Perform operations on vectors and vector-valued functions, and use. Demonstrate the appropriate application of Green’s theorem, Stokes’ theorem, and the divergence theorem. Course Number and Title: MAT 283 Calculus III Analyze functions in three-dimensional space.Apply the concepts of independence of path, potential, and the curl of a vector-valued function.Evaluate the curl or divergence and the physical significance of a vector-valued function.Sketch vector and vector-valued functions (including parametric surfaces) in their appropriate vector fields.Evaluate line integrals over vector fields and physical applications.Find the area of a surface over a given region.Evaluate a triple integral over a solid using rectangular, cylindrical, or spherical coordinates.
Evaluate a double integral over a region that is rectangular or curved using rectangular or polar coordinates.Express the area of a region in terms of one or more iterated integrals using rectangular, polar, or parametric equations.Evaluate multiple integrals, and apply them to solve problems involving areas and volumes over two- and three-dimensional regions.Determine extrema using Lagrange multipliers and the discriminant.Use the concept of directional derivatives and the gradient in determining equations of tangent planes and normal lines.Apply concepts of increments and the chain rule to derivatives of the composition of functions.Determine partial derivatives of a multivariable function.
Use partial derivatives, the gradient, and directional derivatives to solve application problems.Use vectors to solve problems of curvilinear motion involving the concepts of velocity, acceleration, arc length, curvature, tangential, and normal components.Perform operations with vectors and vector-valued functions utilizing the concepts of scalars, unit vectors, dot product, cross product, orthogonal vectors, components, limits, differentiation, and integration.Perform operations on vectors and vector-valued functions, and use them to solve problems in two- and three-dimensional space.Determine equations of surfaces and curves in three-dimensional space.Determine the graph of an equation in three-dimensional space, including quadric surfaces.Determine the domain of a multivariable function.Sketch level curves and surfaces of multivariable functions.Determine limits and continuity of multivariable functions.
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