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,
Sem 2 2023

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


Required Prior Study

You should have satisfactorily completed following course/s before you commence this course.

Alternatively, you may be able to demonstrate the required skills and knowledge before you start this course.

Contact your course coordinator if you think you may be eligible for recognition of prior learning.

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.

Upon successful 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


You will be actively engaged in a range of learning activities such as lectorials, tutorials, practicals, laboratories, seminars, project work, class discussion, individual and group activities. Delivery may be face to face, online or a mix of both. 

You are encouraged to be proactive and self-directed in your learning, asking questions of your lecturer and/or peers and seeking out information as required, especially from the numerous sources available through the RMIT library, and through links and material specific to this course that is available through myRMIT Studies Course

Overview of Learning Resources


RMIT will provide you with resources and tools for learning in this course through myRMIT Studies Course

There are services available to support your learning through the University Library. The Library provides guides on academic referencing and subject specialist help as well as a range of study support services. For further information, please visit the Library page on the RMIT University website and the myRMIT student portal.

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

If you have a long-term medical condition and/or disability it may be possible to negotiate to vary aspects of the learning or assessment methods. You can contact the program coordinator or Equitable Learning Services if you would like to find out more.