Engineering Mathematics Research Articles

Engineering Academics and Students’ Views on the Phases of Teaching and Learning of Engineering Mathematics in an Antenna Design Course

An antenna design course, naturally, aims to teach students to produce an antenna device, which is a vital tool in technological development. Typically, this course is taught and designed in an abstract manner, which may be an inappropriate approach to teaching it. This approach could be due to engineering academics and students’ poor understanding of how to model mathematics concepts. As a result, antennae experts suggest that antenna technology is a difficult device when it comes to mathematical descriptions, which has resulted in a sudden loss of interest among students in a school of engineering. Thus, this paper reports on the four phases of teaching antenna design using mathematical modelling approaches, with the specific aim of resolving the difficulties encountered in teaching an antenna design course. In achieving this teaching, the study explains the approaches and impact of teaching Mathematical Modelling (MM) in antenna design among engineering academics. In this study, the sample population included one engineering academic and four engineering students. The data were collected using a qualitative research approach, utilising an interview guide and an open-ended questionnaire. Finally, the results of this study confirmed the four major phases of teaching antenna design using engineering mathematics.

Literature Review on the Teaching Engineering Mathematics: Issues and Solutions for Student Engagement

Engineering mathematics is essential for fostering analytical and problem-solving abilities in engineering education, especially in Malaysia, where it plays a crucial role in the nation's technical and industrial ambitions. Nevertheless, students encounter substantial obstacles such as the need to strike a balance between grasping abstract concepts and acquiring practical skills, surmounting feelings of apprehension about mathematics, actively participating in crowded classrooms, and adapting to the demands of online education and self-directed study. This paper examines the difficulties and suggests remedies, with a focus on incorporating active learning methods, creating supportive learning environments, and using digital resources to improve student involvement and understanding. The study emphasizes the significance of visualizing abstract mathematical ideas and establishing connections with practical engineering applications. These strategies are important to maintain the sustainable development of engineering education. By using these strategies, instructors may enhance pupils' readiness for prosperous engineering jobs, guaranteeing that they grasp mathematical ideas, and possess the ability to apply them proficiently in real-world situations.

Investigation of solution behavior of Differential Equations by Sumudu methods of random complex Partial Differential Equations

In this study, solutions of random complex partial differential equations were found using the two-dimensional Sumudu transformation method(STM). The initial conditions of a deterministic equation or the non-homogeneous part of the equation are transformed into random variables to obtain a random complex partial differential equation. With the help of the properties of two-dimensional Sumudu and inverse Sumudu transformation, an approximate analytical solution of a complex partial differential equation with random constant coefficients was obtained by selecting a random variable with an initial condition of Normal and Gamma distribution. The probability characteristics of the resulting solutions, such as expected value and variance, were obtained and graphically shown with the help of the Maple package program.

Analysis of the Influence of Rock Mechanics Variables on the Stability of Tunnel Surrounding Rock Based on Engineering Mathematics Applications

Tunnels are essential infrastructure elements, and it is critical to maintain their stability for both operation and safety. Using engineering techniques, this study examines the correlation between rock mass motorized characteristics and tunnel surrounding rock stability. This study utilizes the multi-sensor monitoring data of the surrounding rock mechanical characteristics and tunnel support structure collected during tunnel boring machine construction as its research object. The integrated cuckoo search optimized Upgraded dynamic convolutional neural network (ICSO-UDCNN) has been utilized for predicting the tunnel parameters. In general, the surrounding rock’s hardness correlates with its level, which in turn determines how quickly tunnels are being excavated. There is a stronger correlation of 98\% between the field penetration index (FPI) variables of the rock’s characteristic slope along the conditions surrounding the tunnel. The most significant factor influencing its deformation is the surrounding rock’s mechanical characteristics. For engineers and other decision-makers engaged in tunnel design, building, and maintenance, the study’s findings add a greater understanding of the variables affecting tunnel stability. This research provides an establishment for enhancing security protocols, lowering hazards related to tunneling operation, and optimizing tunnel engineering techniques by quantitatively evaluating the influence of rock mass mechanical factors on solidity.

