Course Title: Real and Complex Analysis

Part A: Course Overview

Course Title: Real and Complex Analysis

Credit Points: 12.00


Course Code




Learning Mode

Teaching Period(s)


City Campus


145H Mathematical & Geospatial Sciences


Sem 2 2006,
Sem 2 2007,
Sem 2 2008,
Sem 2 2009,
Sem 1 2010,
Sem 1 2011,
Sem 1 2012,
Sem 1 2013,
Sem 1 2014,
Sem 1 2015,
Sem 2 2016


City Campus


171H School of Science


Sem 2 2019,
Sem 2 2020,
Sem 2 2021,
Sem 2 2022

Course Coordinator: Prof. Andrew Eberhard

Course Coordinator Phone: +61 3 9925 2616

Course Coordinator Email:

Course Coordinator Availability: By email and then online appointment

Pre-requisite Courses and Assumed Knowledge and Capabilities

You are assumed to have successfully completed the following courses or their equivalent:

MATH1142 Calculus and Analysis 1

MATH1144 Calculus and Analysis 2

MATH2140 Linear Algebra and Vector Calculus

Course Description

This course provides essential mathematical background for many subsequent courses in modern applied mathematics, pure mathematics, numerical analysis, statistics and operations research. Its aim is two fold. Firstly, it develops the foundation of mathematical analysis of functions of real variable in a rigorous manner, demonstrating how these ideas extend to many unfamiliar contexts and then extends the analysis of real functions of one variable to the analysis of functions of two or more real variables in a systematic manner. Secondly it provides sufficient background in the analysis of functions of a complex variable for you to study advanced engineering mathematics or aspects of probability theory. You will also become more familiar and comfortable with the language of abstract formalism and proof techniques that are present in all modern texts on analysis and its applications.

Objectives/Learning Outcomes/Capability Development

 This course contributes to the following Program Learning Outcomes for BP083 Bachelor of Science (Applied Mathematics and Statistics):

Knowledge and Technical Competence

  • the ability to use the appropriate and relevant, fundamental and applied mathematical and statistical knowledge, methodologies and modern computational tools.


  • the ability to bring together and flexibly apply knowledge to characterise, analyse and solve a wide range of problems
  • an understanding of the balance between the complexity / accuracy of the mathematical / statistical models used and the timeliness of the delivery of the solution.

 On completion of this course you should be able to:

  1. Apply the mathematical concept of convergence and its epsilon delta definition to establish the existence of limits and devise proofs of mathematical statements via the definition of convergence.
  2. Use fundamental mathematical concepts and theorems, such as mean value and implicit function theorems, to establish inequalities and estimates, to establish if a function of two variables is continuous and\or differentiable at a given point and explain how its partial derivatives relate to these properties.
  3. Manipulate the calculus of functions of two or more variables and, in particular, make a change of variables using the Jacobian matrix in a multiple integral.
  4. Elaborate the special character of functions of a complex variable and their properties and gain practical skills in analysing and manipulating functions of complex variables (including the evaluation of a line integral of a function of a complex variable using Cauchy’s integral formula, evaluation of real integrals using complex integration, and evaluation of Laurent Series and residues). 
  5. Communicate a mathematical argument and construct some simple mathematical proofs.

Overview of Learning Activities

The basic theory will be delivered in lectorials. Examples provided within lectorials will further be developed in weekly tutorials. Tutorial exercises and assignments will provide timely and continuous feedback so you may gauge your progress during the semester.   

Each week will have lectorial classes for the discussion of worked examples, for discussion of questions on issues relating to the lecture materials. A tutorial will be held in which we will and engage in individual work solving examples for assessment. Lectures are recorded and place online.   

A detailed teaching schedule is available in Canvas. 

Overview of Learning Resources

Lecture notes and recorded online lectures should provide sufficient knowledge in order to perform successfully in this course. Weekly tutorial sheets will provide examples of the type of problems that you are expected to master. Solutions for these will be posted regularly. The RMIT library contains a number of relevant texts that you may use to obtain alternative presentations of the topics given in lectures. 

A Library Guide is available at 

Overview of Assessment

Assessment Tasks:

Assessment item 1: Problem based Analysis Assessments 
Weighting: 50%
These support CLOs 1, 2, 4 and 5

Assessment item 2: Practical assessments for both real and complex analysis. 
Weighting: 30%
These support CLOs 1, 2, 3 and 5

Assessment item 3: Case based assessment of both real and complex analysis. 
Weighting: 20%
These support CLOs 4 and 5