Real and Complex Analysis

Course aim

To develop systematic methods of real analysis and to introduce the classical results of multivariable calculus and complex variable analysis.

Course content

Real and complex numbers; topology of Euclidean spaces; functions, limits and continuity; Cauchy sequences; functions of more than one variable; partial derivatives and differentiability; smooth curves and smooth surfaces; applications of multivariable differential calculus; multiple integrals; Gauss¿ theorem; representation of analytic functions by power series; term by term differentiation of power series; multiplication of power series; inversion of power series; standard power series; Cauchy-Riemann equations; Cauchy integral theorem; Cauchy integral formulae; calculation of Laplace and Fourier transforms and other definite integrals; gamma and beta functions; Dirichlet problems; potential theory; two dimensional steady fluid flow; conformal mapping.

Textbook(s)

Saff, E.B and Snider A.D. 2003, Fundamentals of Complex Analysis, with Applications to Engineering and Science, International edition, 3rd, Prentice Hall

Abbott, Stephen B. 2001, Understanding Analysis, -, Springer-Verlag

Prerequisite(s)

Common to all relevant programs
Subject Area & Catalogue Number	Course Name
MATH 1055	Calculus 2

Corequisite(s)

Nil

Teaching method

Component	Duration
INTERNAL, MAWSON LAKES
Lecture	3 hours x 13 weeks
Tutorial	1 hour x 12 weeks

Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.

Assessment

Assignment 1, Assignment 2, Examination

Fees

EFTSL*: 0.125
Commonwealth Supported program (Band 8A)
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Fee-paying program for domestic and international students
International students and students undertaking this course as part of a postgraduate fee paying program must refer to the relevant program home page to determine the cost for undertaking this course.

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* Equivalent Full Time Study Load. Please note: all EFTSL values are published and calculated at ten decimal places. Values are displayed to three decimal places for ease of interpretation.