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·
Three-Dimensional Space; Vectors o Vectors (Dot
product; Projections , Cross product
) o Parametric equations of lines o Planes in 3-space ·
Vector-Valued Functions o Calculus of Vector-Valued Functions o Change of Parameter; Arc length o Unit Tangent,Normal, and Binormal Vectors o Curvature ·
Partial
Derivatives o Functions of Two or More Variables o Limits and
Continuity, Partial Derivatives o Differentiability,
Differentials, and Local Linearity, The Chain Rule o Directional Derivatives and Gradients o Tangent Planes
and Normal Vectors, Maxima and Minima
of Functions of Two Variables o Lagrange Multipliers ·
Multiple
Integrals o Double Integrals
( Nonrectangular Regions, Polar
Coordinates) o Parametric Surfaces; Surface Area o Cylindrical and Spherical Coordinates o Triple Integrals
( Cylindrical and Spherical Coordinates o Change of Varibales in Multiple Integrals; Jacobians o Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces o Quadratic Surfaces ·
Topics
in Vector Calculus o Vector Fields,
Line Integrals o Independence of Path; Conservative Vector Fields o Green’s Theorem
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