Concept of flexible no-code automation for complex sample preparation procedures

Driven by demographic changes and dwindling Science Technology Engineering Mathematics enrolments, our research introduces no-code automation as a strategic response, aimed at mitigating labor shortages while enhancing productivity and safety in the laboratory environment. Employing a user-friendly, no-code software platform, we automated a complex HPTLC assay, enabling laboratory personnel to configure and modify workflows without requiring specialized programming skills. The manuscript outlines the deployment of a collaborative robot (cobot), a programmable logic controller (PLC), and the utilization of self-developed open-source hardware components to establish automated stations for sample handling, incubation, spraying, detection, and storage within the assay process. The research addresses challenges such as the handling of fragile HPTLC plates and the seamless integration of automated stations, solved through innovative design solutions and adaptive programming methods. This investigation demonstrates the feasibility and efficiency of no-code automation in overcoming skilled labor deficits.

The Behavior of High Scanning Electron Voltage Electron in SEM Due to Mirror Effect

To determine the factors influencing the electron scattering process in a scanning electron microscope caused by the electron mirror, a set of physical and mathematical ideas were used. These equations, which relate the scattering of the input electron with the surface potential energy of the dielectric material under examination using a matched beam ion microscope and scanning electrons, are based on simplified engineering mathematics. After five minutes of charging the insulator to saturation with an acceleration voltage of 30 kV, the accumulated charge was 0.3 nC, from which the surface voltage across the working distance (WD = 15 mm) was determined. The scattering angle (β) was found to be inversely proportional to the incidence angle (θ) in the second stage, when scanning voltages (Vsc=2, 4, and 6 kV) were employed. This was because the angle between the incident and scattered electron (2

Changes in Students’ Approaches to Learning on Engineering Mathematics Courses with Two Different Instructional Models

Changes in Students’ Approaches to Learning on Engineering Mathematics Courses with Two Different Instructional Models

The effectiveness of using educational robots in enhancing engineering mathematics skills among students in basic school

Educational robots foster engaging, democratic, and collaborative learning environments, enhancing students' mathematical and engineering abilities by enabling them to interact, solve problems, assimilate information, and communicate effectively within the classroom. This study aims to examine the impact of educational robots on the development of engineering mathematics skills. The study uses a quantitative approach with a quasi-experimental design for a single pre- and post-test group. The sample consisted of 40 fifth grade students who initially studied geometry using traditional methods, followed by studying the same content using the educational robot. The study found that robot-based education significantly improved engineering mathematics skills. It was concluded that using educational robotics as a tool for teaching mathematics improved computational thinking, engineering mathematics, motivation, creativity, cooperation, and teamwork. It is possible to argue that the study's results corroborate relevant research showing how educational robots raise students' academic performance and improve their critical thinking. These results lend credence to the idea that educational robots improve learning beyond traditional approaches by actively involving students, giving subjects greater concreteness, and capturing their interest and attention. The study recommends the creation of new mathematical activities using educational robots across various mathematical contents and educational stages, further enhancing engineering mathematics among students.

Balance of mixed flow assembly line based on industrial engineering mathematics and simulated annealing improved algorithm

