One way to be the best Mechanical Engineer is to train ourself through pursuing Master of Mechanical Engineering. The study will be 3 semesters for learning advance knowledge – including advance engineering mathematics- and 1 semester for conducting research.
In Mechanical Engineering, more than 50% study is related to mathematic and physics. We must understand the distinction between pure mathematics and engineering mathematics. In engineering mathematics, we learn applied mathematics to solve technical problem during equipment design or during field troubleshooting.
In advance engineering mathematic, we learn Fourier Series. By using Fourier approach, we can re-write a periodic curve with sin & cos equation. Refer to above drawing, blue curve is original which can be approached by black curve.
In this stage, engineering mathematic can provide nearest solution but not exact solution. It is not 100% correct, but can be 99% correct. In most cases, we are satisfy with 99% correct solution.
Another interesting subject is about “forced differential equation” or Forced DE. This subject can be applied to get solution of vibration problem, let say during car shock-breaker design analysis.
Common problem is about a spring supporting a part or component (mass m kg, spring damper c and spring constant k). This spring get an external load F(t) which can be a periodic load. Student is requested to find a response of the system and find how long the transient condition occured.
In Master of Mechanical Engineering study, we also learn applied advance mathematics to find a solution for conduction heat transfer accros a plate. A plate has 4 boundary conditions at each sides, and student find a solution to describe temperature distribution at any location in a plate.
Above are 3 examples how engineering mathematics can support mechanical engineer to solve engineering problem during design or during field troubleshooting.
In next article, I will talk about relation between Mathematical/physics solution, computer / numerical approach and field application.