MAT3016

Complex analysis

Not offered in 1998

Dr John Arkinstall

4 points
* First semester
* Two hours of lectures and one 1-hour tutorial per week
* Gippsland, Peninsula and distance (odd-numbered years only)
* Prerequisite GAS1615 or MAT1085
* Prohibitions: MAT3011, GAS3613
* Note: For distance education students, optional weekend school classes are available.

Objectives The objectives of this subject are for students to develop an understanding of the theory and techniques of calculus, applied to complex valued functions of a complex variable; understand the forms of representation of such functions, including multi-valued functions and series; become skilled in computational techniques involving complex functions and skilled in the choice of appropriate methods; become skilled in the computation of residues of complex functions at singularities, and in the interpretation of these in the context of various types of integrals and in finding inverse Laplace transforms.

Synopsis This subject develops the theory of functions of one complex variable and introduces diverse applications of this theory; complex sequences and series, functions of a complex variable, limits, continuity, points of discontinuity; differentiation of functions of a complex variable, singular points, the Cauchy Riemann equations, harmonic functions; contours, line integrals, contour integration, Cauchy's theorem, Cauchy's integral formulas and related results, Power series, Taylor series, Laurent series, Taylor's theorem, Laurent's theorem, use of complex variables in Fourier series; residues, real infinite integrals, inversion of Laplace transforms using the Bromwich integral formula; transformations, the bilinear transformation, conformal mapping, the Joukowski aerofoil; Laplace's equation in two independent variables, boundary value problems, Poisson's integral formulae for the circle and half-plane.

Assessment Two assignments: 30%
* Examination (3 hours): 70%

Prescribed texts

Fisher S D Complex variables Wadsworth, 1986

Recommended texts

Ahlfors L V Complex analysis 3rd edn, McGraw-Hill, 1976