The frequent changes in customer orders have led to the need for production line rebalancing and design. The increasing complexity of mixed assembly of multiple products makes it an urgent issue to perfect the balance of mixed flow assembly lines. This study proposes an improved simulated annealing algorithm by combining industrial engineering mathematical methods with intelligent optimization algorithms. The purpose is to achieve balanced optimization of mixed flow assembly lines by minimizing production rhythm, balancing load between workstations, and minimizing loss time within workstations. Firstly, industrial engineering methods are used to analyze the mixed flow assembly line, and then a mathematical optimization model is established by combining simulated annealing algorithm and genetic algorithm. Finally, through example simulation, the effectiveness of the algorithm is verified, and the superiority of its performance is verified through algorithm comparison. The experiment shows that the balance rate of the optimized assembly line for a total of 60 processes in 12 workstations has increased by about 6%. The smoothness index decreases by about 4. The loss coefficient has decreased by approximately 0.06. The overall efficiency has increased by about 12%. The smoothness index decreases by 0.3 in comparison with the solution results of Jackson's law in a case of 11 processes in 5 workstations. This fully demonstrates that the hybrid model has higher optimization efficiency, achieves balanced optimization of the mixed flow assembly line, improves production efficiency, and reduces equipment idle rate.

Designing and analysing a teaching proposal about linear algebra through the dialogue of two theories

In this paper we propose a new strategy of dialogue between theories, considering a semiotic cognitive analysis and a praxeological analysis. We examine the implementation of a teaching and learning sequence for introducing eigentheory in a linear algebra course taught during the first year of an engineering degree programme. Initially, the semiotic cognitive analysis based on the Action, Production and Communication space (APC) approach is used in the preliminary, a priori and in vivo phases of the didactic engineering process to propose a teaching strategy that incorporates a variety of semiotic resources. In a second moment, the praxeological analysis intervenes to reformulate the preliminary analysis and to progress on the consideration of a reference epistemological model about eigentheory in a first course of mathematics for engineers. This model is then used in the a priori and a posteriori analysis to integrate the semiotic and epistemological dimensions in the design and implementation of the teaching proposal. The results show the productivity of this new networking strategy and the complementarity of connecting the semiotic with the epistemological analysis.

"Please may I have some more?" – Assessing Student and Instructor Intersubjective Agreement on Part Marks in Engineering Mathematics

Driven by student requests for more marks (some prefer ‘partial credit’), this paper asks if there is evidence that students adapt to the marking rubrics encountered in universities. Through a weekly handout in a first-year engineering mathematics class, we explore the progress students make in their understanding of how instructors grade. How does student expectation of an unknown grading rubric shift with the accumulation of experience in a course? Through our exploration, we reveal unfortunate findings about how well students adapt, a lot of unanswered questions, a few sources of good news, and promising directions for the research to pursue.

The Efficiency of Final Semester Examination Simulation Method in Achieving At Least 20 Marks: A Case Study on Engineering Mathematics 2 Students at Politeknik Kuching Sarawak

The aim of this research is to identify the effectiveness of using the Final Semester Examination Simulation Method in achieving at least 20 marks in the final semester examination. The study focuses on quantitative measurements and employs numerical data. The comparison shows that out of the 10 programs involved, only 1 program shows a decrease in the achievement of the mark, which is the Diploma In Mechanical Engineering (Air Conditioning And Refrigeration) (DPU) programme. This suggests that the method has been effective in helping students achieve at least 20% in the Final Examination. To maintain and enhance the success of the method, it's important to continue monitoring and evaluating its impact on student performance.

Applications of two kinds of Kudryashov methods for time fractional (2 + 1) dimensional Chaffee–Infante equation and its stability analysis

In this study, the beta time fractional (2 + 1) dimensional Chaffee–Infante equation used to describe the behavior of gas diffusion in a homogeneous medium is discussed. Generalized Kudryashov and modified Kudryashov procedures were used to discovered solitons of the equation. These methods can be easily applied and offer different solutions checked to other methods in the literature. At the same time, these two methods use symbolic calculations to better understand various nonlinear wave models and offer a powerful and effective mathematical approach. The solutions created in this article are different from those in the literature and will guide those working in the field of physics and engineering to better understand this model. Figures of the results were made values different from each other. The stability of the equations in applications has been demonstrated by testing the stability feature on some solutions obtained using the features of the Hamilton system. This work demonstrates the power and effectiveness of the methods discussed in applying many different forms of fractional-order nonlinear equations. The results obtained in this paper are original to our research and have the potential to be helpful in the fields of mathematical engineering and physics.

