Tutor profile: Omar K.
Subject: Linear Algebra
Given three vectors, how could you find the volume of the parallelepiped bounded by all three?
Using the mixed product, the volume can be obtained in one computation.
Subject: Mechanical Engineering
In a design context, would you be satisfied with a safety factor of 5? what about a safety margin of 200%?
Although intuitively, one could think that higher safety is always desirable. If a safety factor is mandated by code it should often be incorporated into the design. Otherwise, if an engineer voluntarily chooses a high safety factor it likely indicates lack of knowledge of the failure mechanisms. A safety margin of 200% indicates that the design is 200% far away from failure, which indicates the design is incredibly overdesigned.
Are all functions differentiable? Can you think of a function who's derivative is not defined in real life?
There are many functions who's derivative only exists on certain intervals. In a natural context however, there are few situations where we would encounter a natural discontinuity. A field function representing the pressure in the fluid can contain discontinuities in the form of shockwaves. Mathematically, these can be defined on intervals or approximated using a series of functions.