# MTH307 Mathematical Modelling (8)

This subject develops students' practical skills by using computer software to solve mathematical applications. The two main applications considered are the numerical solutions of differential equations (ordinary and partial); and fitting data to a model using least-squares regression (linear and non-linear).

## Availability

Session 2 (60)
Online
Wagga Wagga Campus

Continuing students should consult the SAL for current offering details: MTH307. Where differences exist between the Handbook and the SAL, the SAL should be taken as containing the correct subject offering details.

## Subject Information

HD/FL

One session

##### School

School of Computing and Mathematics

MTH220

## Learning Outcomes

##### Upon successful completion of this subject, students should:
• be able to write computer programs to solve real-life problems;
• be able to numerically calculate the solutions of ordinary differential equations using various methods;
• be able to adapt existing code to produce numerical solutions for differential equations;
• be able to generate suitable finite difference equations from differential equations;
• be able to determine the stability of a finite difference equation;
• be able to calculate the solutions of partial differential equations using various methods;
• be able to fit data to a model using linear and non-linear regression techniques;
• be able to interpret mathematical models and communicate their output to non-mathematical audiences.

## Syllabus

##### This subject will cover the following topics:
• Introduction to mathematical modelling.
• Programming with Maple.
• Linear regression: simple and multiple; forward selection and backwards elimination methods.
• Numerical solution of ordinary differential equations for both initial and boundary value problems; Euler's method, Runge-Kutta method, shooting method and finite difference methods.
• Fourier series.
• Partial differential equations (parabolic, hyperbolic and elliptic): separation of variables, numerical solution using finite difference methods; stability of finite difference methods and method of characteristics.
• Non-linear regression: various numerical methods: grid, gradient, Gauss-Newton and mixed.

#### Indicative Assessment

The following table summarises the assessment tasks for the online offering of MTH307 in Session 2 2019. Please note this is a guide only. Assessment tasks are regularly updated and can also differ to suit the mode of study (online or on campus).

Item Number
Title
Value %
1
Assignment 1: modelling and odes
6
2
Assignment 2: bvps/fourier series/parabolic eq-s
12
3
Assignment 3: hyperbolic/elliptic eq-s/regression
12
4
Final exam
70

The information contained in the CSU Handbook was accurate at the date of publication: July 2020. The University reserves the right to vary the information at any time without notice.

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