Engineering Education: Challenges for Innovation

“Engineering Education: Challenges for Innovation” is the scope of the 1 International Conference of the Portuguese Society for Engineering Education (in Portuguese: Sociedade Portuguesa para a Educacao em Engenharia, SPEE) [1]. SPEE is a young society now completing four years since its public presentation and launching by the Faculty of Engineering of University of Porto, in February 19, 2010. During its first 12 months of activity, SPEE has launched its working groups named “Ethics in Engineering”, “Continuing Education in Engineering” and “Information Technologies” and, later in 2011, the last one called “Tools to Develop Higher Order Thinking Skills”. The Society was attaining by then its own internal momentum and so, developing the capabilities to go further with similar international associations. So, in October 2011 SPEE, in cooperation with the International Society for Engineering Education (IGIP), SPEE had its first official participation in an International Conference, in the SPEE-IGIP Flash Moment within the 1 World Engineering Education Flash Week. In 2012 the Society carried on with the organization of a Special Track “Talking about Teaching 2012” in the IGIP Annual Conference 2012 (Villach, Austria) and also has launched the call for an International Conference of the Society among its members. And this has been the smooth but firm way for reaching in 2013 its 1 International Conference CISPEE2013, in Porto, Portugal, complemented by the second TaT Special Track within IGIP Annual Conference 2013, TaT’13, in Kazan, Russia. During TaT’12 and TaT’13, Special Issues of the International Journal for Engineering Pedagogy have been published and now, the present Special Issue, will be again propagating works accomplishing one of the missions of the SPEE – to promote Engineering Education by sharing experiences, projects, results and discussions in order to contribute for research and for teachers' scientific and professional development. This has also been the purpose of its Newsletters, which brought, when it was launched and every three months, the cooperation of national and international societies and organizations as well as the Society members and international colleagues [2]. In this way, SPEE “will carry on performing its important task within the engineering education community, blessed with the devoted commitment of its members and the invaluable cooperation of international colleagues and sister societies” [3]. The Polytechnic of Porto – School of Engineering (IPP/ISEP) hosted CISPEE2013 on October 31 and November 1, 2013, in Porto, Portugal. CISPEE2013 received 80 submissions (with authors from 21 different nationalities), from which 48 were accepted as full papers (60% acceptance rate), 18 were proposed for presentation as posters, 10 were rejected and 4 were considered not valid. All submissions were double blind reviewed by at least 3 independent reviewers, with conflicting cases raising additional reviews. This procedure allowed ensuring a high-quality technical program with 8 oral presentation sessions devoted to (1) Designing Courses for Higher Order Thinking, (2) Role of Engineers and Engineering Education in Society, (3) Computers and Mobile Devices in Egineering Education, (4) Problem Solving and Creativity, (5) Using Online Tools to Facilitate Learning, (6) Mathematical Competences and Computacional Tools for Teaching Mathematics in Engineering, (7) Research Aspects in Engineering Education, and (8) Engineering Education Case Studies. The present Special Issue contains a selection of highly rated papers, from CISPEE2013, whose authors were asked to incorporate at least 30% of new / revised material, in relation to the version presented at the conference and included in its proceedings, indexed by IEEE Xplore [4]. We sincerely hope you appreciate reading this selection.

