Vector Geometry

• Vectors in Sage. Vectors in Sage.
• Magnitude of a Vector. Calculating the magnitude of any vector.
• Dot Product. Calculating the dot product of any two vectors.
• Cross Product. Calculating the Cross product of any two vectors.

Concepts for Multivariate Functions

• Multivariable Functions. Multivariable functions in Sage.
• Converting a multivariable function to a parametric function Using sage to convert a multivariable function to a parametric function.
• A simple three-dimensional plot. Plotting $\sin y - \cos x$.
• A simple plot in polar coordinates. Plotting $r = \cos \theta$.

Differentiation of Multivariable Functions

• Partial Derivatives. Calculating partial derivatives.
• Gradients. Calculating the gradient of a multivariate function.

Integration of Multivariable Functions

• Double Integrals. Calculating Double Integrals.

Vector Fields

• Plotting Two-Dimensional Vector Fields. Plotting a vector field for $\mathbf F(x,y) = (\cos x, \sin y)$.