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6E4Z1104: Mathematical Methods 1

Question:

Mathematical modelling emerged as a powerful, indispensable tool for studying a variety of problems in scientific research, product and process development and manufacturing. It may help you to explain a system and to study the effects of different components, and to make predictions about their behaviour.

Aim

The aim of this assignment is to:

• Use mathematical software such as Excel/MATLAB to investigate the correlation between the variables.

• Use MATLAB to create a mathematical model to investigate the impact velocity of the spacecraft.

You are required to write a short report comprising of Tasks 1 and 2. The maximum size of the report should be no longer than 10 pages including Appendices. Save your report as a PDF document and follow the submission guidelines on Moodle.

Any Mathematical Software such as Excel or MATLAB can be used for this Task.

A diesel generator is fitted with multiple sensors and instrumentation, which record a sample every second, and downloaded to an Excel spreadsheet (Engine Output_data.xlsx).

1. Calculate the Pearson product-moment correlation coefficient between Fluid Outlet Temperature °C and Gas Valve Setting (%).

2. Draw a scatter plot of the results and comment on the relationship.

3. Calculate the line of best fit using the method of least squares of the form:

You are a parachute engineer working for the European Space Agency and you are required to design and implement a piece of software to test the consequences of changing the effective cross-sectional area of the parachute, AParachute, to be used on a spacecraft when it is returning to earth from space.

Your MATLAB program should be able to take user input data of the spacecraft mass, m, spacecraft cross-sectional area, ASpacecraft, the parachute effective cross-sectional area, AParachute, and spacecraft height above earth, H.

MATLAB must be used for this Task. Write a short report comprising of the sections below and use your MATLAB program to answer the questions that are included.

1. INTRODUCTION

· Briefly introduce the problem and the rationale for undertaking the work.

· You do not need to include a literature review.

2. METHOD

The method section should include the following:

· Flow chart illustrating how you have designed your code