Vector and Tensor Fields: transformation properties, algebraic and differential operators and identities, geometric interpretation of tensors, integral theorems. Dirac delta-function and Green's function technique for solving linear inhomogeneous equations. N-dimensional complex space: rotations, unitary and hermitian operators, matrix-dyadic-Dirac notation, similarity transformations and diagonalization, Schmidt orthogonalization. Introduction to functions of a complex variable: analyticity, Cauchy's theorem, Taylor and Laurent expansions, analytic continuation, multiple- valued functions, residue theorem, contour integration, asymptotics. As techniques are developed, they are applied to examples in mechanics, electromagnetism and/or transport theory.