Mathematics is essential for mechanical engineering, as it helps you model, analyze, and design complex systems and phenomena. However, many students struggle with the mathematical concepts and skills required for this discipline. How can you build a strong mathematical foundation for mechanical engineering? Here are some tips and resources to help you.
Before you dive into advanced topics, make sure you have a solid grasp of the basic mathematical tools and methods that mechanical engineers use. These include algebra, trigonometry, geometry, calculus, differential equations, linear algebra, and vector analysis. You can use online courses, textbooks, or tutorials to refresh your memory and practice your skills. For example, you can check out Khan Academy, MIT OpenCourseWare, or Coursera for free or low-cost courses on these subjects.
My personal opinion about the branches of Mathematics the modern mechanical engineers need is as follows. I completely agree with the ones mentioned in The Basics. But I'd like to add Geometry, Topology and Numerical Methods to the list. Regarding Topology, it needs the special explanation. Why? Because it is the most abstract and complicated branch of Mathematics. If so, why do mechanical engineers need it if its connection to the practice of Mechanical Engineering looks very weak? In short, using Topology we can see the most intrinsic features and laws of the world we live in. In light of the other branches of Mathematics they are invisible.
I think what a mechanical engineer needs most is a talent for mathematics. A mechanical engineer faces many challenges during the day while doing his job. I suggest that you refer to a reliable source to solve any problem and do all the calculations related to solving the problem. Definitely, if you are weak in any part of mathematics, reviewing mathematical engineering books is useful. Solving mathematical and geometric problems that are related to the main job and expertise of every mechanical engineer can increase the skill level and also improve problem solving and increase the mathematical knowledge of a mechanical engineer.
The core of the foundation lies in having a solid understanding of algebra, which allows you to succeed in calculus. From there really connecting the math to applications is key, a strong base in physics builds on the math and that positions you well.
Second, "The term?engineering?is derived from the word?engineer, which itself dates back to 1390 when an?engine’er?(literally, one who operates an?engine) referred to “a constructor of military engines. ... The word “engine” itself is of even older origin, ultimately deriving from the?Latin?ingenium?(c. 1250), meaning “innate quality, especially mental power, hence a clever invention." Topology helps develop as mental power, so designing intuition since it requires a lot mental efforts for study.
"Mathematics is the language Nature speaks to us. An engineer is much better off understanding this language than trying to avoid it." This is the quote from my recent book, Vibration Control for Optomechanical Systems, World Scientific, 2022. Chapter 2 is titled Mathematical Methods of Vibration Studies. In my opinion, every engineering textbook should contain a chapter devoted to mathematical methods most useful in this particular branch of Engineering (and some of them do!) These chapters are the best way to master the math necessary for your work.
One of the best ways to learn and reinforce math is to apply it to real-world engineering problems. This will help you understand the relevance and usefulness of math, as well as develop your intuition and creativity. You can find many examples of engineering problems that involve math in your textbooks, online platforms, or projects. For instance, you can use math to model the motion of a pendulum, the stress and strain of a beam, the heat transfer in a radiator, or the fluid dynamics of a pipe.
engineering is easy maths. if you can solve algebra and basic integrals you can build a foundation for all understanding of field of engineering. minus chemical which requires chemistry background
I may have a different opinion from that of my comrades in the field. I believe math applied to engineering can be simple, but if one is interested in diving deep in technologically challenging engineering, math can get as deep as fundamentals of PDEs, vectorial calculus and more. If you're planning on following a career as a highly skilled engineer, I'd suggest building a strong basis on these disciplines and refining the studies in the field you want to work in. I for instance work as a CFD engineer, and I have redirected all my efforts towards the comprehension of the tools, physics and techniques involved with it after I had built a strong foundation on math.
I totally agree that one of the best ways to learn and improve math is to apply it to real-world engineering problems. For example, to design a steel storage tank, a mechanical engineer must perform many mathematical calculations. For mathematical calculations related to solving a particular problem, one should refer to the standard and related sources for that work to find the fastest and easiest solution to the problem. To design and build a steel storage tank, a mechanical engineer needs to refer to the principles of mathematical calculations from the relevant standard, which is API 650.
Theoretical Fundamentals of the modern Engineering Mechanics are quite deep, especially when formulated in the framework of Nonlinear Continuum Mechanics, and applied to the numerical solution of the real world problems using powerful Finite Element and Finite Volume tools like ABAQUS, ANSYS, FLUENT, MSC Nastran, COMSOL, and others. Underlying mathematical techniques require solid mathematical background, especially if the users intend to customize/adapt those computational tools to their own specific problems and materials.
Yes. Applying math to engineering problems can work rather well. What is less mentioned is to apply engineering solutions to have a better grasp on the relationship of math with mechanical engineering, and make it fun. Make a real model of an engineering solution, and reverse the calculation from, your results, to the starting premise. It might be that, just looking in a different way, can allow you to see the relationship between these fields and tools. Possibly, in a way that you were never able to see before.
Another effective strategy to build your mathematical foundation is to learn from others who have more experience and expertise in mechanical engineering and math. You can seek guidance from your professors, mentors, tutors, or peers. You can also join online forums, communities, or groups where you can ask questions, share ideas, and get feedback. For example, you can join Stack Exchange, Quora, Reddit, or Facebook groups related to mechanical engineering and math.
