Mathematics

Material on Test 4

13.1 Vector fields: sketch, match plot with formula.

13.2 Line integrals: evaluation, approximate evaluation from a sketch (problem 13), mass of a wire.

13.3 Fundamental theorem for line integrals: checking whether a vector field in the plane is conservative; finding the potential function of a conservative vector field in the plane or space; using a potential function to evaluate a line integral.

13.4 Green's Theorem: can be used to convert a line integral to a double integral, or to convert a double integral to a line integral.

13.5 Curl and divergence: finding curl and divergence; estimating curl and divergence from a sketch; using curl to check whether a vector field in space is conservative.

10.5 and pages 786 - 787 Parametric surfaces: finding a parametric representation; tangent plane.

12.6 Surface area of a parameterized surface.

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