# Tutor profile: Georgije S.

## Questions

### Subject: Mechanical Engineering

Mechanical engineering is such a broad field where it is almost naive to ask a very specific question in one subset of the discipline. With that being said, my question is "What failure theory do you prefer for ductile materials?"

For a ductile material, the appropriate failure theory is likely Von Mises or Tresca. Tresca will give you a more conservative estimate while Von Mises typically gives you a more accurate representation of when the device will actually fail from mechanical stress. Von Mises is typically used in my field with a larger factor of safety, but I have also seen Tresca be used. I personally prefer Von Mises as it is a common output of many FEA packages, and the analysis to be done with it is usually quite simple.

### Subject: Calculus

Can you explain to me what a derivative is?

A derivative is simply the rate at which something is changing over some interval, which is typically time in most problems. A lot of students get tricked out by the formal notation of the derivative using the limit as the interval shrinks to 0, and stop thinking about what the derivative really tells you. If you go step by step, you can see what a derivative is really telling you. We are essentially taking the rise over run for an infinitesimally small run, and this tells us how much we changed in that small run. We can then scale this small run to something that makes more sense to us, like a second, and we can figure out how much something is changing in one second. This can help us do so much in the future, such as find a beginning and an end state, optimize functions, etc.

### Subject: Algebra

Before starting any subject, it is important to grasp what the importance of it is, and why we learn it, so could you please give me your description of what Algebra is, and why we use it?

I think the overarching theme in Algebra is to use variables and parameters to solve many different problems at once. Algebra helps us work backwards to find solutions to problems, which are many times simple arithmetic. For example, asking someone to give you the answer to 5+5 is easy, most people can do it quickly and give you 10. It might take a little bit longer to word something like "what plus five gives you ten?" Sure, most people can quickly work backwards and say this is 5, but Algebra standardizes the way we do this by using common notation in the form of something like: "x+5=10", where we can then use our algebra skills to solve backwards much faster. This has applications in almost every single field.

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