What do you do if you want to master mathematical modeling for engineering design?

It is a given that you must have fresh advanced mathematical knowledge to exercise engineering modeling. Depending on what you are modeling a familiarity or knowledge of systems static and dynamic behavior is necessary. If you are planning on modeling physical components or structures then knowledge of programming and the specific tool available for simulating the item is a must.

Also study dimensional analysis. By ensuring you have dimensional balance, you can eliminate some of the potential mistakes while creating your model.

Grasping the fundamentals is not about knowing the Math, but understanding how to read the Math. A mathematical model is a representation of how critical variables interact with each other, and not just a problem to be solved. For example, I had many models which involved complex integrals, but instead of reaching for an integration table, I took the values of the function and applied various approximations methods(I.e. trapezoidal, secant, etc.). In seeing the result graphed out, I could use additional approximation methods to come up with a representative function. Would it have been the answer on a Math test? Probably not, but it gave an answer that worked and got the job done. All models are approximations, therefore, none are perfect.

Squares and cubes are triangular models of odd numbers For example, Regards S Ragavan BHEL ISG Bengaluru

For mastering the modelling, you need to equipe yourself with the sufficient knowledge in both mathematics and physics. Then start training of modern commercial modelling and simulation packages.

Don't tie yourself onto a single software physics simulation package. An expert simulation engineer should be able to produce results regardless of the codebase or software used. Create a library of verification and validation cases to support your work and software independence.

Learn modeling software by focusing on one tool initially, mastering its capabilities through tutorials and practical projects. Progress to more complex simulations as you gain confidence, exploring advanced features gradually. Utilize online courses, official documentation, and forums for guidance and troubleshooting during your learning journey.

Gaining a familiarity with various software through tutorials can dramatically influence your modeling and problem solving skills. Working tutorials outside of your domain may lead to other modeling insights which can be useful to your designs. Specific software I have found useful for design modeling is Microsoft Excel, Python, and R.

Learning a software for mathematical analysis is important. It saves our lots of time. We need to learn a at-least one simulation software for creating and simulating mathematical models. We can learn from the tutorials as well as from LinkedIn Learning. I preferred LinkedIn learning.

No matter how good you think you are at mathematical modelling, start trying to apply theory to the various challenges you encounter now. The sooner you start the better.

Apply theoretical knowledge by engaging in practical engineering projects, internships, or academic endeavors. Solve real-world problems using modeling techniques, integrating theory with hands-on experience. Reflect on challenges faced and solutions devised, refining your problem-solving skills and deepening your understanding of mathematical modeling in engineering.

Accept that you have a theory and not a proven law; it may not be right and may have unanticipated results / observations. Modelling tends to be for complex systems and behavioural interactions of subcomponents. If subcomponents have proven 'law' relations, ensure they are consistent in the results of your model.

Try to create mathematical models throughout your day, representing the world around you in multiple domains and forms. Always be practicing and the modelling will become second nature.

Study system dynamics and control theory to understand complex engineering systems. Learn to represent systems using transfer functions or state-space representations. Master feedback control principles to ensure desired system performance and accurately model real-world systems' behaviors over time.

The foundation of any Mechanical systems lies in design, therefore, delving into the dynamics of the system will enhance your design skills, foster innovative ideas, and facilitate problem-solving.

'Be like water' - follow Bruce Lee when developing complex models / simulaion. Replicate - ensure your model is a accurate for known examples Interpolate - push the adjustable keys of your model to known practical limits; are results still feasible? Extrapolate - push into theoretical zones, check that results hold. Time / Iterations - Start static and prove your code / software package configuration. Then progress through time advancing steps. The end of each iteration is a new start point - you will quickly run be out of accurately predictable results. Real Time - You will never be as fast as the real world, consider accuracy, execution speed and acceptable simplifications in safety critical or high-stakes commercial applications.

Enhance math skills by practicing regularly, tackling challenging problems, and exploring new techniques. Attend workshops, enroll in advanced courses, and engage with scholarly articles for continuous learning. Apply math concepts to real-world scenarios to strengthen understanding and improve problem-solving abilities for sophisticated engineering modeling.

Yes definitely, math is a bone of engineering. So we need to focus on improving our knowledge of math continuously. It played a major role in our success. We can learn from a teacher and also from the online webinar and workshops.

I don't think you need to do extra courses. You just need to keep on working at it. To help with this, the most important thing to keep in mind is that you should not expect it to work first time. You often need to try a few approaches until you find one that works. It rarely works like it seems to in text books.

Additional courses are of limited value unless learning a completely new branch or software package. Scholarly articles are useful to see what and how other people have been doing; they seldom the latest or most cutting edge that authors are doing! They could interest you (or distracted you) to branch off from your techniques.

Continuously refine your skills in mathematical modeling by working on different challenges and Collaborate with other engineers and experts to gain new insights and perspectives.

If you are in industry, it useful to be 'first to be second' as the bleeding edge is seldom fruitful for the originators. When ideas and practices go free domain collaboration is quite safe. During development the best collaboration are with real world data sources, but there is likely to commercial interest. Your great results could squelched forever. Theory / model collaborations gets tricky when commercialised: your grant sponsor or employers owns at least part of your IP. When open sourcing became full of entrepreneurial 'friends'.

Incorporate mathematics in your language as you discuss designs with your team. Communicating your designs as mathematical models regularly may expose a new understanding of the concepts to you or your team.

Don't stuck in a specific model or dynamic, try to extend your experience in the similar and easier cases and then you can go beyond. Don't stop your creativity, let it fly ...

Mathematical modelling is a genral term that may encompass a wide variety of fields in modelling. Each has its own pathway to excellence. For example FInite Element Analysis, MATLAB.

In my experience learn some programming especially java/python or check out Vega Python.Have some knowlegde on developing and simulating algorithms especially real time and register Github meet have a look at some repositories on the same subject.