This term in school, I'm taking a class that has challenged me more than any academic pursuit has in while. This class is called structural dynamics.At its core, structural dynamics is simple: it's merely the analysis of structures like buildings and bridges as they move. However, the devil is in the details. Even to analyze the response of a structure to a well-behaved loading pattern is fairly complex. This endeavor involves use of 2nd order differential equations to solve an equation of force equilibrium called the 'equation of motion.'
Earthquake motions are not well-behaved like a sine wave or an impulse. These involve complex motion with many cusps and various frequencies of vibration. What it comes down to is that, in order to make even a remotely reasonable approximation of a structure's response to earthquake loading, an engineer must use some sort of mathematical computer program and an approximate numerical model.
Up to this point, the advanced math and numerical models themselves haven't been what's made the class challenging. It has been laborious trying to remember material that I studied 3 years ago (and never learned that well to being with), but this hasn't been the worst part. The thing that has made this class challenging is that, even though the equations used are based on physical principles, it's difficult to visualize how changes in one particular parameter will affect the model of the actual, physical structure. Engineers as a whole, and especially civil engineers, like to be able to visualize what they're working with. A good civil engineer will be able to conjure a mental picture of an entire physical system, all of its component parts, and how physical changes will modify the system and its components. This is often very difficult if not outright impossible to do with many of the principles of structural dynamics because they are based on advanced mathematics.
This is also why mathematical proofs and coding were a challenge for me during my undergrad and so far in grad school. With mathematical proofs, it's also difficult to find motivation, because honestly, who cares? Coding, on the other hand, is an integral part of life for anyone who doesn't aspire to a career that involves french fries and/or garbage. Both of these fields are quite ethereal and don't necessarily have any convenient visual representation for many problems. I've developed some simple visual representations for principles of coding like if statements and loops, but I still find them challenging. I will never be a l337 coder as much as I will be a good civil engineer, just because coding is, at least somewhat, inherently unvisualizable.
I should also mention that my professor in structural dynamics is new (like received his Ph.D. in December new) this term and is still trying to feel out the landscape. The homework assignments have been long and the exam was difficult to decipher. The professor is a good teacher, but he just doesn't have a good idea yet of how much time is takes students to finish assignments when they're new to the concepts. I think he'll get it, but he's not quite there yet. Though, he has assured us that we will get at least Bs if we give the appropriate effort, so I think I'm going to make it. : )
The moral of the story? Knowing how you learn and how you reason through concepts is important if you want to optimize your learning and become more knowledgeable with minimal effort. I learn and reason through things by visualizing them. Things that are difficult to visualize will take slightly more effort to grasp, and I'm planning on being prepared when they come around.
