Material: see the homework assignments

Three handwritten pages of notes are allowed.

Important topics (new):

-- vector line intergral
-- arc length line integral
-- total mass of a wire of variable density
-- normal vectors and curvature
-- divergence
-- curl
-- conservative vector fields and potentials
-- Green's formula
-- surface integrals
-- Gauss' formula
-- Stokes' formula

Important topics (Test 2):

-- Vector partial derivatives.
-- Parametrized surfaces, parametric equations for the tangent plane.
-- Limits. Continuous functions.
-- Differentiable functions. Directional derivatives.
-- Tangent approximation.
-- Gradient fields.
-- Direction of maximum increase, maximum rate of increase.
-- Perpendicularity of the gradient to the level curves (surfaces).
-- Chain rule: in partial derivatives and in matrix form.
-- Inverse function theorem. Derivative of inverse function.
-- Implicit differentiation in partial derivatives.
-- Implicit differentiation in matrix form.
-- Local maxima and minima, second derivative test.
-- Conditional maxima and minima, Lagrange multipliers.
-- Absolute maxima and minima in a bounded domain.
-- Polar, cylindrical and spherical coordinates.
-- Multiple and iterated integrals.
-- Leibniz rule.
-- Change of order of integration in iterated integrals.
-- Change of variable in multiple integrals, Jacobian.
-- Total mass. Center of mass and centroid.
-- Improper integrals.

Important topics (Test 1):

-- dot product and length
-- parallel vectors, perpendicular vectors, angles between vectors
-- unit vectors and projections
-- parametric equation of a line
-- parametric equation of a plane
-- equation of a plane perpendicular to a given vector, standard and normalized equations of a plane
-- distance from point to a plane
-- cross product
-- area of a paralelograms and triangles, volume of a parallelepiped
-- equation of a plane paralell to given vectors
-- equation of a plane through three points
-- solving a system by elimination and by matrix methods
-- reduced matrices
-- homogenious sytem
-- general and particular solutions
-- matrix multiplcation
-- inverse of a matrix and how to find it
-- determinant and how to find it
-- derivatives, velocity and acceleration
-- arc length
-- intergration of vectors
-- level curves and surfaces
-- partial derivatives
-- mixed and higher order partial derivatives