals of functions and of vector fields. Determine the graphs and the equations of tangent planes and normal lines to surfaces in space. Determine if a vector field is conservative, and if so, find the potential function. Determine if a line integral is independent of path. Apply line integrals and surface integrals to solve applied problems. Use the Fundamental Theorem of Line Integrals, Green's Theorem, the Divergence Theorem, and Stokes' Theorem to evaluate various integrals.
• Calculate limits, partial derivatives, directional derivatives, gradients, and differentials of functions of several variables. Determine when a function of several variables is continuous or differentiable and determine extrema using the second partials test and Lagrange multipliers. Apply partial derivatives, gradients, differentials, chain rules, and Lagrange multipliers to solve applied problems.
• Evaluate the derivative and integral of a vector-valued function. Demonstrate the ability to graph lines, planes, and surfaces in space and the ability to determine their equations when given sufficient information. Determine the length of a curve in space, and the curvature of a curve at a point using the unit tangent vector and the principal unit normal vector.

#### Credit Hours: 5

Classroom Hours: 5