# The Matlab Section

## Introduction

Matlab is a high-level language and interactive environment that enables me to perform computationally intensive tasks efficiently therefore it was chosen as the programming tool of choice for the dissertation on heat modelling and other inherently mathematical based projects.

### Integration Program

This program is able to calculate various integration of objects and plot them on a graph

### Task 1

Correct Display of a 50 Hz and 100Hz sine wave on the same axis. Then a development of an informative display of error between given sine and cosine functions. Implemntation of power series and an indication that the approxiamtion improves with more terms.

### Task 2

Correct Intergration of an arbitary order polynomial between given limits

### Task 3

Display the curve of an arbitrary quadratic polynomial between user defined limits. Then be able to display the cubic polynomial determined by intergratiating the given quadratic. Display of an arbitrary order polynomial entered as a string.

### Algorithms for Modelling Heat

In modern science there has been a consistent movement to be able to understand the processes of thermodynamics and heat transfer in materials and subsequently be able to use this knowledge in the simulation heat diffusion through substances. In this paper the research into the theory’s concerned with heat flow through objects is approached. There is discussion on the use and implementation of optimizing properties to increase the efficiency of applying simulation of heat flow in the computer. The implementation and experimentation of techniques to model the behaviour of heat in a time domain is also discussed.