Engineering Applications and Professional Development (4EN504)

MATLAB Programming Coursework Report

Student Number:
Module: 4EN504 MATLAB Programming

Introduction

High-level programming languages are imperative in the current engineering practise since it allows efficient numerical computing, modelling and data visualisation. The MATLAB software is extensively applied in the various fields of engineering because of its intuitive syntax, built-in mathematical operations, and a high tendency towards computing in matrices. These characteristics enable engineers to convert theoretical expressions to practical solutions of calculation clearly and reliably.
This coursework has the purpose of illustrating how MATLAB can be used to solve various mathematical, physical, and engineering-related problems. The presented work is devoted to the basic programming structures, which are arithmetic operations, vectorisation, functions, loops, working with matrices and the graphical way to present the results. Besides finding the solutions to the problems in a computational way, it is also important to focus on proper organisation of the code, proper commenting, and meaningful presentation of results (MathWorks, 2024).
This report describes the layout and design of a MATLAB code created during the assessment and how computer-based methods could be utilised in solving engineering problems. The work directly corresponds to the Learning Outcome 3, which concerns the description of the high-level programming and its use in the engineering field, and the Learning Outcome 4, which deals with the application of the methods of computer-based calculations to engineering problems (Palm, 2021).

Formatting and Design of the MATLAB Programme.

The entire solution to all MATLAB problems is included in a single script file and structured in well-defined sections by the use of the sectioning syntax of MATLAB. Every section is related to a certain question or sub-question on the assessment. Such an organised method will make the code simple to navigate, debug, and evaluate (Attaway, 2022).

Throughout the script, clear and descriptive names are assigned to the variables in order to represent the physical or mathematical meaning of every quantity. There are also inline comments that provide information about the intent of the main lines of code, equations, and calculations. This makes it easier to read, and it will be easy to comprehend the logic of the programme for others (Hahn & Valentine, 2021).
In the command window, only those outputs are printed that are directly connected to the final results. Intermediate or redundant outputs are suppressed to ensure clarity and good practise of programming. Only when necessary, figures are created and are well labelled with relevant axes and titles.
Numerical Expressions and Mathematical Calculations.

The initial area of the MATLAB script deals with the assessment of numerical expressions with arithmetic operations, fractions, powers, logarithms and exponential functions. These expressions are calculated using operators and mathematical functions available in MATLAB, which is why they are calculated with high precision and efficiency.
Wherever possible, honour should be given to the use of the vector based calculations to prevent unnecessary loops. This illustrates that it knows the strength of MATLAB as a high-level programming language that works with matrices and arrays. The code is made shorter and more efficient in computing because it is done in a vectorised format.
Computations of logarithms are done by specifying a vector of input values and computing the logarithmic function element-wise. This approach underscores the fact that MATLAB can process large data and repeat computations with minimal code. The obtained results comply with the expectations of the theory and reveal the proper application of the principles of mathematics (Chapman, 2020).

Application of MATLAB on an Engineering Prob: Arrhenius Equation.

The Arrhenius equation is one of the most important engineering applications that have been discussed in this coursework to model the rate of chemical reactions based on temperature. The Arrhenius equation gives a relationship between reaction rate constant and temperature, activation energy, and universal constants, and is, therefore, an extensive parameter in chemical and process engineering (MathWorks, 2023).
The MATLAB script explicitly defines all the constants that are applied in the equation in the first section, so that the process of making changes is more transparent and easier. A temperature array is generated across the specified range with a uniform increment, and the rate constants associated with this increment are then computed by performing element-wise operations.
These findings have been provided in a tabular format that enhances easy reading, and trends could be easily observed in the data. The calculated values reveal that the reaction rate constant increases exponentially with temperature and that is what the physical theory predicts. This assignment shows how MATLAB may be applied to solve the problem of applying engineering equations and trend analysis, and provide the results in a systematic and valuable way (MathWorks, 2023).

Functions, Loops and Physics-Based Modelling.

Modular programming and reusable code. On the one hand, to illustrate modular programming and the concept of code reusability, a user-defined MATLAB function is developed to compute energy based on mass using the Einstein mass-energy equivalence equation. This calculation can be encapsulated in a function to help structure the code and as a way of professional practise in writing programmes in software engineering (Palm, 2021).
This is done by generating a logarithmically spaced vector of mass values with MATLAB using the built-in function. This enables energy values to be computed over multiple orders of magnitude, which would be hard to plot on a linear scale. The calculated values of energy are then compared with the mass, and a graphical illustration of the linear relationship between the two variables is obtained (MathWorks, 2023).

