Promoting engineering students’ learning with mathematical modelling projects

Mathematics constitutes a key component in engineering education. Engineering students are traditionally offered a number of mathematics courses which provide the knowledge needed at the workplace. Unfortunately, many students perceive mathematics as a discipline that teaches mostly procedures not relevant to their future careers and often view it as one of the main obstacles on their way to an engineering degree. In this paper, we discuss how introducing university students in a standard Differential Equations course to mathematical modelling (MM), a powerful strategy for solving real-life problems, contributes to the development of their mathematical competencies, motivates their interest to mathematics, promotes the use of advanced mathematical thinking, methods of applied mathematics, and digital computational tools

Promoting conceptual understanding of differential equations through inqiury tasks

Courses in Differential Equations (DEs) have been an important part of engineering education for decades. However, students experience difficulties with the understanding of main concepts including differential equation itself and diverse types of solutions (general, particular, stationary). In this paper, we discuss how the work on non-routine problems on the Existence and Uniqueness Theorems (EUTs) helps students to make sense of DEs and their solutions thus contributing to the development of advanced mathematical thinking

Dynamics of a single species in a fluctuating environment under periodic yield harvesting

We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was studied by Brauer and Sanchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. We obtain estimates for positive attracting and repelling periodic solutions and describe behavior of other solutions. Extinction and blow-up times are evaluated for solutions with small and large initial data; dependence of the number of periodic solutions on the parameter sigma associated with the intensity of harvesting is explored. As sigma grows, the number of periodic solutions drops from two to zero. We provide bounds for the bifurcation parameter whose value in practice can be efficiently approximated numerically

Development of students' mathematical discourse through individual and group work with nonstandard problems on existence and uniqueness theorem.

Research shows that students’ learning is affected by the types of tasks. We explore how the use of nonstandard problems influences understanding of the Existence and Uniqueness Theorems (EUTs) by a group of engineering students. The focus is on the development of students’ mathematical discourse during the individual and group work with nonstandard problems. We present the evidence indicating that students developed new mathematical routines gaining a deeper understanding of EUTs and appreciated the experience

Individual and group work with nonstandard problems in an ordinary differential equations course for engineering students

We explore understanding of the Existence and Uniqueness Theorems (EUTs) by a group of engineering students working on nonstandard problems. Students presented three sets of solutions: individual solutions produced in the first tutorial, individual solutions submitted as a homework, and solutions submitted after the discussion with peers in small groups during the second tutorial. The focus of the study is on the role of individual and group work with nonstandard problems. The results show that students gained a deeper understanding of EUTs and appreciated the experience

Non-standard Problems in an Ordinary Differential Equations Course

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A New Tool for the Assessment of the Development of Students’ Mathematical Competencies

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A new tool for the assessment of the development of students' mathematical competencies

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Mathematical models for assessment of vehicle crashworthiness: a review

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Crash Response of a Repaired Vehicle-Influence of Welding UHSS Members

Author's accepted manuscriptAutomakers generally recommend not to weld structural parts after a vehicle crash, and these should be replaced as a whole part in case of a crash event. Sectioning of these members is also not recommended and use of the repair manual is mandatory in case of fracture of such parts. However, repair shops may not adhere to these instructions and use incorrect repair procedures on these members which would modify their strength properties. This study analyses the impact of welding structural members in a vehicle like the A-pillar which use Ultra-High Strength Steels (UHSS) for reducing the weight of the vehicle and improving the crashworthiness of the structure. The research conducted in this paper highlights the differences in the crash performance of a repaired vehicle as opposed to baseline injury values for the vehicle. The performance of the modified vehicle when tested for different loadcases shows reduced crash performance as compared to the baseline performance and it can be concluded that welding or sectioning the UHSS parts would influence the crashworthiness of a vehicle. This paper only focuses on structural integrity of the repaired vehicle in a crash event. The performance of the vehicle in occupant injury is kept out of scope for this study.acceptedVersio