• Discuss the fundamentals of vector calculus from a more advanced perspective (differential forms, gradient, directional derivative, divergence, curl, Laplacian, and differential forms)
• Place them in the physical context for which they were initially developed and learn the story of their creation.
  
• Read a serious mathematics book from page 1 to page 360.  

Learning Outcomes
    Math 350 - Upon successful completion of Math 350 - Vector Analysis, a student will be compute and analyze:

• Scalar and cross product of vectors in 2 and 3 dimensions represented as differential forms or tensors,
• The vector-valued functions of a real variable and their curves and in turn the geometry of such curves including curvature, torsion and the Frenet-Serre frame and intrinsic geometry,
• Scalar and vector valued functions of 2 and 3 variables and surfaces, and in turn the geometry of surfaces,
• Gradient vector fields and constructing potentials,
• Integral curves of vector fields and solving differential equations to find such curves,
• The differential ideas of divergence, curl, and the Laplacian along with their physical interpretations, using differential forms or tensors to represent derivative operations,
• The integral ideas of the functions defined including line, surface and volume integrals - both derivation and calculation in rectangular, cylindrical and spherical coordinate systems and understand the proofs of each instance of the fundamental theorem of calculus, and
• Examples of the fundamental theorem of calculus and see their relation to the fundamental theorems of calculus in calculus 1, leading to the more generalised version of Stokes' theorem in the setting of differential forms.