Editorial

CHIEF EDITOR Ahmad Faris Ismail, IIUM, Malaysia TECHNICAL EDITOR Sany Izan Ihsan, IIUM, Malaysia EXECUTIVE EDITOR AHM Zahirul Alam, IIUM, Malaysia ASSOCIATE EDITOR Nor Farahidah Za’bah, IIUM, Malaysia LANGUAGE EDITOR Lynn Mason, Malaysia COPY EDITOR Hamzah Mohd. Salleh, UNISSA, Brunei Darussalam MALAY TRANSLATOR Nurul Arfah Che Mustapha, IIUM, Malaysia EDITORIAL BOARD MEMBERS Abdullah Al-Mamun, IIUM, Malaysia Abdumalik Rakhimov, IIUM, Malaysia Aishah Najiah Bt. Dahnel, IIUM, Malaysia Alya Naili Binti Rozhan, IIUM, Malaysia Norsinnira Bt. Zainul Azlan, IIUM, Malaysia Hanafy Omar, Saudi Arabia Hazleen Anuar, IIUM, Malaysia Konstantin Khanin, University of Toronto, Canada Ma'an Al-Khatib, IIUM, Malaysia Meftah Hrairi, IIUM, Malaysia Mohamed B. Trabia, United States Mohammad S. Alam, Texas A&M University-Kingsville, United States Mustafizur Rahman, National University Singapore, Singapore Ossama Abdulkhalik, Michigan Technological University, United States Mohamed Hadi Habaebi, IIUM, Malaysia Mohd. Sultan Ibrahim Bin Shaik Dawood, IIUM, Malaysia Muhammad Ibn Ibrahimy, IIUM, Malaysia Nor Fadhillah Mohamed Azmin, IIUM, Malaysia Waqar Asrar, IIUM, Malaysia INTERNATIONAL ADVISORY COMMITTEE A. Anwar, United States Abdul Latif Bin Ahmad, Malaysia Farzad Ismail, USM, Pulau Pinang, Malaysia Hanafy Omar, Saudi Arabia Hany Ammar, United States Idris Mohammed Bugaje, Nigeria K.B. Ramachandran, India Kunzu Abdella, Canada Luis Le Moyne, ISAT, University of Burgundy, France M Mujtaba, United Kingdom Mohamed AI-Rubei, Ireland Mohamed B Trabia, United States Syed Kamrul Islam, United States Tibor Czigany, Budapest University of Technology and Economics, Hungary Yiu-Wing Mai, The University of Sydney, Australia. AIMS & SCOPE OF IIUM ENGINEERING JOURNAL The IIUM Engineering Journal, published biannually (January and July), is a carefully refereed international publication of the International Islamic University Malaysia (IIUM). Contributions of high technical merit within the span of engineering disciplines; covering the main areas of engineering: Electrical and Computer Engineering; Mechanical and Manufacturing Engineering; Automation and Mechatronics Engineering; Material and Chemical Engineering; Environmental and Civil Engineering; Biotechnology and Bioengineering; Engineering Mathematics and Physics; and Computer Science and Information Technology are considered for publication in this journal. Contributions from other areas of Engineering and Applied Science are also welcomed. The IIUM Engineering Journal publishes contributions under Regular papers and Invited review papers. It also welcomes contributions that address solutions to the specific challenges of the developing world and address science and technology issues from an Islamic and multidisciplinary perspective. REFEREES’ NETWORK All papers submitted to IIUM Engineering Journal will be subjected to a rigorous reviewing process through a worldwide network of specialized and competent referees. Each accepted paper should have at least two positive referees’ assessments. SUBMISSION OF A MANUSCRIPT A manuscript should be submitted online to the IIUM Engineering Journal website at http://journals.iium.edu.my/ejournal. The journal website could conduct further correspondence on the paper's status. Whilst the publisher and editorial board make every effort to see that no inaccurate or misleading data, opinion, or statement appears in this Journal, they wish to make it clear that the data and opinions appearing in the articles and advertisements herein are the responsibility of the contributor or advertiser concerned. Accordingly, the publisher and the editorial committee accept no liability whatsoever for the consequence of any such inaccurate or misleading data, opinion, or statement. IIUM Engineering Journal ISSN: 1511-788X E-ISSN: 2289-7860 Published by: IIUM Press, International Islamic University Malaysia Jalan Gombak, 53100 Kuala Lumpur, Malaysia Phone (+603) 6421-5014, Fax: (+603) 6421-6298

