Multivariable Calculus

### 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 $\mathbf F(x,y) = (\cos x, \sin y)$.