Objectives: By the end of this module, students should be able to:

    Define the concept of scalar-valued and vector-valued functions of one or more variables
    Interpret and provide parametric representations of curves and surfaces
    Perform coordinate transformations for multivariable functions
    Define and compute different notions of differentiation for functions from R^n to R^m, including partial derivatives, the gradient, Jacobian matrix, directional derivative, divergence and curl
    Explain the definition of the Riemann integral of a multivariable function and provide geometric interpretations of such integrals
    Demonstrate understanding of integral theorems relating line, surface and volume integrals and use these theorems to evaluate such integrals
    Compute integrals of functions over simple domains and justify the change of area and volume elements when converting coordinates.