Laplace Transforms - Just looking up tables?

[MathWarrior]

I recently have started learning Laplace transforms, it seems like its just a bunch of looking up tables. Along with having a bunch of standard Laplace transforms memorized. Is this how it usually is when dealing with transforms for the first time? I feel like I am not really even doing math, its almost like a bunch of fitting to known equations.

 

[AlephZero]

Haven't you learned what is the definition of the Laplace transform? That is how you can work them out for unknown functions. But in practice you learn the common ones, just like you learn that $d(\sin x)/dx = \cos x$, and look up others in tables.

But the interesting thing about Laplace transforms is what you can do with them, not how to calculate them. Maybe your course hasn't got to that yet.

 

[MathWarrior]

Haven't you learned what is the definition of the Laplace transform?

I have, it still seems like for the most part your just looking up tables though.

 

[Integral]

If you don't like looking them up on a table. Feel free to do the integration.

 

[blue_raver22]

I can understand your frustration with the initial learning process of Laplace transforms. However, I would like to assure you that while it may seem like simply looking up tables and memorizing standard transforms, there is much more to it than that.

Laplace transforms are a powerful mathematical tool that allows us to solve complex differential equations and analyze systems in the time and frequency domains. While it may seem like a bunch of fitting to known equations, it is important to understand that these known equations are representations of real-world systems and phenomena. By using Laplace transforms, we are able to gain a deeper understanding of these systems and make predictions and calculations that would not be possible without them.

Furthermore, the use of tables and memorization is simply a starting point in learning Laplace transforms. As you continue to practice and apply them, you will develop a deeper understanding of the underlying principles and be able to use them more effectively. It is important to also remember that as a scientist, you have the ability to question and explore beyond what is given in a table or a textbook. Use your creativity and critical thinking skills to go beyond just the standard transforms and apply them to new and unique situations.

In conclusion, while the initial learning process of Laplace transforms may seem tedious and mundane, I encourage you to continue exploring and practicing. You will soon see the true value and power of this mathematical tool and how it can enhance your scientific understanding.