Proposal for Developing Learning Materials Focusing on Modified Problem-Posing Using a Probability Game to Promote Understanding of the Problem Structure in Basic Engineering Mathematics

Proposal for Developing Learning Materials Focusing on Modified Problem-Posing Using a Probability Game to Promote Understanding of the Problem Structure in Basic Engineering Mathematics

Enactment and impact analysis of active learning strategies utilized for the basic science courses in the evaluation of engineering students

The new era of teaching learning process demands more clearance of theoretical aspects utilizing visual strategies. Accordingly, this research focuses on usefulness of student team achievement division (STAD) and project based learning (PjBL) as active learning strategies for comprehensive understanding of basic science courses. The study revealed increased effectiveness of learning, encouraging equal participation, active engagement and supportive learning environment for better understanding of concepts in basic science courses. The usefulness of active learning strategies has been studied by conduction of STAD & PjBL activities for the Engineering Mathematics and Engineering Chemistry courses respectively. The appropriate evaluation and comparative analysis done before and after activity allows to elaborate the efficacy of visual strategies utilized for understanding theoretical concepts. Keywords—Active learning tools, Basic Science Courses, Evaluation Rubrics, Project Based Learning, Student Team Achievement Division

Resource-based Course Guide in Teaching Advanced Engineering Mathematics

Resource-based Course Guide in Teaching Advanced Engineering Mathematics

Golden Ratio: Construction, Geometry, Beauty, and Diversity

Nature is attractive due to the proper ratios of various components in them and in between others. In nature, leaves, flowers, fruits, Himalayas, hills, valleys, springs, rivers, etc. show a rhythmic balance and seem harmonic and aesthetically pleasing. The golden ratio or the golden (divine) proportion is considered the most pleasing to human visual sensation and is not limited only to aesthetic beauty but also found prominently in the natural world. It is an irrational number denoted by φ and is approximately 1.618034. It is a fascinating topic for mathematicians, artists, natural scientists, philosophers, biologists, artists, architects, musicians, psychologists, designers, etc.
 This research work presents a panoramic view of the golden ratio; their construction algorithms, and structures; mathematical presentations, geometry, patterns, and properties from mathematical perspectives and opens the broad horizon for further research. Besides these, the paper also presents their existences, diversities, their relationships with nature, the universe, arts, design, architecture, and engineering in ancient and modern mathematics and sciences.

The mediating role of higher-order thinking skill in the relationship between mathematics strength and achievement in electrical and electronic engineering education

Purpose: The paper aims to examine the casual role of higher-order thinking skills as a mediator in the relationship between students’ strength in mathematics and achievement in electrical and electronic engineering education.
 Design/Methodology/Approach: The study adopted a quantitative research design where random cluster sampling was used to select a total of 488 final-year students from four technical universities in Ghana. Mathematics achievement tests were used to gather data on students’ higher-order thinking skills and competence in five areas of mathematics. Also, their examination results were collected from their respective universities. Mediation analysis was done using AMOS 26.
 Finding: The study revealed that the positive effect of students’ strengths in the five selected mathematics topics on their performance in electrical and electronic engineering education is mediated by their higher-order thinking skills.
 Conclusion: The research concludes that there is a partial mediation in the relationship between students’ strength in mathematics and achievement in electrical and electronic engineering education by higher-order thinking skills.
 Research Limitations: It is recommended that further researchers carry out similar research with more mathematics indicators to explain more variations in achievement in electrical and electronic engineering education.
 Practical Implication: Engineering mathematics curriculum developers should stress the need for mathematics, especially algebra, for the development of higher-order thinking skills to facilitate problem-solving in electrical and electronic engineering education and practice.
 Contribution to Literature: This study highlights the relationship between the understanding of the concepts of specific mathematics topics, higher-order thinking skills, and achievement in electrical and electronic engineering education.