Sections: up to section 7.6
Material: see the homework assignments

Two handwritten pages of notes are allowed.

Important topics:
-- 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.