Skip to main content
Unit of study_

Analysis - MATH3068

Year - 2018

Analysis grew out of calculus, which leads to the study of limits of functions, sequences and series. The aim of the unit is to present enduring beautiful and practical results that continue to justify and inspire the study of analysis. The unit starts with the foundations of calculus and the real number system. It goes on to study the limiting behaviour of sequences and series of real and complex numbers. This leads naturally to the study of functions defined as limits and to the notion of uniform convergence. Returning to the beginnings of calculus and power series expansions leads to complex variable theory: analytic functions, Taylor expansions and the Cauchy Integral Theorem. Power series are not adequate to solve the problem of representing periodic phenomena such as wave motion. This requires Fourier theory, the expansion of functions as sums of sines and cosines. This unit deals with this theory, Parseval's identity, pointwise convergence theorems and applications. The unit goes on to introduce Bernoulli numbers, Bernoulli polynomials, the Euler MacLaurin formula and applications, the gamma function and the Riemann zeta function. Lastly we return to the foundations of analysis, and study limits from the point of view of topology.

Three 1 hour lectures and one 1 hour tutorial per week.

One 2 hour exam, tutorial tests, assignments (100%)


12 credit points of Intermediate Mathematics


MATH3008 or MATH2007 or MATH2907 or MATH2962


Faculty: Science

Semester 2

30 Jul 2018

Department/School: Mathematics and Statistics Academic Operations
Study Mode: Normal (lecture/lab/tutorial) day
Census Date: 31 Aug 2018
Unit of study level: Senior
Credit points: 6.0
EFTSL: 0.125
Available for study abroad and exchange: Yes
Faculty/department permission required? No
Courses that offer this unit

Non-award/non-degree study If you wish to undertake one or more units of study (subjects) for your own interest but not towards a degree, you may enrol in single units as a non-award student. Cross-institutional study If you are from another Australian tertiary institution you may be permitted to undertake cross-institutional study in one or more units of study at the University of Sydney.

To help you understand common terms that we use at the University, we offer an online glossary.