MTH2051 - Introduction to computational mathematics

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Overview

When mathematics is used in real-world applications, it almost always involves the use of computers. This unit provides an introduction to numerical methods for solving maths-related problems on computers. Topics covered include an introduction to Matlab programming; error analysis; methods for solving linear systems, methods for finding roots of nonlinear equations; polynomial interpolation; numerical differentiation and integration; and numerical methods for ordinary differential equations. You will receive a solid introduction to the theory of the numerical methods (with derivations of the methods and some proofs), and will learn to implement the computational methods efficiently in Matlab. The methods and techniques learned have broad applicability in areas that include the natural sciences, engineering, the biomedical sciences, finance, business, machine learning, and data science.

Offerings

S2-01-CLAYTON-ON-CAMPUS

Requisites

Prohibition

Prerequisite

MTH2010

6 CP

Multivariable calculus

MTH2015

6 CP

Multivariable calculus (advanced)

ENG2005

6 CP

Advanced engineering mathematics

MAT1830

6 CP

Discrete mathematics for computer science

AND

MTH2040

6 CP

Mathematical modelling

MAT1841

6 CP

Continuous mathematics for computer science

MTH2021

6 CP

Linear algebra with applications

MTH2025

6 CP

Linear algebra (advanced)

Contacts

Chief Examiner(s)

Dr Janosch Rieger

Unit Coordinator(s)

Dr Janosch Rieger

Notes

IMPORTANT NOTICE:
Scheduled teaching activities and/or workload information are subject to change in response to COVID-19, please check your Unit timetable and Unit Moodle site for more details.

Learning outcomes

On successful completion of this unit, you should be able to:

Apply the mathematical theory behind important numerical methods for solving real-life problems on computers.

Implement numerical methods for a variety of problems in Matlab, and test the accuracy and efficiency of implementation.

Apply the approximations introduced in algorithms and be aware of the effects of those approximations on the quality of calculations.

Solve theoretical and applied problems by analysing and employing numerical methods.

Be aware of the reach and importance of numerical methods in science, engineering, finance and technology.

Demonstrate advanced problem solving skills, both individually and collectively with staff and fellow students.

Demonstrate advanced skills in the written and oral presentation of theoretical and applied numerical mathematics problems.

Teaching approach

Active learning

Assessment

1 - In-semester assessment

2 - Examination (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions

Lectures

Workload requirements

Workload

Learning resources

Required resources

Ascher UM, Greif C. A First Course in Numerical Methods. Society for Industrial and Applied Mathematics; 2011. (Introductory.) link

Gander W, Gander MJ, Kwok F. Scientific computing-An introduction using Maple and MATLAB. Springer; 2014. (Introductory.) link

Quarteroni A, Sacco R, Saleri F. Numerical mathematics. Springer; 2010. (More advanced.) link

Hohmann A, Deuflhard P. Numerical analysis in modern scientific computing: an introduction. Springer; 2012. (More advanced.) link

Other unit costs

Costs are indicative and subject to change.
Miscellaneous Items Required (Unit Course Reader, Printing, Stationery) - $120.

Availability in areas of study

Applied mathematics
Financial and insurance mathematics
Mathematical statistics
Mathematics