SYLLABUS:

Functions of several variables. Limits and Continuity of functions of several variables. 14.1, 14.2.

Partial Derivatives. The Chain Rule. 14.3, 14.4

Directional Derivative and Gradient Vectors. Tangent Planes and Differentials. 14.5, 14.6.

Extreme Values and Saddle Points. 14.7.

Lagrange Multipliers. 14.8.

Taylor's Formula for functions of two variables. 14.10.

MIDTERM 1 EXAMINATION

Polar coordinates. Graphing in polar coordinates. 10.5, 10.6.

Double integrals. Areas as a Double integral. Double Integrals in polar coordinates. 15.1, 15.2, 15.3.

Cylindrical and Quadric Surfaces. 12.6.

Triple Integrals in Rectangular Coordinates.  15.4.

Triple Integrals in Cylindrical and Spherical Coordinates. 15.6.

Substitution in Multiple Integrals. 15.7.

Vector Valued functions.  Arc Length and the unit tangent vector. 13.1, 13.3.

MIDTERM II EXAMINATION

Line Integrals and Vector Fields 16.1, 16.2.

Path Independence. Potential Functions. 15.7

Green's Theorem. 16.4.

Surface Integrals. Parametric surfaces. 16.5, 16.6.

Stokes' Theorem. 16.7.

Divergence Theorem. 16.8.