MAT 241  Calculus III [SUN# MAT 2241] 4 Credits, 4 Contact Hours 4 lecture periods 0 lab periods
Continuation of MAT 231 . Includes vectors in two and three dimensions, vectorvalued functions, differentiation and integration of multivariable functions, and calculus of vector fields.
Prerequisite(s): Within the last three years: MAT 231 with a grade of C or better. GenEd: Meets AGEC  MATH; Meets CTE  M&S.
Course Learning Outcomes 1. Use vector operations to calculate equations of planes and vector equations of lines.
2. Use partial derivatives to analyze rates of change of multivariable functions in a variety of contexts.
3. Evaluate double and triple integrals of multivariable functions in a variety of coordinate systems.
4. Evaluate line and surface integrals in vector fields using a variety of theorems and techniques. Performance Objectives: 1. Use a Cartesian coordinate system in 3dimensional space; perform vector operations including the dot and cross products; and find the orthogonal projection onto a vector.
2. Determine equations of lines and planes in space, and identify and classify quadric surfaces.
3. Evaluate limits, derivatives and integrals of vectorvalued functions; analyze motion along a curve; and calculate the unit tangent vector, the unit normal vector, and the curvature.
4. Evaluate limits, determine continuity, and calculate partial derivatives of multivariable functions; apply the chain rule and use implicit differentiation; calculate directional derivatives and gradient vectors; find equations of tangent planes; determine extrema and saddle points; and use Lagrange multipliers to find constrained maximum and minimum.
5. Evaluate double integrals in rectangular and polar coordinates; convert between rectangular, cylindrical, and spherical coordinates; evaluate triple integrals in rectangular, cylindrical, and spherical coordinates; and use double and triple integrals to calculate volumes.
6. Determine if a vector field is conservative and find a potential function; evaluate line integrals of realvalued functions and vector fields; evaluate surface integrals of realvalued functions and vector fields; and use Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem to evaluate line integrals and surface integrals. Outline:
 Vectors and Analytic Geometry in the Plane and in Space
 Vectors in the plane and in space
 Dot product and cross product
 Orthogonal projections
 Lines, Planes, and Surfaces
 Lines and planes in space
 Quadric surfaces
 Vector Valued Functions
 Graph of a vector valued function
 Parametrized curves
 Arc length
 Unit tangent vector, unit normal vector, and curvature
 Projectile motion
 Functions of Two or More Variables
 Domain
 Limits and continuity
 Partial derivatives
 Differentiability
 Chain rule
 Implicit differentiation
 Linearization and differentials
 Directional derivatives, gradient vectors, and tangent planes
 Local extrema and saddle points
 Absolute extrema
 Lagrange multipliers
 Multiple Integrals
 Double integrals in rectangular and polar coordinates
 Cylindrical and spherical coordinates
 Triple integrals in rectangular, cylindrical, and spherical coordinates
 Applications
 Calculus of Vector Fields
 Vector fields
 Line integrals
 Path independence, potential functions, and conservative vector fields
 Parametrized surfaces
 Surface area and surface integrals
 Divergence and curl
 Green’s Theorem
 Divergence Theorem and Stokes’ Theorem
 Applications
Effective Term: Spring 2020
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