# 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.