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.        

Fall semester.