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# 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 vector-valued 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
1. Use and understand vectors in space
1. Define vectors in the plane and space
2. Calculate the dot product of two vectors
3. Calculate the cross product of two vectors
2. Apply vectors to the geometry of space
1. Construct the equations of lines and planes in space
2. Construct the equations of surfaces in space
3. Evaluate vector-valued functions
1. Define vector-valued functions
2. Differentiate and Integrate of vector-valued functions
4. Apply vector valued functions
1. Compute velocity and acceleration
2. Compute tangent, normal and bi-normal vectors
3. Compute arc length and curvature
5. Utilize vector analysis is 2D
1. Define and use vector fields
2. Compute line integrals
3. Use and understand Green’s Theorem
6. Utilize vector analysis is 3D
1. Compute parametric surfaces
2. Compute surface integrals
3. Use and understand the Divergence Theorem
4. Use and understand Stroke’s Theorem
7. Analyze multi-variable functions
1. Evaluate the limit of a multi-variable function
2. Discuss continuity of a multi-variable function
3. Evaluate the partial derivative of a multi-variable function
4. calculate the differential of a multi-variable function
5. Evaluate the derivative of multi-variable function using the chain rule
6. Find and discuss the directional derivatives of multi-variable function
7. find and discuss gradient of a multi-variable function
8. find the equation for a tangent plane
9. Calculate optimum value of a multi-variable function, with or without constraints