Engineering Mathematics Course Research Articles

Appraisal on Bloom's Separation in Final Examination Question of Engineering Mathematics Courses using Rasch Measurement Model

This paper studied and analyzed the separation of Bloom's cognitive level in the final exam questions (items) for KKKQ2114 Mathematics Engineering III (Differential Equation) course using Rasch Mesurement Model. The purpose of this study is to use Rasch Measurement Model as a tool to assists lecturers to develop and monitor the distribution and separation of items across content and task domain based on Bloom's Taxonomy (cognitive skill levels). The construction of the item and responses, as well as the process and content of the item contribute to the classification of an item by Bloom's cognitive level. This study revealed that the separation and the distribution of the final exam questions for KKKQ2114 should be revised because there is a large gap in each cognitive level of Bloom's. The level of difficulty for each cognitive skill also need to be reviewed and adapted to CO and PO of the course.

Tablet PCs in engineering mathematics courses at the J.B. Speed School of Engineering

In fall 2007, J.B. Speed School of Engineering at the University of Louisville joined the ranks of universities requiring the purchase of Tablet PCs for all new entering students. This article presents a description of how the Department of Engineering Fundamentals incorporated Tablet PCs into their instruction, a review of the literature pertaining to the use of Tablet PCs for instruction and preliminary survey results from the students in engineering mathematics courses at the end of the first year, after students had been exposed to Tablet PCs for 1 year. Results show that a large majority of students in the Department of Engineering Fundamentals agree that presentation of engineering mathematics material using the Tablet PCs and DyKnow software is a vast improvement over overhead projector, blackboard, or PowerPoint lectures and course packs. However, students are split as to whether the Tablet PC is something they actually want to use for their own note-taking. Finally, a plan for assessment of tablet impact on student learning is presented.

Obstacles in the Learning of Two-variable Functions through Mathematical Thinking Approach

Function of several variables is one of the most important concepts in mathematics and its applications. The lack of its understanding will cause certain obstacles in the learning of next concepts or even subjects. The researchers at Universiti Teknologi Malaysia (UTM) tend to support students to overcome their deficiencies in the learning of two-variable functions by promoting mathematical thinking. The purpose of this study is to demonstrate how this method can help students in the learning of two-variable functions when they encounter non-routine problems in face-to-face Engineering Mathematics (Multivariable Calculus) course through this method. The data collection for this study was collected from a Multivariable Calculus class at UTM during semester II 2009-2010. Data collection for the study was carried out through written assessments and structured questionnaires. The data analysis reveals that students still display difficulties in their learning. Specifically, students’ common difficulties are: students’ met-before (previous experience), selecting appropriate representation of the three worlds of mathematical thinking, the transition from one world to another world of mathematical thinking, lack of understanding two different embodiments, and lack of understanding two different symbolic for a concept. The findings reveal that the sketching the graph of two-variable functions in 3-dimensions is the greatest difficulty for majority of students in this method. Additionally, the quite entrenching of students in their learning behaviour and styles is the most important reason for the lack of using prompts and questions as guides by students and then no enough effectively of this method.

Critical Times in One- and Two-Layered Diffusion

SummaryThe study of diffusion is commonplace in engineering mathematics courses as a classic example of partial differential equations and separation of variables. However, many textbooks stop at a derived solution without going further to explore what the solution means. The analysis of the critical diffusion time is used here to demonstrate how the solutions obtained can be used to explore additional useful results for diffusion through a single layer of material. We also show how consideration of diffusion through two layers gives rise to some surprising new results. This problem was motivated by analysing the annealing of steel coils, where knowledge of the time to heat a system of air and steel layers is critical in the manufacturing process.

