Functions of Several Variables. Limits and Continuity in Higher Dimensions. Partial Derivatives. The Chain Rule. Directional Derivatives and Gradient Vectors. Tangent Planes and Differentials. Extreme Values and Saddle Points. Lagrange Multipliers. Taylor’s Formula for Two Variables. Double and Iterated Integrals over Rectangles. Double Integrals over General Regions. Area by Double Integration. Double Integrals in Polar Forms. Triple Integrals in Rectangular Coordinates. Triple Integrals in Cylindrical and Spherical Coordinates. Substitutions in Multiple integrals. Line Integrals. Vector Fields. Green’s Theorem in the Plane. Surface Integrals. Stokes’ Theorem. The Divergence Theorem.
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