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Topics covered:
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Series. Review of series concepts, power series expansion
and interval of convergence, Taylor and Maclaurin
series.
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Parametric equations and polar coordinates. Parametric equations,
tangents, areas, polar coordinate system, graphs, areas.
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Vectors and the geometry of space. Vectors and vector operations,
dot and cross products, equations of lines and planes, quadric surfaces,
cylindrical and spherical coordinates.
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Vector functions. Vector functions and space curves, differentiation
and integration of vector functions, arc length, velocity and acceleration.
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Partial derivatives. Functions of several variables,
limits and continuity, partial derivatives, tangent planes, the chain rule,
directional derivatives and the gradient vector, maximum and minimum values,
Lagrange multipliers.
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Multiple integrals. Double integrals over rectangles, iterated
integrals, double integrals over general regions, double integrals in polar
coordinates, triple integrals.
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Here are some useful links.
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