Continuous learning is important, and no one can know everything on their own. By learning from others, you gain a better perspective and expand your thinking and problem-solving abilities. It also helps you develop teamwork and idea-sharing skills, and teaches you that there are multiple ways to approach a problem. This flexibility enhances your ability to retain knowledge. In addition to joining communities, you can also create your own club to attract talented individuals and improve your technical skills.
Man is a social being and must always communicate with other people. A good mechanical engineer must have direct communication with colleagues in his field of expertise. Joining groups in your field of expertise on Telegram, WhatsApp, and LinkedIn, as well as communicating with mechanical engineers in the real world and reading what colleagues share is very important and practical in improving individual abilities.
Collaboration and knowledge sharing are invaluable when building your mathematical prowess. Engage with peers, mentors, or online communities of engineers and mathematicians. Participate in discussions, attend workshops, or follow industry experts on platforms like LinkedIn. Learning from the experiences and insights of others can provide fresh perspectives and proven strategies to conquer the intricate mathematical challenges encountered in mechanical engineering.
You can also enhance your mathematical skills and knowledge by using software and tools that can help you perform calculations, simulations, and visualizations. These can save you time and effort, as well as allow you to explore more complex and realistic scenarios. Some of the common software and tools that mechanical engineers use are MATLAB, Mathematica, Excel, SolidWorks, ANSYS, and AutoCAD. You can learn how to use these software and tools by following online tutorials, courses, or manuals.
Certainly, in today's world, the use of software is very necessary for mechanical engineers. In my opinion, every mechanical engineer should be completely familiar with the software of his field of expertise. Of course, mastering the software is not enough, and he must know the standard related to his field. For example, a mechanical engineer can use PDMS software to design process piping, and besides that, he must have sufficient mastery of ASME B31.3 standard. It is also very important to know and master the English language
One useful tip which helped me develop my mathematical skills was to always make an attempt to write excel formulas or use functions to solve parts of a mathematical question.
Softwares are great but only if you know which math you are solving first and you are able to interpret your results. If you want to use softwares, do problems that you already have the answers for, Ie: verification/ validation and try to match your results with theoretical answers.
Modern mechanical engineering relies heavily on specialized software and tools. Invest time in mastering applications such as MATLAB, AutoCAD, or computational simulation software. These tools simplify complex mathematical calculations and provide visualizations, making abstract concepts more tangible. Familiarizing yourself with these technologies not only enhances your problem-solving capabilities but also makes you more marketable to prospective employers.
Nowadays, you can not discover any software that has not hired math to create it. In fact, when we utilize 3D simulation software, we unconsciously use our knowledge of vectors in math. In a similar way, mechanics, dynamics, statics, etc. utilize trigonometry, algebra, and geometry for their essentials.
Finally, the most important tip to build your mathematical foundation is to keep practicing and learning. Math is not a static or fixed subject, but a dynamic and evolving one. You need to constantly challenge yourself, review your concepts, and update your skills. You can do this by solving more problems, taking more courses, reading more books, or doing more projects. You can also follow the latest trends and developments in mechanical engineering and math by reading journals, blogs, podcasts, or newsletters.
Using fun magazines that are in the nature of solving math exercises will help a mechanical engineer's mind stay active. It is also useful to do different projects that challenge the mind. For example, it can be very useful to carry out design calculations for process piping systems with different pressures and thicknesses for different units and different industries. You should always keep in mind that knowledge has no end point. It should always be growing. studying and solving mathematical calculations in different specialized standards can help improve a person's knowledge a lot.
Like any skill, mathematical proficiency in mechanical engineering improves with consistent practice. Regularly challenge yourself with mathematical problem-solving exercises, engage in thought-provoking projects, and explore advanced mathematical topics. This continuous learning process keeps your skills sharp and adaptable, ensuring you stay at the forefront of developments in the dynamic field of mechanical engineering.
It is only through practice that you can truly learn. So, keep on practicing and making mistakes. Make a lot of mistakes. At least, you can say you found several ways that it doesn’t work!
Mathematical simulations can be used as a model or prototype for certain physical properties (temperature distributions; stress and strain, overload failure limits and tolerances , etc… )of a conceptual design, and can perhaps, be further verified with empirical data and statistical studies. Just a thought. I never got to implement the above process from ground zero to the finish.
In my opinion, solving mathematical problems makes the mind very open and dynamic and increases the problem-solving power of the human mind in various cases. for this reason, the ability to analyze mathematical problems is very important.
Look for varieties of mathematical models or concepts that can be employed for your problem that will allow you to widen you concepts as well as vision for various types of problems out there. For instance, a problem can be solved with trigonometric functions, check if some triangle properties are applicable or circular properties that might give you a different perspective and easy solution.
Beyond mathematical expertise, consider staying updated with industry trends and emerging technologies. Explore the possibility of pursuing advanced degrees or certifications in specialized mathematical areas relevant to mechanical engineering, such as computational mathematics or numerical analysis. Furthermore, don't underestimate the importance of honing your communication skills. Effectively conveying your mathematical insights to non-technical stakeholders is crucial in the professional world. Building a strong mathematical foundation is a lifelong journey in mechanical engineering, so remain dedicated to your personal and professional growth.