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Apr 16, 2024
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MATH 2254 - Calculus III* 4 Credits
Calculus III introduces three-dimensional mathematics. Topics include vector geometry and vector functions; space curves and the calculus of vector functions; multi-variable functions and their graphs in three dimensions; partial derivatives; applications of partial differentiation including directional derivatives and three-dimensional optimization; multiple integrals; triple integrals using spherical and cylindrical coordinates; vector fields and Green’s Theorem and Stoke’s Theorem if time permits.
Prerequisite: MATH 2224 - Calculus II* with a grade of “C” or better
Course Level Objectives
Upon successful completion of this course the student will be able to:
1. Utilize basic vector operations such as the dot product and cross product in applications. (GEO 3)
2. Find equations of lines and planes in 3-space. (GEO 3)
3. Identify basic quadric surfaces and cylinders. (GEO 3)
4. Evaluate limits, derivatives, and integrals of vector-valued functions of one variable and for the associated curves find arc length, curvature, tangent lines, unit tangent vectors, principle unit normal vectors, and binormal vectors. (GEO 2, 3)
5. Compute limits, partial derivatives, directional derivatives, and gradients for functions of several variables. (GEO 3)
6. Use differentiation to determine tangent planes, relative extrema, and absolute extrema of continuous functions on closed and bounded regions for functions of several variables. (GEO 3)
7. Use Lagrange multipliers to find extrema of a function subject to one constraint. (GEO 3)
8. Apply multiple integrals in 2 and 3 dimensions, in various coordinate systems to calculate areas, volumes, surface areas, mass, and centers of mass. (GEO 2, 3)
9. Evaluate line integrals, surface integrals and flux integrals directly. (GEO 3)
10. Apply the Fundamental Theorem of Calculus for Line Integrals, and Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem appropriately. (GEO 1, 3)
11. Identify conservative vector fields and find potential functions for conservative vector fields. (GEO 3)
12. Solve 2nd order linear differential equations. (GEO 3)
13. Use technology to collaborate, solve problems, represent data, and present solutions. (GEO 1, 4)
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