How and what to teach on a second-year Engineering Mathematics?

[matqkks]

In the late 80’s and early 90’s there was the idea of ‘calculus reform’ and some emphasis and syllabus changed. The order of doing things in calculus also changed with the advantage of technology.

Similarly in linear algebra, there was a linear algebra curriculum study group that produced some really good ways of teaching linear algebra and highlighted curriculum changes. This was produced in the January 1993 College Mathematics Journal.

Has any similar work been covered in (Further) Engineering Mathematics? I am looking for what are important topics to cover and any work or research on the teaching of Engineering Mathematics. I am looking for some sort of framework.

 

[Astronuc]

Has any similar work been covered in (Further) Engineering Mathematics? I am looking for what are important topics to cover and any work or research on the teaching of Engineering Mathematics. I am looking for some sort of framework.

It appears the answer is yes, but it's more complicated than a yes/no answer.

Take for example - https://link.springer.com/article/10.1007/s40753-021-00139-8 - one article in a journal entitled, International Journal of Research in Undergraduate Mathematics Education. The article may point one to other more general references.

My direct experience with respect to university education is from the 1970s and 1980s, and since through using mathematics in research at work. Some is fairly basic, but some research (modeling and simulation) can become quite complex. One only need to look at article involving 'computational multiphysics' to see how complex it has become, and the types of applied mathematics varies among the different engineering disciplines, e.g., electrical engineering (circuit theory, power T&D systems, control theory) vs mechanical and aerospace engineering (heat transfer and fluid dynamics (CFD)) vs civil and structural engineering vs nuclear engineering.

Ideally, second year (sophomore) university physics/engineering students encounter partial differential equations and complex analysis.

 

[martane]

I haven't come across any specific curriculum reform or study group for (Further) Engineering Mathematics, but there have been discussions and efforts to improve the teaching of this subject in recent years.

One important topic that has gained more attention in recent years is the use of technology in teaching (Further) Engineering Mathematics. With the advancement of technology, it has become easier to visualize and solve complex mathematical problems, and incorporating technology into the curriculum can make the subject more engaging and relevant for students.

Another important aspect is the integration of real-world applications in teaching (Further) Engineering Mathematics. This not only makes the subject more interesting for students but also helps them see the practical applications of what they are learning.

In terms of research, there have been studies on the effectiveness of different teaching methods and approaches in (Further) Engineering Mathematics. For example, some research has shown that using problem-based learning or project-based learning can be more effective in teaching this subject compared to traditional lecture-based methods.

Overall, there is a growing recognition of the need to update and improve the teaching of (Further) Engineering Mathematics, and there are ongoing efforts to develop a framework for teaching this subject in a more effective and engaging way. I would suggest looking into current literature and attending conferences or workshops on engineering mathematics education to stay updated on the latest developments in this area.