
MAT 219  Calculus III Credits: 4 Lecture Hours: 4 Lab Hours: 0 Practicum Hours: 0 Work Experience: 0 Course Type: Core Continuation of Calculus II. Topics include vectors and vectorvalued functions, tangent and normal vectors, arc length and curvature, vector fields, line and surface integrals, Green’s theorem, the divergence theorem and Stokes’s theorem, multivariable functions, partial derivatives, directional derivatives and gradients, optimization of multivariable functions. Prerequisite: MAT 217 or equivalent with a C or better Competencies
 Use and understand vectors in space
 Define vectors in the plane and space
 Calculate the dot product of two vectors
 Calculate the cross product of two vectors
 Apply vectors to the geometry of space
 Construct the equations of lines and planes in space
 Construct the equations of surfaces in space
 Evaluate vectorvalued functions
 Define vectorvalued functions
 Differentiate and Integrate of vectorvalued functions
 Apply vector valued functions
 Compute velocity and acceleration
 Compute tangent, normal and binormal vectors
 Compute arc length and curvature
 Utilize vector analysis is 2D
 Define and use vector fields
 Compute line integrals
 Use and understand Green’s Theorem
 Utilize vector analysis is 3D
 Compute parametric surfaces
 Compute surface integrals
 Use and understand the Divergence Theorem
 Use and understand Stroke’s Theorem
 Analyze multivariable functions
 Evaluate the limit of a multivariable function
 Discuss continuity of a multivariable function
 Evaluate the partial derivative of a multivariable function
 calculate the differential of a multivariable function
 Evaluate the derivative of multivariable function using the chain rule
 Find and discuss the directional derivatives of multivariable function
 find and discuss gradient of a multivariable function
 find the equation for a tangent plane
 Calculate optimum value of a multivariable function, with or without constraints
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