Why is trig important?
Trigonometry is one of the most fundamental components of not only an engineering degree but many technical trades. For example, when analyzing and studying gas turbine engines, you require a broad understanding of trig to be able to identify how the rotors and stators must be set to create the best efficiency. Also, when building houses, trig is used to deploy angular structural components at their correct locations.
What do I believe is the best way to improve your understanding of calculus?
Going back to the basics and building on that knowledge, as if there are gaps, such as not understanding trigonometric identities, calculus can get very difficult at more advanced stages.
What is my favorite part of PDE's?
Being able to solve difficult equations such as simplified versions of the Navier Stokes equations and applying it to real-world applications.