Figure 1: Energy versus Mass using Einsteins massenergy equivalence equation (???? = ?????????2;)
Besides the use of function-based programming, iterative calculations are done by the use of for loops. A loop is used to add the members of a vector, and the output is tested with the help of the built-in summation command in MATLAB. This comparison shows that it has an idea of both manual iteration and built-in functionality (Palm, 2021).
The subsequent application of loops is demonstrated by computing trigonometric functions within a given range. The script demonstrates how loops may be employed to compute functions on continuous domains by calculating their sine, cosine and tangent values in successive stages.

Figure 2. Sine, cosine, and tangent functions evaluated from 0 to 2? using a step size of 0.1.
Arrays, Matrices and Indexing Techniques.

MATLAB programming is based on arrays and matrices, as well as a key aspect in engineering applications. Here, equally spaced values within a specified range are used to generate vectors and trigonometric functions are used on each element to generate the same (Attaway, 2022).
Predefined matrices are used in performing matrix operations such as addition, subtraction and multiplication. Such operations show that MATLAB can solve a problem in linear algebra efficiently and correctly. The outcome of such operations is in agreement with the regular rules of matrix algebra.
Specific rows, columns and sub matrices in a bigger matrix are then extracted using indexing techniques. This involves typing in rows or columns, and picking out sets of items, as well as accessing single elements of the matrices. The techniques are needed in engineering processes that deal with data analysis, finite element processes, and system modelling.

Plotting and Visualisation of Data.

A graphical representation of the data is an important point of engineering analysis because it gives us the opportunity to know complex relationships more intuitively. The plotting functions of MATLAB have been applied in this coursework to plot numerical results clearly and accurately (Chapman, 2020).

Figure 3. Comparison of cos(x), cos(2x), and cos(3x) over the interval -?/2 to ?/2.
Several cosine functions are drawn on the same axes so as to compare them directly. The selection of appropriate axis labels, titles and smooth intervals in plotting is done to guarantee clarity and accuracy. The sampling distance between the input vectors is selected to generate smooth curves without excessive computing costs.
The output of all the figures created in the MATLAB script is linked to the problems under solution. The plots mirror the underlying data well and aid in the interpretation. This is in accordance with the assessment rubric requirement that one needs to have all the information needed to interpret the solution plotted out (Palm, 2021).

Discussion

The MATLAB solutions that were created in this course work show that high-level programming techniques can be appropriately used in solving engineering problems. Code complexity can be greatly minimised through the use of vectorisation, modular functions and structured plotting, which increase readability and performance.
MATLAB provides engineers with the ability to analyse behaviour, test theory, and investigate parameter variations efficiently by converting mathematical and physical equations into computational algorithms. The activities undertaken during this coursework show an element of typical activities in engineering, like numerical analysis, system modelling and data analysis (Hahn & Valentine, 2021).
The attention to the organisation of the code, commenting, and controlled output is such that the solutions are not only right but also presented professionally. These are needed in group engineering situations where readability and maintainability of the code are vital.

Conclusion

This coursework illustrates the proficient application of MATLAB as high level programming language in resolving mathematical, physical and engineering problems. By the use of numerical calculation, matrix manipulation, designing functions, and data visualisation, the work submitted demonstrates that the computer-based methods could be employed to solve real-life engineering problems.
The systematic manner in which the programming was done, with proper explanation and the relevant graphical output, depicts the excellent knowledge of the concept of programming and its application in the engineering practice. In general, the work addresses the learning outcomes of the module and emphasises the significance of MATLAB programming skills in the contemporary engineering practise.

References

Attaway, S. (2022). MATLAB: A practical introduction to programming and problem solving (6th ed.).
Chapman, S. J. (2020). MATLAB programming for engineers (6th ed.).
Hahn, B. D., & Valentine, D. T. (2021). Essential MATLAB for engineers and scientists (6th ed.). Academic Press. https://doi.org/10.1016/C2020-0-02056-7
Karris, S. T. (2020). Numerical analysis using MATLAB and Excel (3rd ed.). Orchard Publications.
MathWorks, Inc. (2023). MATLAB programming fundamentals. https://www.mathworks.com/learn/tutorials/matlab-fundamentals.html
MathWorks, Inc. (2024). MATLAB documentation. https://www.mathworks.com/help/matlab/
Palm, W. J. (2021). Introduction to MATLAB for engineers (4th ed.). McGraw-Hill Education.
Yang, X.-S. (2020). Engineering mathematics with MATLAB. Academic Press. https://doi.org/10.1016/C2018-0-01124-0