VECTORS Rectangular coordinates in 3-space – Vectors – Dot product – Cross product – parametric equations of a line – planes in 3-space -Cylindrical and spherical coordinates VECTOR-VALUED FUNCTIONS Calculus of vector-valued functions – change of parameter – Arc length – Unit tangent and normal vectors – Curvature – Motion along a curve
FUNCTIONS OF TWO VARIABLES Limits and continuity – partial derivatives – Differentiability – the chain rule – Directional derivative – Tangent planes – Maxima and minima of functions of two variables – Lagrange multipliers
LINEAR ALGEBRA Systems of linear systems – Matrices -Determinants – Vectors – Vector spaces – Inner product spaces - Eigenvalues and eigenfunctions – Linear transformations
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