Online formative tests as a learning tool in Engineering mathematics

We report on the results of the online mathematics project developed and implemented at Swinburne University of Technology. The trial was incorporated within the existing first year engineering mathematics course over the second semester of 2007. A detailed discussion is given on the structure of the item bank of mathematical multiple-choice questions and a brief description on the method by which they were generated. Over the duration of the trial, statistical data on several variables, including the distribution of incorrect student answers for a given multiple-choice question was collated. An example of the statistics of student responses based on Blackboard's tracking facility for one of the tests is presented. Finally, we discuss the future direction of the project. References M. Boylan, What have we learned from 15 years of supporting the development of innovative teaching technology?, Social Science Computer Review, vol. 22, no. 4, p. 405, 2004. doi:10.1177/0894439304268646 A. Zemel, F. Xhafa, and G. Stahl, Analyzing the organization of collaborative math problem-solving in online chats using statistics and conversation analysis., Lecture notes in computer science, no. 3706, p. 271, 2005. http://www.springerlink.com/content/d4h9fyp05hnp052d/fulltext.pdf Q. Li, Would we teach without technology? a professor's experience of teaching mathematics education incorporating the internet., Educational Research, vol. 45, no. 1, p. 61, 2003. doi:10.1080/0013188032000086127 D. Bourne, A self-paced course in pharmaceutical mathematics using web-based databases., American Journal of Pharmaceutical Education, vol. 5, no. 70, p. 271, 2006. http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1637015&blobtype=pdf W. Hwang, N. Chen, and R. Hsu, Development and evaluation of multimedia whiteboard system for improving mathematical problem solving., Computers and Education, vol. 46, no. 2, p. 105, 2006. doi:10.1016/j.compedu.2004.05.005 Q. Li, Infusing technology into a mathematics methods course: any impact?, Educational Research, vol. 47, no. 2, p. 217, 2005. doi:10.1080/00131880500104341 G. Stefansson, The tutor-web: An educational system for classroom presentation, evaluation and self-study., Computers and Education, vol. 43, no. 4, p. 315, 2004. doi:10.1016/j.compedu.2003.09.004 Respondus version 3.5: http://www.respondus.com, Copyright 2000--2007 Respondus, Inc., 2007. C. Barling, N. Li, D. Lucy, D. Richards, J. Sampson, J. Steiner, and P. Tobin, {HMS}111: Engineering Mathematics 1, Copyright 2006 Swinburne University of Technology, 2007. B. Leary, D. Lucy, J. Sampson, D. Gilliam, and D. Roberts, {HMS}112: Engineering Mathematics 2, Copyright 2006 Swinburne University of Technology, 2006.

Newton-Raphson Solution of Poisson's Equation in a Pn Diode

This paper presents a numerical solution, using MATLAB, of the electrostatic potential in a pn junction, which obeys Poisson's equation. This numerical method is based on the Newton-Raphson technique and is useful for educational purposes. It can be incorporated in an undergraduate course on semiconductor devices to demonstrate the applications of numerical analysis techniques in device physics. It may also be appropriate for a section on numerical analysis techniques in an engineering mathematics course.

Does computer confidence relate to levels of achievement in ICT-enriched learning models?

Employer expectations have changed: university students are expected to graduate with computer competencies appropriate for their field. Educators are also harnessing technology as a medium for learning in the belief that information and communication technologies (ICT’s) can enliven and motivate learning across a wide range of disciplines. Alongside developing students’ computer skills and introducing them to the use of professional software, educators are also harnessing professional and scientific packages for learning in some disciplines. As the educational use of information and communication technologies increases dramatically, questions arise about the effects on learners. While the use of computers for delivery, support, and communication, is generally easy and unthreatening, higher-level use may pose a barrier to learning for those who lack confidence or experience. Computer confidence may mediate in how well students perform in learning environments that require interaction with computers. This paper examines the role played by computer confidence (or computer self-efficacy) in a technology-enriched science and engineering mathematics course in an Australian university. Findings revealed that careful and appropriate use of professional software did indeed enliven learning for the majority of students. However, computer confidence occupied a very different dimension to mathematics confidence: and was not a predictor of achievement in the mathematics tasks, not even those requiring use of technology. Moreover, despite careful and nurturing support for use of the software, students with low computer confidence levels felt threatened and disadvantaged by computer laboratory tasks. The educational implications of these findings are discussed with regard to teaching and assessment, in particular. The TCAT scales used to measure technology attitudes, computer confidence/self-efficacy and mathematics confidence are included in an Appendix. Well-established, reliable, internally consistent, they may be useful to other researchers. The development of the computer confidence scale is outlined, and guidelines are offered for the design of other discipline-specific confidence/self-efficacy scales appropriate for use alongside the computer confidence scale.

The importance of ‘low-level’ CAS commands in teaching engineering mathematics

When a professional engineer solves a mathematical problem using technology, he/she generally uses a single one-step ‘high-level’ command of a readily available computer package to obtain the solution immediately. This should not happen during his/her learning cursus. In an engineering mathematics course, the educator should decompose the solution process into elementary steps and reinforce each step by a ‘low-level’ usage of a CAS. This approach is absolutely essential in order to provide the future engineer with the conceptual insight into the solution process. We illustrate this with the teaching of the solution of ordinary differential equations using Laplace transforms.

