Text: Basic Multivariable Calculusby Marsden, Tromba, Weinstein

• Vectors; dot and cross products; lines and planes (1.1 - 1.5)

• Curves in Euclidean space; tangent vectors and lines (1.6)

• Graphs, level surfaces, partial derivatives and continuity (2.1 - 2.2)

• Differentiability, the derivative matrix, tangent planes (2.3)

• The Chain Rule (2.4)

• Gradients, Directional Derivatives (2.5)

• Implicit Differentiation, Curves and acceleration (2.6, 4.1)

• Arc length (4.2)

• Vector Fields (4.3)

• Divergence and Curl (4.4)

• Divergence and Curl / Volumes (4.4 – 5.1)

• Double Integrals and Riemann sums (5.2)

• Double Integral over rectangle (5.2 – 5.3)

• Double integrals over other regions (5.3)

• Triple Integrals (5.4)

• Change of variables (cylindrical and spherical coordinates) (5.5)

• Change of variables (cylindrical and spherical coordinates) (5.5)

• Line Integrals (6.1)

• Line Integrals (6.1)

• Parametrized surfaces (6.2)

• Area of a surface (6.3)