# MTH3051 - Introduction to computational mathematics - 2019

## 6 points, SCA Band 2, 0.125 EFTSL

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Chief examiner(s)

Coordinator(s)

Unit guides

Offered

Clayton

• Second semester 2019 (On-campus)

Prerequisites

Students must be enrolled in the Master of Financial Mathematics or have passed one unit from MTH2010, MTH2015, ENG2005 or MAT1830; and one unit from MTH2021, MTH2025, MTH2040 or MAT1841

Prohibitions

MTH2051

## Synopsis

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, least-squares problems and eigenvalue problems; methods for finding roots of nonlinear equations; polynomial interpolation; numerical differentiation and integration; and numerical methods for ordinary differential equations. Students 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.

## Outcomes

On completion of this unit students will be able to:

1. Demonstrate an understanding of the mathematical theory behind important numerical methods for solving real-life problems on computers.
2. Implement numerical methods for a variety of problems in Matlab, and test the accuracy and efficiency of implementation.
3. Demonstrate an understanding of the approximations introduced in algorithms and the effects of those approximations on the quality of calculations.
4. Solve theoretical and applied problems of analysing and employing numerical methods.
5. Demonstrate an awareness of the reach and importance of numerical methods in science, engineering, finance and technology.
6. Demonstrate advanced problem-solving skills, both individually and in collaboration.
7. Demonstrate advanced skills in the written and oral presentation of theoretical and applied numerical mathematics problems.

## Assessment

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

End of semester examination (3 hours): 60% (Hurdle)

Continuous assessment: 40% (Hurdle)

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for both the end-of-semester examination and continuous assessment components.