Designing a 401(k): A Case Study

Over the past decade or so, many private and publicly held companies have moved away from providing employees with company-funded pensions upon retirement to a retirement system that requires both employee and company contributions to fund an individual's retirement. These so-called 401(k) retirement plans usually require the employee to choose among different investment vehicles, including mutual funds, in order to allocate their retirement savings. This study presents the results of an analysis of the allocation of a lump-sum rollover of money into a typical 401(k) plan, subject to certain restrictions. The mathematics required to complete this analysis includes those topics that are typically covered in an undergraduate course in linear algebra. All of the following material was used in a sophomore-level engineering mathematics course taught at Rowan University.

An Example of the Use of Microfiches as an Aid to the Teaching of First‐Year University Engineering Mathematics

AbstractThis paper is a report on the introduction of microfiches to replace conventional pre‐prepared handouts for solutions to exercises in the first‐year engineering mathematics course at Nottingham University. Details of the arrangement of material on the microfiches are described, as is the system of labelling the frames of the microfiches and the equations. Some general comments on the preparation of material are also made. The microfiches are very popular with the students and their cost compares very favourably with that of the production of large numbers of photocopies of conventional handouts. The system may be easily adapted for use in many other subjects.

A report on the introduction of a multiple choice examination for a first year university engineering mathematics course

The paper is an account of the experience of introducing a multiple choice mathematics examination paper for the first year engineering mathematics course at Nottingham University. The form of the paper is described, as is a system for providing the candidates with feedback on their performance without the publication of the examination paper.

A Course of Mathematics for Engineers and Scientists—Vol. 1. By B.H. Chirgwin and C. Plumpton. Pp. 548. £2.50. 1970. (Pergamon)

A Course of Mathematics for Engineers and Scientists—Vol. 1. By B.H. Chirgwin and C. Plumpton. Pp. 548. £2.50. 1970. (Pergamon)

An Eigenvalue Analysis for Calculating the Vibrational Modes of Steam Turbine Discs

Summary This paper describes the application of numerical procedures to an engineering design problem of considerable practical importance. The problem is that of calculating the natural frequencies of vibration of steam turbine discs. The analysis is based on a variational formulation in conjunction with finite difference procedures to transform the problem to an eigenvalue problem. This is characterized by a symmetric band matrix, and the vibrational frequencies which correspond to the eigenvalues are computed using standard eigenvalue programming packages. The analysis includes a description of both natural and forced boundary conditions for the problem. An essential feature of this investigation is the relative simplicity in elasticity theory used and the associated computational procedures. As such it should be of interest to teachers of final year engineering mathematics courses and to mechanical engineering students embarking on an M.Sc. programme. From a research standpoint, the paper offers the p...

A Course of Mathematics for Engineers and Scientists. Volume 6. By C. Plumpton and B. H. Chirgwin. Pp. (vii), 509. 50s. 1966. (Pergamon Press)

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.

A Course of Mathematics for Engineers and Scientists. Vol. 5. By C. Plumpton and B. H. Chirgwin. Pp. viii, 202. (Pergamon Press.)

A Course of Mathematics for Engineers and Scientists. Vol. 5. By C. Plumpton and B. H. Chirgwin. Pp. viii, 202. (Pergamon Press.)

A Course of Mathematics for Engineers and Scientists.

A Course of Mathematics for Engineers and Scientists.

A Course of Mathematics for Engineers and Scientists. Vol. 4. By B. H. Chirgwin and C. Plumpton. Pp. viii + 353. 35s. 1964. (Pergamon)

A Course of Mathematics for Engineers and Scientists. Vol. 4. By B. H. Chirgwin and C. Plumpton. Pp. viii + 353. 35s. 1964. (Pergamon)

A Course of Mathematics for Engineers and Scientists. By B. H. Chirgwin and C. Plumpton. Vol. 2. Pp. 382. 30s. 1961. (Pergamon Press).

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.

A Course of Mathematics for Engineers and Scientists.

A Course of Mathematics for Engineers and Scientists.

Mathematics for Scientists: A Course of Mathematics for Engineers and Scientists . vols. 1 and 2. C. Plumpton and B. H. Chirgwin. Pergamon, New York, 1961. vol. 1, 326 pp. $6.50; vol. 2, 382 pp. $7.50.; A Course of Advanced Mathematics for Technical Schools . N. P. Tarasov. Translated from the Russian by D. E. Brown and B. G. Walker.

Mathematics for Scientists: <i>A Course of Mathematics for Engineers and Scientists</i> . vols. 1 and 2. C. Plumpton and B. H. Chirgwin. Pergamon, New York, 1961. vol. 1, 326 pp. $6.50; vol. 2, 382 pp. $7.50.; <i>A Course of Advanced Mathematics for Technical Schools</i> . N. P. Tarasov. Translated from the Russian by D. E. Brown and B. G. Walker.