MATH 241 — CALCULUS IV
Learning Objectives & Matches
Calculate partial derivatives of functions of two or more variables
Calculate directional derivatives and gradients for functions of two or more variables
Provide a geometrical interpretation of the cross product, directional derivative and gradient
Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
Find the equation of a plane tangent to a given surface at a specified point
Calculate the exact horizontal and vertical position of points on the Earth's surface.
Calculate higher-order partial derivatives
Find and analyze critical points for functions from R^n to R
Identify critical points in the manufacturing process and specify sampling procedures to be used at these points.
Evaluate double and triple integrals
Apply the techniques of multiple integration and partial derivatives to applied problems
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
Adapt statistical methods to solve specific problems in many fields, such as economics, biology, and engineering.
Perform computations and apply methods of numerical analysis to data.
Propose solutions in engineering, the sciences, and other fields using mathematical theories and techniques.
Formulate mathematical or simulation models of problems, relating constants and variables, restrictions, alternatives, conflicting objectives, and their numerical parameters.
Analyze problems to develop solutions involving computer hardware and software.
Develop methods for integrating different products so they work properly together, such as customizing commercial databases to fit specific needs.
Conduct logical analyses of business, scientific, engineering, and other technical problems, formulating mathematical models of problems for solution by computers.
Observe the current system in operation, and gather and analyze information about each of the component problems, using a variety of sources.
Calculate line and surface integrals
Calculate the exact horizontal and vertical position of points on the Earth's surface.
Compute dimensions, areas, volumes, and weights.
Smooth, polish, and bevel surfaces, using hand tools and power tools.
Measure surfaces or review work orders to estimate the quantities of materials needed.
Determine reference points, machine cutting paths, or hole locations, and compute angular and linear dimensions, radii, and curvatures.
Calculate amounts of required materials and estimate costs, based on surface measurements or work orders.
Demonstrate a facility with Green's, the divergence and Stokes' theorems
Install green plumbing equipment, such as faucet flow restrictors, dual-flush or pressure-assisted flush toilets, or tankless hot water heaters.