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

In summary: The emphasis in physics and engineering undergraduate curricula for the past decade or so has been on developing intuition and understanding of the mathematical concepts rather than just translating the mathematics into terms that can be readily applied in physics or engineering problems. In summary, it appears that there is research on various aspects of the teaching of engineering mathematics.
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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.
 
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matqkks said:
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.
 
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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.
 

1. How can I make sure my students understand the basics of Engineering Mathematics in their second year?

The best way to ensure understanding of the basics is to start with a thorough review of the material covered in the first year. This will refresh students' memories and ensure they have a strong foundation before moving on to more advanced topics. Additionally, incorporating real-life examples and applications of the concepts can help make them more relatable and easier to understand.

2. What are the key topics that should be covered in a second-year Engineering Mathematics course?

Some key topics that should be covered in a second-year Engineering Mathematics course include linear algebra, differential equations, vector calculus, and complex numbers. These topics are essential for understanding more advanced engineering concepts and applications.

3. How can I make the course more engaging for students?

One way to make the course more engaging is to incorporate hands-on activities and projects that allow students to apply the concepts they are learning. This can also help students see the real-world relevance of Engineering Mathematics. Additionally, using multimedia resources such as videos and interactive simulations can help keep students interested and engaged.

4. Is there a recommended teaching approach for second-year Engineering Mathematics?

There is no one-size-fits-all approach for teaching Engineering Mathematics, as every student and class is different. However, a combination of lectures, problem-solving sessions, and group work can be effective in helping students understand and apply the concepts. It is also important to provide ample opportunities for students to ask questions and seek clarification.

5. How can I help struggling students in the course?

One way to help struggling students is to offer additional resources and support, such as review sessions, office hours, and online tutorials. It may also be helpful to assign group projects or pair struggling students with stronger students for peer-to-peer learning. Providing regular feedback and encouragement can also go a long way in helping struggling students succeed in the course.

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