Complex analysis
BS BT DT BC BP BDT
Dr John Arkinstall
3 points * First semester * 2 hours per week * Gippsland/Distance (odd-numbered years only) * Prerequisites: GAS1611 * Prohibitions: Subject 7263 (previously named Complex analysis 1)
This subject develops the theory of functions of a 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 equation, 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, residues, the real 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. For Gippsland students, there is one two-hour lecture/tutorial class each week for thirteen weeks. For distance students, four two-hour problem-solving and expository classes are held over the semester, to supplement full notes, textbook, and assignments.
Assessment
Assignments: 40% * Examination: 60%
Prescribed texts
Fisher S D Complex variables Wadsworth, 1986
Recommended texts
Ahlfors L V Complex analysis 3rd edn, McGraw-Hill, 1976